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class="vector-toc-numb">2</span> <span>Positional notation</span> </div> </a> <ul id="toc-Positional_notation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Symbols" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Symbols"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Symbols</span> </div> </a> <button aria-controls="toc-Symbols-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Symbols subsection</span> </button> <ul id="toc-Symbols-sublist" class="vector-toc-list"> <li id="toc-Glyph_comparison" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Glyph_comparison"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Glyph comparison</span> </div> </a> <ul id="toc-Glyph_comparison-sublist" 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href="#Development"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Development</span> </div> </a> <ul id="toc-Development-sublist" class="vector-toc-list"> <li id="toc-Medieval_Islamic_world" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Medieval_Islamic_world"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2.1</span> <span>Medieval Islamic world</span> </div> </a> <ul id="toc-Medieval_Islamic_world-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Adoption_in_Europe" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Adoption_in_Europe"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Adoption in Europe</span> </div> </a> <ul id="toc-Adoption_in_Europe-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Adoption_in_East_Asia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Adoption_in_East_Asia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Adoption in East Asia</span> </div> </a> <ul id="toc-Adoption_in_East_Asia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spread_of_the_Western_Arabic_variant" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spread_of_the_Western_Arabic_variant"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Spread of the Western Arabic variant</span> </div> </a> <ul id="toc-Spread_of_the_Western_Arabic_variant-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Bibliography</span> </div> </a> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Hindu–Arabic numeral system</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 28 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-28" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">28 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%A7%D9%85_%D8%A7%D9%84%D8%B9%D8%AF_%D8%A7%D9%84%D9%87%D9%86%D8%AF%D9%8A_%D8%A7%D9%84%D8%B9%D8%B1%D8%A8%D9%8A" title="نظام العد الهندي العربي – Arabic" lang="ar" hreflang="ar" data-title="نظام العد الهندي العربي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B9%E0%A6%BF%E0%A6%A8%E0%A7%8D%E0%A6%A6%E0%A7%81-%E0%A6%86%E0%A6%B0%E0%A6%AC%E0%A6%BF_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE_%E0%A6%AA%E0%A6%A6%E0%A7%8D%E0%A6%A7%E0%A6%A4%E0%A6%BF" title="হিন্দু-আরবি সংখ্যা পদ্ধতি – Bangla" lang="bn" hreflang="bn" data-title="হিন্দু-আরবি সংখ্যা পদ্ধতি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%B9%E0%A4%BF%E0%A4%82%E0%A4%A6%E0%A5%82%E2%80%93%E0%A4%85%E0%A4%B0%E0%A4%AC%E0%A5%80_%E0%A4%85%E0%A4%82%E0%A4%95_%E0%A4%B8%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%9F%E0%A4%AE" title="हिंदू–अरबी अंक सिस्टम – Bhojpuri" lang="bh" hreflang="bh" data-title="हिंदू–अरबी अंक सिस्टम" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Sistema_de_numeraci%C3%B3_Hind%C3%BA-%C3%80rab" title="Sistema de numeració Hindú-Àrab – Catalan" lang="ca" hreflang="ca" data-title="Sistema de numeració Hindú-Àrab" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Indicko-arabsk%C3%A1_%C4%8D%C3%ADseln%C3%A1_soustava" title="Indicko-arabská číselná soustava – Czech" lang="cs" hreflang="cs" data-title="Indicko-arabská číselná soustava" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/System_rhifolion_Hind%C5%B5-Arabaidd" title="System rhifolion Hindŵ-Arabaidd – Welsh" lang="cy" hreflang="cy" data-title="System rhifolion Hindŵ-Arabaidd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hindu-arabertal_systemet" title="Hindu-arabertal systemet – Danish" lang="da" hreflang="da" data-title="Hindu-arabertal systemet" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Numeraci%C3%B3n_indo-ar%C3%A1biga" title="Numeración indo-arábiga – Spanish" lang="es" hreflang="es" data-title="Numeración indo-arábiga" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Hind%E2%80%93araba_nombrosistemo" title="Hind–araba nombrosistemo – Esperanto" lang="eo" hreflang="eo" data-title="Hind–araba nombrosistemo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF%D9%86%D9%88%DB%8C%D8%B3%DB%8C_%D9%87%D9%86%D8%AF%DB%8C-%D8%B9%D8%B1%D8%A8%DB%8C" title="عددنویسی هندی-عربی – Persian" lang="fa" hreflang="fa" data-title="عددنویسی هندی-عربی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Syst%C3%A8me_de_num%C3%A9ration_indo-arabe" title="Système de numération indo-arabe – French" lang="fr" hreflang="fr" data-title="Système de numération indo-arabe" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%A6%E0%AA%B6%E0%AA%BE%E0%AA%82%E0%AA%B6_%E0%AA%B8%E0%AA%82%E0%AA%96%E0%AB%8D%E0%AA%AF%E0%AA%BE_%E0%AA%AA%E0%AB%8D%E0%AA%B0%E0%AA%A3%E0%AA%BE%E0%AA%B2%E0%AB%80" title="દશાંશ સંખ્યા પ્રણાલી – Gujarati" lang="gu" hreflang="gu" data-title="દશાંશ સંખ્યા પ્રણાલી" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AD%E0%A4%BE%E0%A4%B0%E0%A4%A4%E0%A5%80%E0%A4%AF_%E0%A4%85%E0%A4%82%E0%A4%95_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A3%E0%A4%BE%E0%A4%B2%E0%A5%80" title="भारतीय अंक प्रणाली – Hindi" lang="hi" hreflang="hi" data-title="भारतीय अंक प्रणाली" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sistem_bilangan_Hindu-Arab" title="Sistem bilangan Hindu-Arab – Indonesian" lang="id" hreflang="id" data-title="Sistem bilangan Hindu-Arab" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B9%E0%A4%BF%E0%A4%82%E0%A4%A6%E0%A5%82-%E0%A4%85%E0%A4%B0%E0%A4%AC%E0%A5%80_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A3%E0%A4%BE%E0%A4%B2%E0%A5%80" title="हिंदू-अरबी संख्या प्रणाली – Marathi" lang="mr" hreflang="mr" data-title="हिंदू-अरबी संख्या प्रणाली" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sistem_angka_Hindu-Arab" title="Sistem angka Hindu-Arab – Malay" lang="ms" hreflang="ms" data-title="Sistem angka Hindu-Arab" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Sistema_num%C3%A9rico_hindu-ar%C3%A1bico" title="Sistema numérico hindu-arábico – Mirandese" lang="mwl" hreflang="mwl" data-title="Sistema numérico hindu-arábico" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Indiase_cijfers" title="Indiase cijfers – Dutch" lang="nl" hreflang="nl" data-title="Indiase cijfers" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Sistema_num%C3%A9rico_hindu-ar%C3%A1bico" title="Sistema numérico hindu-arábico – Portuguese" lang="pt" hreflang="pt" data-title="Sistema numérico hindu-arábico" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Sistemul_de_numera%C8%9Bie_indo-arab" title="Sistemul de numerație indo-arab – Romanian" lang="ro" hreflang="ro" data-title="Sistemul de numerație indo-arab" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system – Simple English" lang="en-simple" hreflang="en-simple" data-title="Hindu–Arabic numeral system" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%A8%E0%AF%8D%E0%AE%A4%E0%AF%81-%E0%AE%85%E0%AE%B0%E0%AE%AA%E0%AF%81_%E0%AE%8E%E0%AE%A3%E0%AF%8D%E0%AE%A3%E0%AF%81%E0%AE%B0%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B3%E0%AF%8D" title="இந்து-அரபு எண்ணுருக்கள் – Tamil" lang="ta" hreflang="ta" data-title="இந்து-அரபு எண்ணுருக்கள்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B0%E0%B8%9A%E0%B8%9A%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B8%AE%E0%B8%B4%E0%B8%99%E0%B8%94%E0%B8%B9%E2%80%93%E0%B8%AD%E0%B8%B2%E0%B8%AB%E0%B8%A3%E0%B8%B1%E0%B8%9A" title="ระบบเลขฮินดู–อาหรับ – Thai" lang="th" hreflang="th" data-title="ระบบเลขฮินดู–อาหรับ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Hint-Arap_rakam_sistemi" title="Hint-Arap rakam sistemi – Turkish" lang="tr" hreflang="tr" data-title="Hint-Arap rakam sistemi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%BD%D0%B4%D0%BE-%D0%B0%D1%80%D0%B0%D0%B1%D1%81%D1%8C%D0%BA%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%BD%D1%8F" title="Індо-арабська система числення – Ukrainian" lang="uk" hreflang="uk" data-title="Індо-арабська система числення" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DB%81%D9%86%D8%AF%DB%8C_-%D8%B9%D8%B1%D8%A8%DB%8C_%D9%86%D8%B8%D8%A7%D9%85_%D8%B9%D8%AF%D8%AF" title="ہندی -عربی نظام عدد – Urdu" lang="ur" hreflang="ur" data-title="ہندی -عربی نظام عدد" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a 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.mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><table class="sidebar sidebar-collapse nomobile nowraplinks hlist"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:Numeral_systems" title="Category:Numeral systems">a series</a> on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Numeral_system" title="Numeral system">Numeral systems</a></th></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Positional_notation" title="Positional notation">Place-value notation</a></div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a class="mw-selflink selflink">Hindu–Arabic numerals</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Arabic_numerals" title="Arabic numerals">Western Arabic</a></li> <li><a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic</a></li></ul> <hr /> <ul><li><a href="/wiki/Bengali_numerals" title="Bengali numerals">Bengali</a></li> <li><a href="/wiki/Devanagari_numerals" title="Devanagari numerals">Devanagari</a></li> <li><a href="/wiki/Gujarati_numerals" title="Gujarati numerals">Gujarati</a></li> <li><a href="/wiki/Gurmukhi_numerals" class="mw-redirect" title="Gurmukhi numerals">Gurmukhi</a></li> <li><a href="/wiki/Odia_numerals" title="Odia numerals">Odia</a></li> <li><a href="/wiki/Sinhala_numerals" title="Sinhala numerals">Sinhala</a></li> <li><a href="/wiki/Tamil_numerals" title="Tamil numerals">Tamil</a></li> <li><a href="/wiki/Malayalam_numerals" title="Malayalam numerals">Malayalam</a></li> <li><a href="/wiki/Telugu_script#Numerals" title="Telugu script">Telugu</a></li> <li><a href="/wiki/Kannada_script#Numerals" title="Kannada script">Kannada</a></li> <li><a href="/wiki/Dzongkha_numerals" title="Dzongkha numerals">Dzongkha</a></li></ul> <hr /> <ul><li><a href="/wiki/Tibetan_numerals" title="Tibetan numerals">Tibetan</a></li> <li><a href="/wiki/Balinese_numerals" title="Balinese numerals">Balinese</a></li> <li><a href="/wiki/Burmese_numerals" title="Burmese numerals">Burmese</a></li> <li><a href="/wiki/Javanese_numerals" title="Javanese numerals">Javanese</a></li> <li><a href="/wiki/Khmer_numerals" title="Khmer numerals">Khmer</a></li> <li><a href="/wiki/Lao_script#Numerals" title="Lao script">Lao</a></li> <li><a href="/wiki/Mongolian_numerals" title="Mongolian numerals">Mongolian</a></li> <li><a href="/wiki/Sundanese_numerals" title="Sundanese numerals">Sundanese</a></li> <li><a href="/wiki/Thai_numerals" title="Thai numerals">Thai</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">East Asian systems</div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Contemporary</dt></dl> <ul><li><a href="/wiki/Chinese_numerals" title="Chinese numerals">Chinese</a> <ul><li><a href="/wiki/Suzhou_numerals" title="Suzhou numerals">Suzhou</a></li></ul></li> <li><a href="/wiki/Hokkien_numerals" title="Hokkien numerals">Hokkien</a></li> <li><a href="/wiki/Japanese_numerals" title="Japanese numerals">Japanese</a></li> <li><a href="/wiki/Korean_numerals" title="Korean numerals">Korean</a></li> <li><a href="/wiki/Vietnamese_numerals" title="Vietnamese numerals">Vietnamese</a></li></ul> <hr /> <dl><dt>Historic</dt></dl> <ul><li><a href="/wiki/Counting_rods" title="Counting rods">Counting rods</a></li> <li><a href="/wiki/Tangut_numerals" title="Tangut numerals">Tangut</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Other systems</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/History_of_ancient_numeral_systems" title="History of ancient numeral systems">History</a></li></ul> <hr /> <dl><dt><a href="/wiki/Ancient_history" title="Ancient history">Ancient</a></dt></dl> <ul><li><a href="/wiki/Babylonian_cuneiform_numerals" title="Babylonian cuneiform numerals">Babylonian</a></li></ul> <hr /> <dl><dt><a href="/wiki/Post-classical_history" title="Post-classical history">Post-classical</a></dt></dl> <ul><li><a href="/wiki/Cistercian_numerals" title="Cistercian numerals">Cistercian</a></li> <li><a href="/wiki/Maya_numerals" title="Maya numerals">Mayan</a></li> <li><a href="/wiki/Muisca_numerals" title="Muisca numerals">Muisca</a></li> <li><a href="/wiki/Pentadic_numerals" title="Pentadic numerals">Pentadic</a></li> <li><a href="/wiki/Quipu" title="Quipu">Quipu</a></li> <li><a href="/wiki/Rumi_Numeral_Symbols" title="Rumi Numeral Symbols">Rumi</a></li></ul> <hr /> <dl><dt>Contemporary</dt></dl> <ul><li><a href="/wiki/Cherokee_syllabary#Numerals" title="Cherokee syllabary">Cherokee</a></li> <li><a href="/wiki/Kaktovik_numerals" title="Kaktovik numerals">Kaktovik</a> (Iñupiaq)</li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">By <a href="/wiki/Radix" title="Radix">radix/base</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Common radices/bases</dt></dl> <ul><li><a href="/wiki/Binary_number" title="Binary number">2</a></li> <li><a href="/wiki/Ternary_numeral_system" title="Ternary numeral system">3</a></li> <li><a href="/wiki/Quaternary_numeral_system" title="Quaternary numeral system">4</a></li> <li><a href="/wiki/Quinary" title="Quinary">5</a></li> <li><a href="/wiki/Senary" title="Senary">6</a></li> <li><a href="/wiki/Octal" title="Octal">8</a></li> <li><a href="/wiki/Decimal" title="Decimal">10</a></li> <li><a href="/wiki/Duodecimal" title="Duodecimal">12</a></li> <li><a href="/wiki/Hexadecimal" title="Hexadecimal">16</a></li> <li><a href="/wiki/Vigesimal" title="Vigesimal">20</a></li> <li><a href="/wiki/Sexagesimal" title="Sexagesimal">60</a></li></ul> <hr /> <dl><dt><a href="/wiki/Non-standard_positional_numeral_systems" title="Non-standard positional numeral systems">Non-standard radices/bases</a></dt></dl> <ul><li><a href="/wiki/Bijective_numeration" title="Bijective numeration">Bijective</a><span class="nowrap"> </span>(<a href="/wiki/Unary_numeral_system" title="Unary numeral system">1</a>)</li> <li><a href="/wiki/Signed-digit_representation" title="Signed-digit representation">Signed-digit</a><span class="nowrap"> </span>(<a href="/wiki/Balanced_ternary" title="Balanced ternary">balanced ternary</a>)</li> <li><a href="/wiki/Mixed_radix" title="Mixed radix">Mixed</a><span class="nowrap"> </span>(<a href="/wiki/Factorial_number_system" title="Factorial number system">factorial</a>)</li> <li><a href="/wiki/Negative_base" title="Negative base">Negative</a></li> <li><a href="/wiki/Complex-base_system" title="Complex-base system">Complex</a><span class="nowrap"> </span>(<a href="/wiki/Quater-imaginary_base" title="Quater-imaginary base">2<i>i</i></a>)</li> <li><a href="/wiki/Non-integer_base_of_numeration" title="Non-integer base of numeration">Non-integer</a><span class="nowrap"> </span>(<a href="/wiki/Golden_ratio_base" title="Golden ratio base">φ</a>)</li> <li><a href="/wiki/Asymmetric_numeral_systems" title="Asymmetric numeral systems">Asymmetric</a></li></ul></div></div></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Sign-value_notation" title="Sign-value notation">Sign-value notation</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Non-alphabetic</dt></dl> <ul><li><a href="/wiki/Aegean_numerals" title="Aegean numerals">Aegean</a></li> <li><a href="/wiki/Attic_numerals" title="Attic numerals">Attic</a></li> <li><a href="/wiki/Aztec_script#Numerals" title="Aztec script">Aztec</a></li> <li><a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brahmi</a></li> <li><a href="/wiki/Chuvash_numerals" title="Chuvash numerals">Chuvash</a></li> <li><a href="/wiki/Egyptian_numerals" title="Egyptian numerals">Egyptian</a></li> <li><a href="/wiki/Etruscan_numerals" title="Etruscan numerals">Etruscan</a></li> <li><a href="/wiki/Kharosthi_numerals" class="mw-redirect" title="Kharosthi numerals">Kharosthi</a></li> <li><a href="/wiki/Prehistoric_counting" title="Prehistoric counting">Prehistoric counting</a></li> <li><a href="/wiki/Proto-cuneiform" title="Proto-cuneiform">Proto-cuneiform</a></li> <li><a href="/wiki/Roman_numerals" title="Roman numerals">Roman</a></li> <li><a href="/wiki/Tally_marks" title="Tally marks">Tally marks</a></li></ul> <hr /> <dl><dt><a href="/wiki/Alphabetic_numeral_system" title="Alphabetic numeral system">Alphabetic</a></dt></dl> <ul><li><a href="/wiki/Abjad_numerals" title="Abjad numerals">Abjad</a></li> <li><a href="/wiki/Armenian_numerals" title="Armenian numerals">Armenian</a></li> <li><a href="/wiki/Alphasyllabic_numeral_system" title="Alphasyllabic numeral system">Alphasyllabic</a> <ul><li><a href="/wiki/Aksharapalli" title="Aksharapalli">Akṣarapallī</a></li> <li><a href="/wiki/%C4%80ryabha%E1%B9%ADa_numeration" title="Āryabhaṭa numeration">Āryabhaṭa</a></li> <li><a href="/wiki/Katapayadi_system" title="Katapayadi system">Kaṭapayādi</a></li></ul></li> <li><a href="/wiki/Coptic_numerals" class="mw-redirect" title="Coptic numerals">Coptic</a></li> <li><a href="/wiki/Cyrillic_numerals" title="Cyrillic numerals">Cyrillic</a></li> <li><a href="/wiki/Ge%CA%BDez_script#Numerals" title="Geʽez script">Geʽez</a></li> <li><a href="/wiki/Georgian_numerals" title="Georgian numerals">Georgian</a></li> <li><a href="/wiki/Glagolitic_numerals" title="Glagolitic numerals">Glagolitic</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek</a></li> <li><a href="/wiki/Hebrew_numerals" title="Hebrew numerals">Hebrew</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <a href="/wiki/List_of_numeral_systems" title="List of numeral systems">List of numeral systems</a></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Numeral_systems" title="Template:Numeral systems"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Numeral_systems" title="Template talk:Numeral systems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Numeral_systems" title="Special:EditPage/Template:Numeral systems"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:EgyptphoneKeypad.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d8/EgyptphoneKeypad.jpg/260px-EgyptphoneKeypad.jpg" decoding="async" width="260" height="260" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/d/d8/EgyptphoneKeypad.jpg 1.5x" data-file-width="300" data-file-height="300" /></a><figcaption>Modern-day Arab telephone keypad with two forms of Arabic numerals: Western Arabic numerals on the left and Eastern Arabic numerals on the right</figcaption></figure> <p>The <b>Hindu–Arabic numeral system</b> (also known as the <b>Indo-Arabic numeral system</b>,<sup id="cite_ref-booksmith_1-0" class="reference"><a href="#cite_note-booksmith-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <b>Hindu numeral system</b>, <b>Arabic numeral system</b>)<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup> is a <a href="/wiki/Positional_notation" title="Positional notation">positional</a> <a href="/wiki/Decimal" title="Decimal">base-ten</a> <a href="/wiki/Numeral_system" title="Numeral system">numeral system</a> for representing <a href="/wiki/Integers" class="mw-redirect" title="Integers">integers</a>; its extension to non-integers is the <a href="/wiki/Decimal" title="Decimal">decimal numeral system</a>, which is presently the most common numeral system. </p><p>The system was invented between the 1st and 4th centuries by <a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian mathematicians</a>. By the 9th century, the system was adopted by <a href="/wiki/Arabic_mathematics" class="mw-redirect" title="Arabic mathematics">Arabic mathematicians</a> who extended it to include <a href="/wiki/Fraction_(mathematics)" class="mw-redirect" title="Fraction (mathematics)">fractions</a>. It became more widely known through the writings in <a href="/wiki/Arabic" title="Arabic">Arabic</a> of the Persian mathematician <a href="/wiki/Al-Khw%C4%81rizm%C4%AB" class="mw-redirect" title="Al-Khwārizmī">Al-Khwārizmī</a><sup id="cite_ref-Brezina2006_4-0" class="reference"><a href="#cite_note-Brezina2006-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> (<i>On the Calculation with Hindu Numerals</i>, <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 825</span>) and Arab mathematician <a href="/wiki/Al-Kindi" title="Al-Kindi">Al-Kindi</a> (<i>On the Use of the Hindu Numerals</i>, <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 830</span>). The system had spread to medieval Europe by the <a href="/wiki/High_Middle_Ages" title="High Middle Ages">High Middle Ages</a>, notably following <a href="/wiki/Fibonacci" title="Fibonacci">Fibonacci</a>'s 13th century <i><a href="/wiki/Liber_Abaci" title="Liber Abaci">Liber Abaci</a></i>; until the evolution of the <a href="/wiki/Printing_press" title="Printing press">printing press</a> in the 15th century, use of the system in Europe was mainly confined to <a href="/wiki/Northern_Italy" title="Northern Italy">Northern Italy</a>.<sup id="cite_ref-Danna_2021_pp._5–48_5-0" class="reference"><a href="#cite_note-Danna_2021_pp._5–48-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>It is based upon ten <a href="/wiki/Glyph" title="Glyph">glyphs</a> representing the numbers from zero to nine, and allows representing any <a href="/wiki/Natural_number" title="Natural number">natural number</a> by a unique sequence of these glyphs. The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from <a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brahmi numerals</a> and have split into various typographical variants since the <a href="/wiki/Middle_Ages" title="Middle Ages">Middle Ages</a>. </p><p>These symbol sets can be divided into three main families: <a href="/wiki/Western_Arabic_numerals" class="mw-redirect" title="Western Arabic numerals">Western Arabic numerals</a> used in the <a href="/wiki/Greater_Maghreb" class="mw-redirect" title="Greater Maghreb">Greater Maghreb</a> and in <a href="/wiki/Europe" title="Europe">Europe</a>; <a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a> used in the <a href="/wiki/Middle_East" title="Middle East">Middle East</a>; and the Indian numerals in various scripts used in the <a href="/wiki/Indian_subcontinent" title="Indian subcontinent">Indian subcontinent</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Origins">Origins</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=1" title="Edit section: Origins"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sometime around 600 CE, a change began in the writing of dates in the <a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brāhmī</a>-derived scripts of India and Southeast Asia, transforming from an additive system with separate numerals for numbers of different magnitudes to a positional place-value system with a single set of glyphs for 1–9 and a dot for zero, gradually displacing additive expressions of numerals over the following several centuries.<sup id="cite_ref-FOOTNOTEChrisomalis2010194–197_6-0" class="reference"><a href="#cite_note-FOOTNOTEChrisomalis2010194–197-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>When this system was adopted and extended by medieval Arabs and Persians, they called it <i>al-ḥisāb al-hindī</i> ("Indian arithmetic"). These numerals were gradually adopted in Europe starting around the 10th century, probably transmitted by Arab merchants;<sup id="cite_ref-FOOTNOTESmithKarpinski1911[httpsarchiveorgdetailshinduarabicnumer00smitrichpage99_Ch._7,_pp.&nbsp;99–127]_7-0" class="reference"><a href="#cite_note-FOOTNOTESmithKarpinski1911[httpsarchiveorgdetailshinduarabicnumer00smitrichpage99_Ch._7,_pp.&nbsp;99–127]-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> medieval and Renaissance European mathematicians generally recognized them as Indian in origin,<sup id="cite_ref-FOOTNOTESmithKarpinski1911[httpsarchiveorgdetailshinduarabicnumer00smitrichpage2_p.&nbsp;2]_8-0" class="reference"><a href="#cite_note-FOOTNOTESmithKarpinski1911[httpsarchiveorgdetailshinduarabicnumer00smitrichpage2_p.&nbsp;2]-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> however a few influential sources credited them to the Arabs, and they eventually came to be generally known as "Arabic numerals" in Europe.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> According to some sources, this number system may have originated in Chinese Shang numerals (1200 BCE), which was also a <a href="/wiki/Decimal" title="Decimal">decimal</a> <a href="/wiki/Positional_notation" title="Positional notation">positional</a> numeral system.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Positional_notation">Positional notation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=2" title="Edit section: Positional notation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Positional_notation" title="Positional notation">Positional notation</a> and <a href="/wiki/0_(number)" class="mw-redirect" title="0 (number)">0 (number)</a></div> <p>The Hindu–Arabic system is designed for <a href="/wiki/Positional_notation" title="Positional notation">positional notation</a> in a <a href="/wiki/Decimal" title="Decimal">decimal</a> system. In a more developed form, positional notation also uses a <a href="/wiki/Decimal_separator" title="Decimal separator">decimal marker</a> (at first a mark over the ones digit but now more commonly a decimal point or a decimal comma which separates the ones place from the tenths place), and also a symbol for "these digits recur <i><a href="/wiki/Ad_infinitum" title="Ad infinitum">ad infinitum</a></i>". In modern usage, this latter symbol is usually a <a href="/wiki/Vinculum_(symbol)" title="Vinculum (symbol)">vinculum</a> (a horizontal line placed over the repeating digits). In this more developed form, the numeral system can symbolize any <a href="/wiki/Rational_number" title="Rational number">rational number</a> using only 13 symbols (the ten digits, decimal marker, vinculum, and a prepended <a href="/wiki/Minus_sign" class="mw-redirect" title="Minus sign">minus sign</a> to indicate a <a href="/wiki/Negative_number" title="Negative number">negative number</a>). </p><p>Although generally found in text written with the Arabic <a href="/wiki/Abjad" title="Abjad">abjad</a> ("alphabet"), which is written right-to-left, numbers written with these numerals place the most-significant digit to the left, so they read from left to right (though digits are not always said in order from most to least significant<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>). The requisite changes in reading direction are found in text that mixes left-to-right writing systems with right-to-left systems. </p> <div class="mw-heading mw-heading2"><h2 id="Symbols">Symbols</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=3" title="Edit section: Symbols"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, most of which developed from the <a href="/wiki/Brahmi_numeral" class="mw-redirect" title="Brahmi numeral">Brahmi numerals</a>. </p><p>The symbols used to represent the system have split into various typographical variants since the <a href="/wiki/Middle_Ages" title="Middle Ages">Middle Ages</a>, arranged in three main groups: </p> <ul><li>The widespread Western "<a href="/wiki/Arabic_numerals" title="Arabic numerals">Arabic numerals</a>" used with the <a href="/wiki/Latin_alphabet" title="Latin alphabet">Latin</a>, <a href="/wiki/Cyrillic_script" title="Cyrillic script">Cyrillic</a>, and <a href="/wiki/Greek_alphabet" title="Greek alphabet">Greek alphabets</a> in the table, descended from the "West Arabic numerals" which were developed in <a href="/wiki/Al-Andalus" title="Al-Andalus">al-Andalus</a> and the <a href="/wiki/Maghreb" title="Maghreb">Maghreb</a> (there are two <a href="/wiki/Typography" title="Typography">typographic</a> styles for rendering western Arabic numerals, known as lining figures and <a href="/wiki/Text_figures" title="Text figures">text figures</a>).</li> <li>The "Arabic–Indic" or "<a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a>" used with Arabic script, developed primarily in what is now <a href="/wiki/Iraq" title="Iraq">Iraq</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2020)">citation needed</span></a></i>]</sup> A variant of the Eastern Arabic numerals is used in Persian and Urdu.</li> <li>The <a href="/wiki/Indian_numerals" class="mw-redirect" title="Indian numerals">Indian numerals</a> in use with scripts of the <a href="/wiki/Brahmic_family" class="mw-redirect" title="Brahmic family">Brahmic family</a> in India and Southeast Asia. Each of the roughly dozen major scripts of India has its own numeral glyphs (as one will note when perusing Unicode character charts).</li></ul> <div class="mw-heading mw-heading3"><h3 id="Glyph_comparison">Glyph comparison</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=4" title="Edit section: Glyph comparison"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center;"> <tbody><tr style=""> <th colspan="10">Symbol</th> <th>Used with scripts</th> <th>Numerals </th></tr> <tr> <td>0</td> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> <td>9</td> <td><a href="/wiki/Arabic_alphabet" title="Arabic alphabet">Arabic</a>, <a href="/wiki/Latin_alphabet" title="Latin alphabet">Latin</a>, <a href="/wiki/Cyrillic_script" title="Cyrillic script">Cyrillic</a>, and <a href="/wiki/Greek_alphabet" title="Greek alphabet">Greek</a></td> <td><a href="/wiki/Arabic_numerals" title="Arabic numerals">Arabic numerals</a> </td></tr> <tr> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">٠</span></span></td> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">١</span></span></td> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">٢</span></span></td> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">٣</span></span></td> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">٤</span></span></td> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">٥</span></span></td> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">٦</span></span></td> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">٧</span></span></td> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">٨</span></span></td> <td><span title="Arabic-language text"><span lang="ar" dir="rtl">٩</span></span></td> <td><a href="/wiki/Arabic" title="Arabic">Arabic</a></td> <td rowspan="3"><a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a> </td></tr> <tr> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۰</span></span></td> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۱</span></span></td> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۲</span></span></td> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۳</span></span></td> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۴</span></span></td> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۵</span></span></td> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۶</span></span></td> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۷</span></span></td> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۸</span></span></td> <td><span title="Persian-language text"><span lang="fa" dir="rtl">۹</span></span></td> <td><a href="/wiki/Persian_alphabet" title="Persian alphabet">Persian</a> / <a href="/wiki/Dari" title="Dari">Dari</a> / <a href="/wiki/Pashto_alphabet" title="Pashto alphabet">Pashto</a> </td></tr> <tr> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۰</span></span></span></td> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۱</span></span></span></td> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۲</span></span></span></td> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۳</span></span></span></td> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۴</span></span></span></td> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۵</span></span></span></td> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۶</span></span></span></td> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۷</span></span></span></td> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۸</span></span></span></td> <td><span class="Nastaliq" dir="rtl" title="Nastaliq" style="font-family: 'Jameel Noori Nastaleeq', 'Urdu Typesetting', 'Noto Nastaliq Urdu', 'Noto Nastaliq Urdu Draft', 'Hussaini Nastaleeq', 'AlQalam Taj Nastaleeq', IranNastaliq, 'Awami Nastaliq', 'Awami Nastaliq Beta3', 'Awami Nastaliq Beta2', 'Awami Nastaliq Beta1', 'Nafees Nastaleeq', 'Nafees Nastaleeq v1.01', 'Pak Nastaleeq', 'PDMS_Jauhar', 'Alvi Lahori Nastaleeq'; font-size: 110%; font-style: normal;"><span title="Urdu-language text"><span lang="ur" dir="rtl">۹</span></span></span></td> <td><a href="/wiki/Urdu_alphabet" title="Urdu alphabet">Urdu</a> / <a href="/wiki/Shahmukhi" title="Shahmukhi">Shahmukhi</a> </td></tr> <tr> <td><span class="brai_cell" title=" ⠚ (braille pattern dots-245) U+281A" style="background: #eaecf0;">⠚</span></td> <td><span class="brai_cell" title=" ⠁ (braille pattern dots-1) U+2801" style="background: #eaecf0;">⠁</span></td> <td><span class="brai_cell" title=" ⠃ (braille pattern dots-12) U+2803" style="background: #eaecf0;">⠃</span></td> <td><span class="brai_cell" title=" ⠉ (braille pattern dots-14) U+2809" style="background: #eaecf0;">⠉</span></td> <td><span class="brai_cell" title=" ⠙ (braille pattern dots-145) U+2819" style="background: #eaecf0;">⠙</span></td> <td><span class="brai_cell" title=" ⠑ (braille pattern dots-15) U+2811" style="background: #eaecf0;">⠑</span></td> <td><span class="brai_cell" title=" ⠋ (braille pattern dots-124) U+280B" style="background: #eaecf0;">⠋</span></td> <td><span class="brai_cell" title=" ⠛ (braille pattern dots-1245) U+281B" style="background: #eaecf0;">⠛</span></td> <td><span class="brai_cell" title=" ⠓ (braille pattern dots-125) U+2813" style="background: #eaecf0;">⠓</span></td> <td><span class="brai_cell" title=" ⠊ (braille pattern dots-24) U+280A" style="background: #eaecf0;">⠊</span></td> <td><a href="/wiki/Braille" title="Braille">Braille</a></td> <td><a href="/wiki/Braille#Derivation" title="Braille">Braille numerals</a> </td></tr> <tr> <td>〇</td> <td>一</td> <td>二</td> <td>三</td> <td>四</td> <td>五</td> <td>六</td> <td>七</td> <td>八</td> <td>九</td> <td><a href="/wiki/Written_Chinese" title="Written Chinese">Chinese</a> / <a href="/wiki/Japanese_writing_system" title="Japanese writing system">Japanese</a> </td> <td scope="row"><a href="/wiki/Chinese_numerals" title="Chinese numerals">Chinese</a> and <a href="/wiki/Japanese_numerals" title="Japanese numerals">Japanese numerals</a> </td></tr> <tr> <td>영 </td> <td>일 </td> <td>이 </td> <td>삼 </td> <td>사 </td> <td>오 </td> <td>육 </td> <td>칠 </td> <td>팔 </td> <td>구 </td> <td><a href="/wiki/Korean_language" title="Korean language">Korean</a> </td> <td><a href="/wiki/Korean_numerals" title="Korean numerals">Korean numerals</a> (Sino cardinals)<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>note 2<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td>𑁦</td> <td>𑁧</td> <td>𑁨</td> <td>𑁩</td> <td>𑁪</td> <td>𑁫</td> <td>𑁬</td> <td>𑁭</td> <td>𑁮</td> <td>𑁯</td> <td><a href="/wiki/Brahmi_script" title="Brahmi script">Brahmi</a></td> <td><a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brahmi numerals</a> </td></tr> <tr> <td>०</td> <td>१</td> <td>२</td> <td>३</td> <td>४</td> <td>५</td> <td>६</td> <td>७</td> <td>८</td> <td>९</td> <td><a href="/wiki/Devanagari" title="Devanagari">Devanagari</a></td> <td><a href="/wiki/Devanagari_numerals" title="Devanagari numerals">Devanagari numerals</a> </td></tr> <tr> <td><span title="Tamil-language text"><span lang="ta">௦</span></span></td> <td><span title="Tamil-language text"><span lang="ta">௧</span></span></td> <td><span title="Tamil-language text"><span lang="ta">௨</span></span></td> <td><span title="Tamil-language text"><span lang="ta">௩</span></span></td> <td><span title="Tamil-language text"><span lang="ta">௪</span></span></td> <td><span title="Tamil-language text"><span lang="ta">௫</span></span></td> <td><span title="Tamil-language text"><span lang="ta">௬</span></span></td> <td><span title="Tamil-language text"><span lang="ta">௭</span></span></td> <td><span title="Tamil-language text"><span lang="ta">௮</span></span></td> <td><span title="Tamil-language text"><span lang="ta">௯</span></span></td> <td><a href="/wiki/Tamil_script" title="Tamil script">Tamil</a></td> <td><a href="/wiki/Tamil_numerals" title="Tamil numerals">Tamil numerals</a> </td></tr> <tr> <td>০</td> <td>১</td> <td>২</td> <td>৩</td> <td>৪</td> <td>৫</td> <td>৬</td> <td>৭</td> <td>৮</td> <td>৯</td> <td><a href="/wiki/Bengali%E2%80%93Assamese_script" title="Bengali–Assamese script">Eastern Nagari</a></td> <td><a href="/wiki/Bengali_numerals" title="Bengali numerals">Bengali numerals</a> </td></tr> <tr> <td>𐴰</td> <td>𐴱</td> <td>𐴲</td> <td>𐴳</td> <td>𐴴</td> <td>𐴵</td> <td>𐴶</td> <td>𐴷</td> <td>𐴸</td> <td>𐴹</td> <td><a href="/wiki/Hanifi_Rohingya_script" title="Hanifi Rohingya script">Hanifi Rohingya</a></td> <td><a href="/wiki/Hanifi_Rohingya_script#Numbers" title="Hanifi Rohingya script">Hanifi Rohingya script § Numbers</a> </td></tr> <tr> <td>੦</td> <td>੧</td> <td>੨</td> <td>੩</td> <td>੪</td> <td>੫</td> <td>੬</td> <td>੭</td> <td>੮</td> <td>੯</td> <td><a href="/wiki/Gurmukhi" title="Gurmukhi">Gurmukhi</a></td> <td><a href="/wiki/Gurmukhi_numerals" class="mw-redirect" title="Gurmukhi numerals">Gurmukhi numerals</a> </td></tr> <tr> <td>૦</td> <td>૧</td> <td>૨</td> <td>૩</td> <td>૪</td> <td>૫</td> <td>૬</td> <td>૭</td> <td>૮</td> <td>૯</td> <td><a href="/wiki/Gujarati_script" title="Gujarati script">Gujarati</a></td> <td><a href="/wiki/Gujarati_numerals" title="Gujarati numerals">Gujarati numerals</a> </td></tr> <tr> <td>𑙐</td> <td>𑙑</td> <td>𑙒</td> <td>𑙓</td> <td>𑙔</td> <td>𑙕</td> <td>𑙖</td> <td>𑙗</td> <td>𑙘</td> <td>𑙙</td> <td><a href="/wiki/Modi_script" title="Modi script">Modi</a></td> <td><a href="/wiki/Modi_script#Unicode" title="Modi script">Modi numerals</a> </td></tr> <tr> <td>𑋰</td> <td>𑋱</td> <td>𑋲</td> <td>𑋳</td> <td>𑋴</td> <td>𑋵</td> <td>𑋶</td> <td>𑋷</td> <td>𑋸</td> <td>𑋹</td> <td><a href="/wiki/Khudabadi_script" title="Khudabadi script">Khudabadi</a></td> <td><a href="/wiki/Khudabadi_script#Numerals" title="Khudabadi script">Khudabadi script § Numerals</a> </td></tr> <tr> <td>୦</td> <td>୧</td> <td>୨</td> <td>୩</td> <td>୪</td> <td>୫</td> <td>୬</td> <td>୭</td> <td>୮</td> <td>୯</td> <td><a href="/wiki/Odia_script" title="Odia script">Odia</a></td> <td><a href="/wiki/Odia_numerals" title="Odia numerals">Odia numerals</a> </td></tr> <tr> <td>᱐</td> <td>᱑</td> <td>᱒</td> <td>᱓</td> <td>᱔</td> <td>᱕</td> <td>᱖</td> <td>᱗</td> <td>᱘</td> <td>᱙</td> <td><a href="/wiki/Ol_Chiki_script" title="Ol Chiki script">Santali</a></td> <td><a href="/wiki/Ol_Chiki_script#Digits" title="Ol Chiki script">Santali numerals</a> </td></tr> <tr> <td>𑇐</td> <td>𑇑</td> <td>𑇒</td> <td>𑇓</td> <td>𑇔</td> <td>𑇕</td> <td>𑇖</td> <td>𑇗</td> <td>𑇘</td> <td>𑇙</td> <td><a href="/wiki/Sharada_script" title="Sharada script">Sharada</a></td> <td><a href="/wiki/Sharada_script#Numerals" title="Sharada script">Sharada numerals</a> </td></tr> <tr> <td>౦</td> <td>౧</td> <td>౨</td> <td>౩</td> <td>౪</td> <td>౫</td> <td>౬</td> <td>౭</td> <td>౮</td> <td>౯</td> <td><a href="/wiki/Telugu_script" title="Telugu script">Telugu</a></td> <td><a href="/wiki/Telugu_script#Numerals" title="Telugu script">Telugu script § Numerals</a> </td></tr> <tr> <td>೦</td> <td>೧</td> <td>೨</td> <td>೩</td> <td>೪</td> <td>೫</td> <td>೬</td> <td>೭</td> <td>೮</td> <td>೯</td> <td><a href="/wiki/Kannada_script" title="Kannada script">Kannada</a></td> <td><a href="/wiki/Kannada_script#Numerals" title="Kannada script">Kannada script § Numerals</a> </td></tr> <tr> <td>൦</td> <td>൧</td> <td>൨</td> <td>൩</td> <td>൪</td> <td>൫</td> <td>൬</td> <td>൭</td> <td>൮</td> <td>൯</td> <td><a href="/wiki/Malayalam_script" title="Malayalam script">Malayalam</a></td> <td><a href="/wiki/Malayalam_numerals" title="Malayalam numerals">Malayalam numerals</a> </td></tr> <tr> <td><style data-mw-deduplicate="TemplateStyles:r1259558396">.mw-parser-output .script-Mtei,.mw-parser-output .script-mtei,.mw-parser-output .script-meetei_mayek,.mw-parser-output .script-meithei{font-family:"Noto Sans Meetei Mayek","Eeyek","Eeyek Unicode","Nirmala UI"}</style><span class="script-meetei_mayek">꯰</span> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1259558396"><span class="script-meetei_mayek">꯱</span> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1259558396"><span class="script-meetei_mayek">꯲</span> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1259558396"><span class="script-meetei_mayek">꯳</span> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1259558396"><span class="script-meetei_mayek">꯴</span> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1259558396"><span class="script-meetei_mayek">꯵</span> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1259558396"><span class="script-meetei_mayek">꯶</span> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1259558396"><span class="script-meetei_mayek">꯷</span> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1259558396"><span class="script-meetei_mayek">꯸</span> </td> <td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1259558396"><span class="script-meetei_mayek">꯹</span> </td> <td><a href="/wiki/Meitei_script" title="Meitei script">Meitei</a> </td> <td><a href="/wiki/Meitei_script#Numerals" title="Meitei script">Meitei script § Numerals</a> </td></tr> <tr> <td>෦</td> <td>෧</td> <td>෨</td> <td>෩</td> <td>෪</td> <td>෫</td> <td>෬</td> <td>෭</td> <td>෮</td> <td>෯</td> <td><a href="/wiki/Sinhala_script" title="Sinhala script">Sinhala</a></td> <td><a href="/wiki/Sinhala_numerals" title="Sinhala numerals">Sinhala numerals</a> </td></tr> <tr> <td>𑓐</td> <td>𑓑</td> <td>𑓒</td> <td>𑓓</td> <td>𑓔</td> <td>𑓕</td> <td>𑓖</td> <td>𑓗</td> <td>𑓘</td> <td>𑓙</td> <td><a href="/wiki/Tirhuta_script" title="Tirhuta script">Tirhuta Mithilakshar</a></td> <td><a href="/wiki/Tirhuta_script#Numerals" title="Tirhuta script">Maithili numerals</a> </td></tr> <tr> <td>༠</td> <td>༡</td> <td>༢</td> <td>༣</td> <td>༤</td> <td>༥</td> <td>༦</td> <td>༧</td> <td>༨</td> <td>༩</td> <td><a href="/wiki/Tibetan_script" title="Tibetan script">Tibetan</a></td> <td><a href="/wiki/Tibetan_numerals" title="Tibetan numerals">Tibetan numerals</a> </td></tr> <tr> <td>᠐</td> <td>᠑</td> <td>᠒</td> <td>᠓</td> <td>᠔</td> <td>᠕</td> <td>᠖</td> <td>᠗</td> <td>᠘</td> <td>᠙</td> <td><a href="/wiki/Mongolian_script" title="Mongolian script">Mongolian</a></td> <td><a href="/wiki/Mongolian_numerals" title="Mongolian numerals">Mongolian numerals</a> </td></tr> <tr> <td>᥆</td> <td>᥇</td> <td>᥈</td> <td>᥉</td> <td>᥊</td> <td>᥋</td> <td>᥌</td> <td>᥍</td> <td>᥎</td> <td>᥏</td> <td><a href="/wiki/Limbu_script" title="Limbu script">Limbu</a></td> <td><a href="/wiki/Limbu_script#Digits" title="Limbu script">Limbu script § Digits</a> </td></tr> <tr> <td>၀</td> <td>၁</td> <td>၂</td> <td>၃</td> <td>၄</td> <td>၅</td> <td>၆</td> <td>၇</td> <td>၈</td> <td>၉</td> <td><a href="/wiki/Burmese_script" class="mw-redirect" title="Burmese script">Burmese</a></td> <td><a href="/wiki/Burmese_numerals" title="Burmese numerals">Burmese numerals</a> </td></tr> <tr> <td>႐</td> <td>႑</td> <td>႒</td> <td>႓</td> <td>႔</td> <td>႕</td> <td>႖</td> <td>႗</td> <td>႘</td> <td>႙</td> <td><a href="/wiki/Shan_alphabet" title="Shan alphabet">Shan</a></td> <td><a href="/wiki/Shan_alphabet#Numerals" title="Shan alphabet">Shan alphabet § Numerals</a> </td></tr> <tr> <td>០</td> <td>១</td> <td>២</td> <td>៣</td> <td>៤</td> <td>៥</td> <td>៦</td> <td>៧</td> <td>៨</td> <td>៩</td> <td><a href="/wiki/Khmer_script" title="Khmer script">Khmer</a></td> <td><a href="/wiki/Khmer_numerals" title="Khmer numerals">Khmer numerals</a> </td></tr> <tr> <td>๐</td> <td>๑</td> <td>๒</td> <td>๓</td> <td>๔</td> <td>๕</td> <td>๖</td> <td>๗</td> <td>๘</td> <td>๙</td> <td><a href="/wiki/Thai_script" title="Thai script">Thai</a></td> <td><a href="/wiki/Thai_numerals" title="Thai numerals">Thai numerals</a> </td></tr> <tr> <td>໐</td> <td>໑</td> <td>໒</td> <td>໓</td> <td>໔</td> <td>໕</td> <td>໖</td> <td>໗</td> <td>໘</td> <td>໙</td> <td><a href="/wiki/Lao_script" title="Lao script">Lao</a></td> <td><a href="/wiki/Lao_script#Numerals" title="Lao script">Lao script § Numerals</a> </td></tr> <tr> <td>᧐</td> <td>᧑/᧚</td> <td>᧒</td> <td>᧓</td> <td>᧔</td> <td>᧕</td> <td>᧖</td> <td>᧗</td> <td>᧘</td> <td>᧙</td> <td><a href="/wiki/New_Tai_Lue_script" class="mw-redirect" title="New Tai Lue script">New Tai Lue</a></td> <td><a href="/wiki/New_Tai_Lue_script#Digits" class="mw-redirect" title="New Tai Lue script">New Tai Lue script § Digits</a> </td></tr> <tr> <td>꩐</td> <td>꩑</td> <td>꩒</td> <td>꩓</td> <td>꩔</td> <td>꩕</td> <td>꩖</td> <td>꩗</td> <td>꩘</td> <td>꩙</td> <td><a href="/wiki/Cham_script" title="Cham script">Cham</a></td> <td><a href="/wiki/Cham_script#Numerals" title="Cham script">Cham script § Numerals</a> </td></tr> <tr> <td>𑽐</td> <td>𑽑</td> <td>𑽒</td> <td>𑽓</td> <td>𑽔</td> <td>𑽕</td> <td>𑽖</td> <td>𑽗</td> <td>𑽘</td> <td>𑽙</td> <td><a href="/wiki/Kawi_script" title="Kawi script">Kawi</a></td> <td><a href="/wiki/Kawi_script#Digits" title="Kawi script">Kawi script § Digits</a> </td></tr> <tr> <td>꧐</td> <td>꧑</td> <td>꧒</td> <td>꧓</td> <td>꧔</td> <td>꧕</td> <td>꧖</td> <td>꧗</td> <td>꧘</td> <td>꧙</td> <td><a href="/wiki/Javanese_script" title="Javanese script">Javanese</a></td> <td><a href="/wiki/Javanese_numerals" title="Javanese numerals">Javanese numerals</a> </td></tr> <tr> <td>᭐</td> <td>᭑</td> <td>᭒</td> <td>᭓</td> <td>᭔</td> <td>᭕</td> <td>᭖</td> <td>᭗</td> <td>᭘</td> <td>᭙</td> <td><a href="/wiki/Balinese_script" title="Balinese script">Balinese</a></td> <td><a href="/wiki/Balinese_numerals" title="Balinese numerals">Balinese numerals</a> </td></tr> <tr> <td>᮰</td> <td>᮱</td> <td>᮲</td> <td>᮳</td> <td>᮴</td> <td>᮵</td> <td>᮶</td> <td>᮷</td> <td>᮸</td> <td>᮹</td> <td><a href="/wiki/Sundanese_script" title="Sundanese script">Sundanese</a></td> <td><a href="/wiki/Sundanese_numerals" title="Sundanese numerals">Sundanese numerals</a> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=5" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_system" title="History of the Hindu–Arabic numeral system">History of the Hindu–Arabic numeral system</a></div> <div class="mw-heading mw-heading3"><h3 id="Predecessors">Predecessors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=6" title="Edit section: Predecessors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Edicts_of_Ashoka_numerals.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Edicts_of_Ashoka_numerals.jpg/220px-Edicts_of_Ashoka_numerals.jpg" decoding="async" width="220" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Edicts_of_Ashoka_numerals.jpg/330px-Edicts_of_Ashoka_numerals.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Edicts_of_Ashoka_numerals.jpg/440px-Edicts_of_Ashoka_numerals.jpg 2x" data-file-width="1240" data-file-height="284" /></a><figcaption>The first <a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brahmi numerals</a>, ancestors of Hindu-Arabic numerals, used by <a href="/wiki/Ashoka" title="Ashoka">Ashoka</a> in his <a href="/wiki/Edicts_of_Ashoka" title="Edicts of Ashoka">Edicts of Ashoka</a> <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 250 BC</span></figcaption></figure> <p>The <a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brahmi numerals</a> at the basis of the system predate the <a href="/wiki/Common_Era" title="Common Era">Common Era</a>. They replaced the earlier <a href="/wiki/Kharosthi_numerals" class="mw-redirect" title="Kharosthi numerals">Kharosthi numerals</a> used since the 4th century BCE. Brahmi and Kharosthi numerals were used alongside one another in the <a href="/wiki/Maurya_Empire" title="Maurya Empire">Maurya Empire</a> period, both appearing on the 3rd century BCE <a href="/wiki/Edicts_of_Ashoka" title="Edicts of Ashoka">edicts of Ashoka</a>.<sup id="cite_ref-FOOTNOTEFlegg1984[httpsarchiveorgdetailsnumberstheirhist0000flegpage67_p.&nbsp;67ff.]_13-0" class="reference"><a href="#cite_note-FOOTNOTEFlegg1984[httpsarchiveorgdetailsnumberstheirhist0000flegpage67_p.&nbsp;67ff.]-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hindustani_numerals.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Hindustani_numerals.svg/220px-Hindustani_numerals.svg.png" decoding="async" width="220" height="136" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/Hindustani_numerals.svg/330px-Hindustani_numerals.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/Hindustani_numerals.svg/440px-Hindustani_numerals.svg.png 2x" data-file-width="744" data-file-height="461" /></a><figcaption>Nagari and Devanagari numerals with handwritten variants</figcaption></figure> <p><a href="/wiki/Buddhist" class="mw-redirect" title="Buddhist">Buddhist</a> inscriptions from around 300 BCE use the symbols that became 1, 4, and 6. One century later, their use of the symbols that became 2, 4, 6, 7, and 9 was recorded. These <a href="/wiki/Brahmi_numeral" class="mw-redirect" title="Brahmi numeral">Brahmi numerals</a> are the ancestors of the Hindu–Arabic glyphs 1 to 9, but they were not used as a <a href="/wiki/Positional_system" class="mw-redirect" title="Positional system">positional system</a> with a <a href="/wiki/0_(number)" class="mw-redirect" title="0 (number)">zero</a>, and there were rather<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="This word is vague. (October 2024)">clarification needed</span></a></i>]</sup> separate numerals for each of the tens (10, 20, 30, etc.). </p><p>The actual numeral system, including positional notation and use of zero, is in principle independent of the glyphs used, and significantly younger than the Brahmi numerals. </p> <div class="mw-heading mw-heading3"><h3 id="Development">Development</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=7" title="Edit section: Development"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The place-value system is used in the <a href="/wiki/Bakhshali_manuscript" title="Bakhshali manuscript">Bakhshali manuscript</a>, the earliest leaves being radiocarbon dated to the period 224–383 CE.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The development of the positional decimal system <span class="cleanup-needed-content" style="padding-left:0.1em; padding-right:0.1em; color:var(--color-subtle, #54595d); border:1px solid var(--border-color-subtle, #c8ccd1);">takes its origins in</span><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The meaning of this phrase is unclear. (October 2024)">clarification needed</span></a></i>]</sup> <a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian mathematics</a> during the <a href="/wiki/Gupta_period" class="mw-redirect" title="Gupta period">Gupta period</a>. Around 500, the astronomer <a href="/wiki/Aryabhata" title="Aryabhata">Aryabhata</a> uses the word <i>kha</i> ("emptiness") to mark "zero" in tabular arrangements of digits. The 7th century <i><a href="/wiki/Brahmasphutasiddhanta" class="mw-redirect" title="Brahmasphutasiddhanta">Brahmasphuta Siddhanta</a></i> contains a comparatively advanced understanding of the mathematical role of <a href="/wiki/0_(number)" class="mw-redirect" title="0 (number)">zero</a>. The Sanskrit translation of the lost 5th century Prakrit <a href="/wiki/Jain_cosmology" title="Jain cosmology">Jaina cosmological</a> text <i><a href="/wiki/Lokavibhaga" title="Lokavibhaga">Lokavibhaga</a></i> may preserve an early instance of the positional use of zero.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>The first dated and undisputed inscription showing the use of a symbol for zero appears on a stone inscription found at the <a href="/wiki/Chaturbhuj_Temple,_Gwalior" title="Chaturbhuj Temple, Gwalior">Chaturbhuja Temple</a> at <a href="/wiki/Gwalior" title="Gwalior">Gwalior</a> in India, dated 876 CE.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Medieval_Islamic_world">Medieval Islamic world</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=8" title="Edit section: Medieval Islamic world"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>These Indian developments were taken up in <a href="/wiki/Islamic_mathematics" class="mw-redirect" title="Islamic mathematics">Islamic mathematics</a> in the 8th century, as recorded in <a href="/wiki/Al-Qifti" title="Al-Qifti">al-Qifti</a>'s <i>Chronology of the scholars</i> (early 13th century).<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>In 10th century <a href="/wiki/Mathematics_in_medieval_Islam" class="mw-redirect" title="Mathematics in medieval Islam">Islamic mathematics</a>, the system was extended to include fractions, as recorded in a treatise by <a href="/wiki/Abbasid_Caliphate" title="Abbasid Caliphate">Abbasid Caliphate</a> mathematician <a href="/wiki/Abu%27l-Hasan_al-Uqlidisi" title="Abu'l-Hasan al-Uqlidisi">Abu'l-Hasan al-Uqlidisi</a>, who was the first to describe positional decimal fractions.<sup id="cite_ref-Berggren_18-0" class="reference"><a href="#cite_note-Berggren-18"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> According to J. L. Berggren, the Muslims were the first to represent numbers as we do since they were the ones who initially extended this system of numeration to represent parts of the unit by decimal fractions, something that the Hindus did not accomplish. Thus, we refer to the system as "Hindu–Arabic" rather appropriately.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Berggrenn_20-0" class="reference"><a href="#cite_note-Berggrenn-20"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>The numeral system came to be known to both the <a href="/wiki/Persian_people" class="mw-redirect" title="Persian people">Persian</a> mathematician <a href="/wiki/Khwarizmi" class="mw-redirect" title="Khwarizmi">Khwarizmi</a>, who wrote a book, <i>On the Calculation with Hindu Numerals</i> in about 825, and the <a href="/wiki/Arab_people" class="mw-redirect" title="Arab people">Arab</a> mathematician <a href="/wiki/Al-Kindi" title="Al-Kindi">Al-Kindi</a>, who wrote a book, <i>On the Use of the Hindu Numerals</i> (<span title="Arabic-language text"><span lang="ar" dir="rtl">كتاب في استعمال العداد الهندي</span></span> [<i>kitāb fī isti'māl al-'adād al-hindī</i>]) around 830. <a href="/wiki/Persian_people" class="mw-redirect" title="Persian people">Persian</a> scientist <a href="/wiki/Kushyar_Gilani" title="Kushyar Gilani">Kushyar Gilani</a> who wrote <i>Kitab fi usul hisab al-hind (<a href="/wiki/Principles_of_Hindu_Reckoning" title="Principles of Hindu Reckoning">Principles of Hindu Reckoning</a>)</i> is one of the oldest surviving manuscripts using the Hindu numerals.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> These books are principally responsible for the diffusion of the Hindu system of numeration throughout the <a href="/wiki/Islamic_world" class="mw-redirect" title="Islamic world">Islamic world</a> and ultimately also to Europe. </p> <div class="mw-heading mw-heading3"><h3 id="Adoption_in_Europe">Adoption in Europe</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=9" title="Edit section: Adoption in Europe"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Arabic_numerals" title="Arabic numerals">Arabic numerals</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Codex_Vigilanus_Primeros_Numeros_Arabigos.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Codex_Vigilanus_Primeros_Numeros_Arabigos.jpg/220px-Codex_Vigilanus_Primeros_Numeros_Arabigos.jpg" decoding="async" width="220" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Codex_Vigilanus_Primeros_Numeros_Arabigos.jpg/330px-Codex_Vigilanus_Primeros_Numeros_Arabigos.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Codex_Vigilanus_Primeros_Numeros_Arabigos.jpg/440px-Codex_Vigilanus_Primeros_Numeros_Arabigos.jpg 2x" data-file-width="595" data-file-height="248" /></a><figcaption>The Arabic numeral system first appeared in Europe in the Spanish <i><a href="/wiki/Codex_Vigilanus" title="Codex Vigilanus">Codex Vigilanus</a></i>, year 976.</figcaption></figure> <p>In Christian Europe, the first mention and representation of Hindu–Arabic numerals (from one to nine, without zero), is in the <i><span title="Latin-language text"><i lang="la"><a href="/wiki/Codex_Vigilanus" title="Codex Vigilanus">Codex Vigilanus</a></i></span></i> (aka <i>Albeldensis</i>), an <a href="/wiki/Illuminated_manuscript" title="Illuminated manuscript">illuminated</a> compilation of various historical documents from the <a href="/wiki/Visigoths" title="Visigoths">Visigothic</a> period in <a href="/wiki/Hispania" title="Hispania">Spain</a>, written in the year 976 by three monks of the <a href="/wiki/La_Rioja_(Spain)" class="mw-redirect" title="La Rioja (Spain)">Riojan</a> monastery of <a href="/wiki/San_Mart%C3%ADn_de_Albelda" title="San Martín de Albelda">San Martín de Albelda</a>. Between 967 and 969, <a href="/wiki/Pope_Sylvester_II" title="Pope Sylvester II">Gerbert of Aurillac</a> discovered and studied Arab science in the Catalan abbeys. Later he obtained from these places the book <i><span title="Latin-language text"><i lang="la">De multiplicatione et divisione</i></span></i> (<i>On multiplication and division</i>). After becoming <a href="/wiki/Pope_Sylvester_II" title="Pope Sylvester II">Pope Sylvester II</a> in the year 999, he introduced a new model of <a href="/wiki/Abacus" title="Abacus">abacus</a>, the so-called <a href="/wiki/Pope_Sylvester_II#Abacus_and_numerals" title="Pope Sylvester II">Abacus of Gerbert</a>, by adopting tokens representing Hindu–Arabic numerals, from one to nine. </p><p><a href="/wiki/Fibonacci" title="Fibonacci">Leonardo Fibonacci</a> brought this system to Europe. His book <i><span title="Latin-language text"><i lang="la"><a href="/wiki/Liber_Abaci" title="Liber Abaci">Liber Abaci</a></i></span></i> introduced <a href="/wiki/Liber_Abaci#Modus_Indorum" title="Liber Abaci">Modus Indorum</a> (the method of the Indians), today known as Hindu–Arabic numeral system or base-10 positional notation, the use of zero, and the decimal place system to the Latin world. The numeral system came to be called "Arabic" by the Europeans. It was used in European mathematics from the 12th century, and entered common use from the 15th century to replace <a href="/wiki/Roman_numerals" title="Roman numerals">Roman numerals</a>.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>The familiar shape of the Western Arabic glyphs as now used with the Latin alphabet (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are the product of the late 15th to early 16th century, when they entered early <a href="/wiki/Typesetting" title="Typesetting">typesetting</a>. Muslim scientists used the <a href="/wiki/Babylonian_numerals" class="mw-redirect" title="Babylonian numerals">Babylonian numeral system</a>, and merchants used the <a href="/wiki/Abjad_numerals" title="Abjad numerals">Abjad numerals</a>, a system similar to the <a href="/wiki/Greek_numerals" title="Greek numerals">Greek numeral system</a> and the <a href="/wiki/Hebrew_numerals" title="Hebrew numerals">Hebrew numeral system</a>. Similarly, Fibonacci's introduction of the system to Europe was restricted to learned circles. The credit for first establishing widespread understanding and usage of the decimal positional notation among the general population goes to <a href="/wiki/Adam_Ries" title="Adam Ries">Adam Ries</a>, an author of the <a href="/wiki/German_Renaissance" title="German Renaissance">German Renaissance</a>, whose 1522 <i><span title="German-language text"><i lang="de">Rechenung auff der linihen und federn</i></span></i> (Calculating on the Lines and with a Quill) was targeted at the apprentices of businessmen and craftsmen. </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Gregor_Reisch,_Margarita_Philosophica,_1508_(1230x1615).png" class="mw-file-description" title="Gregor Reisch, Madame Arithmatica, 1508"><img alt="Gregor Reisch, Madame Arithmatica, 1508" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png/91px-Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png" decoding="async" width="91" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png/136px-Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png/182px-Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png 2x" data-file-width="1205" data-file-height="1591" /></a></span></div> <div class="gallerytext"><span title="German-language text"><i lang="de"><a href="/wiki/Gregor_Reisch" title="Gregor Reisch">Gregor Reisch</a></i></span>, <i><span title="Latin-language text"><i lang="la">Madame Arithmatica</i></span></i>, 1508</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Rechentisch.png" class="mw-file-description" title="A calculation table [de], used for arithmetic using Roman numerals"><img alt="A calculation table [de], used for arithmetic using Roman numerals" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Rechentisch.png/120px-Rechentisch.png" decoding="async" width="120" height="79" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Rechentisch.png/180px-Rechentisch.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Rechentisch.png/240px-Rechentisch.png 2x" data-file-width="598" data-file-height="393" /></a></span></div> <div class="gallerytext">A <a href="/w/index.php?title=Calculation_table&action=edit&redlink=1" class="new" title="Calculation table (page does not exist)">calculation table</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Rechnen_auf_Linien" class="extiw" title="de:Rechnen auf Linien">de</a>]</span>, used for arithmetic using <a href="/wiki/Roman_numerals" title="Roman numerals">Roman numerals</a></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Rechnung_auff_der_Linihen_und_Federn.JPG" class="mw-file-description" title="Adam Ries, Rechenung auff der linihen und federn, 1522"><img alt="Adam Ries, Rechenung auff der linihen und federn, 1522" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Rechnung_auff_der_Linihen_und_Federn.JPG/78px-Rechnung_auff_der_Linihen_und_Federn.JPG" decoding="async" width="78" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Rechnung_auff_der_Linihen_und_Federn.JPG/118px-Rechnung_auff_der_Linihen_und_Federn.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Rechnung_auff_der_Linihen_und_Federn.JPG/157px-Rechnung_auff_der_Linihen_und_Federn.JPG 2x" data-file-width="232" data-file-height="354" /></a></span></div> <div class="gallerytext"><span title="German-language text"><i lang="de"><a href="/wiki/Adam_Ries" title="Adam Ries">Adam Ries</a></i></span>, <i><span title="German-language text"><i lang="de">Rechenung auff der linihen und federn</i></span></i>, 1522</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:K%C3%B6bel_B%C3%B6schenteyn_1514.jpg" class="mw-file-description" title="Two arithmetic books published in 1514 – Köbel (left) using a calculation table and Böschenteyn using numerals"><img alt="Two arithmetic books published in 1514 – Köbel (left) using a calculation table and Böschenteyn using numerals" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/K%C3%B6bel_B%C3%B6schenteyn_1514.jpg/120px-K%C3%B6bel_B%C3%B6schenteyn_1514.jpg" decoding="async" width="120" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/K%C3%B6bel_B%C3%B6schenteyn_1514.jpg/180px-K%C3%B6bel_B%C3%B6schenteyn_1514.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/K%C3%B6bel_B%C3%B6schenteyn_1514.jpg/240px-K%C3%B6bel_B%C3%B6schenteyn_1514.jpg 2x" data-file-width="645" data-file-height="478" /></a></span></div> <div class="gallerytext">Two arithmetic books published in 1514 – <span title="German-language text"><i lang="de">Köbel</i></span> (left) using a calculation table and <span title="German-language text"><i lang="de">Böschenteyn</i></span> using numerals</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Rechnung_auff_der_linihen_1525_Adam_Ries.PNG" class="mw-file-description" title="Adam Ries, Rechenung auff der linihen und federn (2nd Ed.), 1525"><img alt="Adam Ries, Rechenung auff der linihen und federn (2nd Ed.), 1525" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Rechnung_auff_der_linihen_1525_Adam_Ries.PNG/88px-Rechnung_auff_der_linihen_1525_Adam_Ries.PNG" decoding="async" width="88" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Rechnung_auff_der_linihen_1525_Adam_Ries.PNG/132px-Rechnung_auff_der_linihen_1525_Adam_Ries.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Rechnung_auff_der_linihen_1525_Adam_Ries.PNG/176px-Rechnung_auff_der_linihen_1525_Adam_Ries.PNG 2x" data-file-width="331" data-file-height="450" /></a></span></div> <div class="gallerytext"><span title="German-language text"><i lang="de"><a href="/wiki/Adam_Ries" title="Adam Ries">Adam Ries</a></i></span>, <i><span title="German-language text"><i lang="de">Rechenung auff der linihen und federn</i></span></i> (2nd Ed.), 1525</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:1543_Robert_Recorde.PNG" class="mw-file-description" title="Robert Recorde, The ground of artes, 1543"><img alt="Robert Recorde, The ground of artes, 1543" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/1543_Robert_Recorde.PNG/120px-1543_Robert_Recorde.PNG" decoding="async" width="120" height="88" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/1543_Robert_Recorde.PNG/180px-1543_Robert_Recorde.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/1543_Robert_Recorde.PNG/240px-1543_Robert_Recorde.PNG 2x" data-file-width="444" data-file-height="324" /></a></span></div> <div class="gallerytext"><a href="/wiki/Robert_Recorde" title="Robert Recorde">Robert Recorde</a>, <i>The ground of artes</i>, 1543</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Peter_Apian_1544.PNG" class="mw-file-description" title="Peter Apian, Kaufmanns Rechnung, 1527"><img alt="Peter Apian, Kaufmanns Rechnung, 1527" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Peter_Apian_1544.PNG/120px-Peter_Apian_1544.PNG" decoding="async" width="120" height="61" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Peter_Apian_1544.PNG/180px-Peter_Apian_1544.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Peter_Apian_1544.PNG/240px-Peter_Apian_1544.PNG 2x" data-file-width="859" data-file-height="435" /></a></span></div> <div class="gallerytext"><span title="German-language text"><i lang="de"><a href="/wiki/Petrus_Apianus" title="Petrus Apianus">Peter Apian</a></i></span>, <i><span title="German-language text"><i lang="de">Kaufmanns Rechnung</i></span></i>, 1527</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Adam_riesen.jpg" class="mw-file-description" title="Adam Ries, Rechenung auff der linihen und federn (2nd Ed.), 1525"><img alt="Adam Ries, Rechenung auff der linihen und federn (2nd Ed.), 1525" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Adam_riesen.jpg/75px-Adam_riesen.jpg" decoding="async" width="75" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Adam_riesen.jpg/112px-Adam_riesen.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Adam_riesen.jpg/150px-Adam_riesen.jpg 2x" data-file-width="702" data-file-height="1123" /></a></span></div> <div class="gallerytext"><span title="German-language text"><i lang="de"><a href="/wiki/Adam_Ries" title="Adam Ries">Adam Ries</a></i></span>, <i><span title="German-language text"><i lang="de">Rechenung auff der linihen und federn</i></span></i> (2nd Ed.), 1525</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Adoption_in_East_Asia">Adoption in East Asia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=10" title="Edit section: Adoption in East Asia"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In AD 690, <a href="/wiki/Wu_Zetian" title="Wu Zetian">Empress Wu</a> promulgated <a href="/wiki/Chinese_characters_of_Empress_Wu" title="Chinese characters of Empress Wu">Zetian characters</a>, one of which was "〇". The word is now used as a synonym for the number zero. </p><p>In <a href="/wiki/China" title="China">China</a>, <a href="/wiki/Gautama_Siddha" title="Gautama Siddha">Gautama Siddha</a> introduced Hindu numerals with zero in 718, but <a href="/wiki/Chinese_mathematics" title="Chinese mathematics">Chinese mathematicians</a> did not find them useful, as they had already had the decimal positional <a href="/wiki/Counting_rods" title="Counting rods">counting rods</a>.<sup id="cite_ref-qian_24-0" class="reference"><a href="#cite_note-qian-24"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p>In Chinese numerals, a circle (〇) is used to write zero in <a href="/wiki/Suzhou_numerals" title="Suzhou numerals">Suzhou numerals</a>. Many historians think it was imported from <a href="/wiki/Indian_numerals" class="mw-redirect" title="Indian numerals">Indian numerals</a> by <a href="/wiki/Gautama_Siddha" title="Gautama Siddha">Gautama Siddha</a> in 718, but some Chinese scholars think it was created from the Chinese text space filler "□".<sup id="cite_ref-qian_24-1" class="reference"><a href="#cite_note-qian-24"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>Chinese and <a href="/wiki/Japan" title="Japan">Japanese</a> finally adopted the Hindu–Arabic numerals in the 19th century, abandoning counting rods. </p> <div class="mw-heading mw-heading3"><h3 id="Spread_of_the_Western_Arabic_variant">Spread of the Western Arabic variant</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=11" title="Edit section: Spread of the Western Arabic variant"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The "Western Arabic" numerals as they were in common use in Europe since the <a href="/wiki/Baroque" title="Baroque">Baroque</a> period have secondarily found worldwide use together with the <a href="/wiki/Latin_alphabet" title="Latin alphabet">Latin alphabet</a>, and even significantly beyond the contemporary <a href="/wiki/Spread_of_the_Latin_alphabet" class="mw-redirect" title="Spread of the Latin alphabet">spread of the Latin alphabet</a>, intruding into the writing systems in regions where other variants of the Hindu–Arabic numerals had been in use, but also in conjunction with <a href="/wiki/Chinese_script" class="mw-redirect" title="Chinese script">Chinese</a> and <a href="/wiki/Japanese_script" class="mw-redirect" title="Japanese script">Japanese</a> writing (see <a href="/wiki/Chinese_numerals" title="Chinese numerals">Chinese numerals</a>, <a href="/wiki/Japanese_numerals" title="Japanese numerals">Japanese numerals</a>). </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/History_of_mathematics" title="History of mathematics">History of mathematics</a></li> <li><a href="/wiki/Numeral_system" title="Numeral system">Numeral system</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=13" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a href="/wiki/Hindustan" title="Hindustan">Hindu</a> was the Persian name for "Indian" in the 10th century, when the Arabs adopted the number system. The use of "<a href="/wiki/Hinduism" title="Hinduism">Hindu</a>" to refer to a religion was a later development.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">6 is 륙 in North Korea.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-booksmith-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-booksmith_1-0">^</a></b></span> <span class="reference-text"><a href="/w/index.php?title=Audun_Holme&action=edit&redlink=1" class="new" title="Audun Holme (page does not exist)">Audun Holme</a>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=zXwQGo8jyHUC&dq=%22indo+arabic+numeral+system%22&pg=PA188">Geometry: Our Cultural Heritage</a>, 2000</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFWilliam_Darrach_Halsey,_Emanuel_Friedman1983" class="citation book cs1">William Darrach Halsey, Emanuel Friedman (1983). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=uIgxAQAAIAAJ&q=%22empire+was+expanding+and+contact+was+made+with+India%22"><i>Collier's Encyclopedia, with bibliography and index</i></a>. <q>When the Arabian empire was expanding and contact was made with India, the Hindu numeral system and the early algorithms were adopted by the Arabs</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Collier%27s+Encyclopedia%2C+with+bibliography+and+index&rft.date=1983&rft.au=William+Darrach+Halsey%2C+Emanuel+Friedman&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DuIgxAQAAIAAJ%26q%3D%2522empire%2Bwas%2Bexpanding%2Band%2Bcontact%2Bwas%2Bmade%2Bwith%2BIndia%2522&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Brezina2006-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Brezina2006_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrezina2006" class="citation cs2">Brezina, Corona (2006), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3Sfrxde0CXIC&pg=PA39"><i>Al-Khwarizmi: The Inventor of Algebra</i></a>, The Rosen Publishing Group, pp. 39–40, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4042-0513-0" title="Special:BookSources/978-1-4042-0513-0"><bdi>978-1-4042-0513-0</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Al-Khwarizmi%3A+The+Inventor+of+Algebra&rft.pages=39-40&rft.pub=The+Rosen+Publishing+Group&rft.date=2006&rft.isbn=978-1-4042-0513-0&rft.aulast=Brezina&rft.aufirst=Corona&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D3Sfrxde0CXIC%26pg%3DPA39&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Danna_2021_pp._5–48-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Danna_2021_pp._5–48_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDanna2021" class="citation journal cs1">Danna, Raffaele (13 Jan 2021). <a rel="nofollow" class="external text" href="https://doi.org/10.1163%2F18253911-bja10004">"Figuring Out: The Spread of Hindu-Arabic Numerals in the European Tradition of Practical Mathematics (13th–16th Centuries)"</a>. <i>Nuncius</i>. <b>36</b> (1): 5–48. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1163%2F18253911-bja10004">10.1163/18253911-bja10004</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0394-7394">0394-7394</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nuncius&rft.atitle=Figuring+Out%3A+The+Spread+of+Hindu-Arabic+Numerals+in+the+European+Tradition+of+Practical+Mathematics+%2813th%E2%80%9316th+Centuries%29&rft.volume=36&rft.issue=1&rft.pages=5-48&rft.date=2021-01-13&rft_id=info%3Adoi%2F10.1163%2F18253911-bja10004&rft.issn=0394-7394&rft.aulast=Danna&rft.aufirst=Raffaele&rft_id=https%3A%2F%2Fdoi.org%2F10.1163%252F18253911-bja10004&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEChrisomalis2010194–197-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEChrisomalis2010194–197_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFChrisomalis2010">Chrisomalis 2010</a>, pp. 194–197.</span> </li> <li id="cite_note-FOOTNOTESmithKarpinski1911[httpsarchiveorgdetailshinduarabicnumer00smitrichpage99_Ch._7,_pp.&nbsp;99–127]-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESmithKarpinski1911[httpsarchiveorgdetailshinduarabicnumer00smitrichpage99_Ch._7,_pp.&nbsp;99–127]_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSmithKarpinski1911">Smith & Karpinski 1911</a>, <a rel="nofollow" class="external text" href="https://archive.org/details/hinduarabicnumer00smitrich/page/99">Ch. 7, pp. 99–127</a>.</span> </li> <li id="cite_note-FOOTNOTESmithKarpinski1911[httpsarchiveorgdetailshinduarabicnumer00smitrichpage2_p.&nbsp;2]-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESmithKarpinski1911[httpsarchiveorgdetailshinduarabicnumer00smitrichpage2_p.&nbsp;2]_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSmithKarpinski1911">Smith & Karpinski 1911</a>, <a rel="nofollow" class="external text" href="https://archive.org/details/hinduarabicnumer00smitrich/page/2/">p. 2</a>.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Of particular note is <a href="/wiki/Johannes_de_Sacrobosco" title="Johannes de Sacrobosco">Johannes de Sacrobosco</a>'s 13th century <i>Algorismus</i>, which was extremely popular and influential. See <a href="#CITEREFSmithKarpinski1911">Smith & Karpinski 1911</a>, <a rel="nofollow" class="external text" href="https://archive.org/details/hinduarabicnumer00smitrich/page/134/">pp. 134–135</a>.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSwetz1984" class="citation book cs1">Swetz, Frank (1984). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PFNsm_IaymYC&pg=PA28">"The Evolution of Mathematics in Ancient China"</a>. In Campbell, Douglas M.; Higgins, John C. (eds.). <i>Mathematics: People, Problems, Results</i>. Taylor & Francis. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-534-02879-4" title="Special:BookSources/978-0-534-02879-4"><bdi>978-0-534-02879-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Evolution+of+Mathematics+in+Ancient+China&rft.btitle=Mathematics%3A+People%2C+Problems%2C+Results&rft.pub=Taylor+%26+Francis&rft.date=1984&rft.isbn=978-0-534-02879-4&rft.aulast=Swetz&rft.aufirst=Frank&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPFNsm_IaymYC%26pg%3DPA28&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLam1988" class="citation journal cs1">Lam, Lay Yong (1988). "A Chinese Genesis: Rewriting the History of Our Numeral System". <i>Archive for History of Exact Sciences</i>. <b>38</b> (2): 101–108. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00348453">10.1007/BF00348453</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41133830">41133830</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=A+Chinese+Genesis%3A+Rewriting+the+History+of+Our+Numeral+System&rft.volume=38&rft.issue=2&rft.pages=101-108&rft.date=1988&rft_id=info%3Adoi%2F10.1007%2FBF00348453&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F41133830%23id-name%3DJSTOR&rft.aulast=Lam&rft.aufirst=Lay+Yong&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span> <div class="paragraphbreak" style="margin-top:0.5em"></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLam2008" class="citation encyclopaedia cs1"><a href="/wiki/Lam_Lay_Yong" title="Lam Lay Yong">Lam, Lay Yong</a> (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=kt9DIY1g9HYC&pg=RA1-PA197">"Computation: Chinese Counting Rods"</a>. In Selin, Selaine (ed.). <i>Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-4559-2" title="Special:BookSources/978-1-4020-4559-2"><bdi>978-1-4020-4559-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Computation%3A+Chinese+Counting+Rods&rft.btitle=Encyclopaedia+of+the+History+of+Science%2C+Technology%2C+and+Medicine+in+Non-Western+Cultures&rft.pub=Springer&rft.date=2008&rft.isbn=978-1-4020-4559-2&rft.aulast=Lam&rft.aufirst=Lay+Yong&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dkt9DIY1g9HYC%26pg%3DRA1-PA197&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">In German, a number like 21 is said like "one and twenty", as though being read from right to left. In Biblical Hebrew, this is sometimes done even with larger numbers, as in Esther 1:1, which literally says, "Ahasuerus which reigned from India even unto Ethiopia, over seven and twenty and a hundred provinces".</span> </li> <li id="cite_note-FOOTNOTEFlegg1984[httpsarchiveorgdetailsnumberstheirhist0000flegpage67_p.&nbsp;67ff.]-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEFlegg1984[httpsarchiveorgdetailsnumberstheirhist0000flegpage67_p.&nbsp;67ff.]_13-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFFlegg1984">Flegg 1984</a>, <a rel="nofollow" class="external text" href="https://archive.org/details/numberstheirhist0000fleg/page/67">p. 67ff.</a>.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPearce,_Ian2002" class="citation web cs1">Pearce, Ian (May 2002). <a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/HistTopics/Bakhshali_manuscript.html">"The Bakhshali manuscript"</a>. The MacTutor History of Mathematics archive<span class="reference-accessdate">. Retrieved <span class="nowrap">2007-07-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Bakhshali+manuscript&rft.pub=The+MacTutor+History+of+Mathematics+archive&rft.date=2002-05&rft.au=Pearce%2C+Ian&rft_id=http%3A%2F%2Fwww-history.mcs.st-andrews.ac.uk%2FHistTopics%2FBakhshali_manuscript.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Ifrah, G. The Universal History of Numbers: From prehistory to the invention of the computer. John Wiley and Sons Inc., 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBill_Casselman2007" class="citation web cs1"><a href="/wiki/Bill_Casselman_(mathematician)" class="mw-redirect" title="Bill Casselman (mathematician)">Bill Casselman</a> (Feb 2007). <a rel="nofollow" class="external text" href="https://www.ams.org/featurecolumn/archive/india-zero.html">"All for Nought"</a>. <i>Feature Column</i>. AMS.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Feature+Column&rft.atitle=All+for+Nought&rft.date=2007-02&rft.au=Bill+Casselman&rft_id=https%3A%2F%2Fwww.ams.org%2Ffeaturecolumn%2Farchive%2Findia-zero.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><a href="/wiki/Al-Qifti" title="Al-Qifti">al-Qifti</a>'s <i>Chronology of the scholars</i> (early 13th century): <dl><dd><i>... a person from India presented himself before the <a href="/wiki/Caliph" class="mw-redirect" title="Caliph">Caliph</a> <a href="/wiki/Al-Mansur" title="Al-Mansur">al-Mansur</a> in the year 776 who was well versed in the siddhanta method of calculation related to the movement of the heavenly bodies, and having ways of calculating equations based on the half-chord [essentially the sine] calculated in half-degrees ... Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets ...</i></dd></dl> </span></li> <li id="cite_note-Berggren-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Berggren_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBerggren2007" class="citation book cs1">Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". In Katz, Victor J. (ed.). <i>The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook</i>. Princeton University Press. p. 530. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-11485-9" title="Special:BookSources/978-0-691-11485-9"><bdi>978-0-691-11485-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Mathematics+in+Medieval+Islam&rft.btitle=The+Mathematics+of+Egypt%2C+Mesopotamia%2C+China%2C+India%2C+and+Islam%3A+A+Sourcebook&rft.pages=530&rft.pub=Princeton+University+Press&rft.date=2007&rft.isbn=978-0-691-11485-9&rft.aulast=Berggren&rft.aufirst=J.+Lennart&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBerggren2017" class="citation book cs1">Berggren, J. L. (18 Jan 2017). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=I-jwDQAAQBAJ&dq=However%2C+the+Hindus+did+not+extend+this+system+to+represent+parts+of+the+unit+by&pg=PA30"><i>Episodes in the Mathematics of Medieval Islam</i></a>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4939-3780-6" title="Special:BookSources/978-1-4939-3780-6"><bdi>978-1-4939-3780-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Episodes+in+the+Mathematics+of+Medieval+Islam&rft.pub=Springer&rft.date=2017-01-18&rft.isbn=978-1-4939-3780-6&rft.aulast=Berggren&rft.aufirst=J.+L.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DI-jwDQAAQBAJ%26dq%3DHowever%252C%2Bthe%2BHindus%2Bdid%2Bnot%2Bextend%2Bthis%2Bsystem%2Bto%2Brepresent%2Bparts%2Bof%2Bthe%2Bunit%2Bby%26pg%3DPA30&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Berggrenn-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-Berggrenn_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBerggren2007" class="citation book cs1">Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". <i>The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook</i>. Princeton University Press. p. 518. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-11485-9" title="Special:BookSources/978-0-691-11485-9"><bdi>978-0-691-11485-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Mathematics+in+Medieval+Islam&rft.btitle=The+Mathematics+of+Egypt%2C+Mesopotamia%2C+China%2C+India%2C+and+Islam%3A+A+Sourcebook&rft.pages=518&rft.pub=Princeton+University+Press&rft.date=2007&rft.isbn=978-0-691-11485-9&rft.aulast=Berggren&rft.aufirst=J.+Lennart&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIbn_Labbān1965" class="citation book cs1"><a href="/wiki/Kushyar_Gilani" title="Kushyar Gilani">Ibn Labbān, Kūshyār</a> (1965). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/kushyaribnlabban0000mart/page/n5"><i>Kitab fi usul hisab al-hind</i></a></span> [<i><a href="/wiki/Principles_of_Hindu_Reckoning" title="Principles of Hindu Reckoning">Principles of Hindu Reckoning</a></i>]. Translated by <a href="/w/index.php?title=Martin_Levey&action=edit&redlink=1" class="new" title="Martin Levey (page does not exist)">Levey, Martin</a>; Petruck, Marvin. Madison: University of Wisconsin Press. p. 3. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/65012106">65012106</a>. <a href="/wiki/OL_(identifier)" class="mw-redirect" title="OL (identifier)">OL</a> <a rel="nofollow" class="external text" href="https://openlibrary.org/books/OL5941486M">5941486M</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Kitab+fi+usul+hisab+al-hind&rft.place=Madison&rft.pages=3&rft.pub=University+of+Wisconsin+Press&rft.date=1965&rft_id=https%3A%2F%2Fopenlibrary.org%2Fbooks%2FOL5941486M%23id-name%3DOL&rft_id=info%3Alccn%2F65012106&rft.aulast=Ibn+Labb%C4%81n&rft.aufirst=K%C5%ABshy%C4%81r&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fkushyaribnlabban0000mart%2Fpage%2Fn5&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.halexandria.org/dward093.htm">"Fibonacci Numbers"</a>. <i>www.halexandria.org</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.halexandria.org&rft.atitle=Fibonacci+Numbers&rft_id=http%3A%2F%2Fwww.halexandria.org%2Fdward093.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">H<a rel="nofollow" class="external text" href="https://www.britannica.com/eb/article-4153/Leonardo-Pisano">Leonardo Pisano: "Contributions to number theory"</a>. <a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Encyclopædia Britannica</a> Online, 2006. p. 3. Retrieved 18 September 2006.</span> </li> <li id="cite_note-qian-24"><span class="mw-cite-backlink">^ <a href="#cite_ref-qian_24-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-qian_24-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFQian1964" class="citation cs2">Qian, Baocong (1964), <i>Zhongguo Shuxue Shi (The history of Chinese mathematics)</i>, Beijing: Kexue Chubanshe</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Zhongguo+Shuxue+Shi+%28The+history+of+Chinese+mathematics%29&rft.place=Beijing&rft.pub=Kexue+Chubanshe&rft.date=1964&rft.aulast=Qian&rft.aufirst=Baocong&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWáng1999" class="citation cs2">Wáng, Qīngxiáng (1999), <i>Sangi o koeta otoko (The man who exceeded counting rods)</i>, Tokyo: Tōyō Shoten, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/4-88595-226-3" title="Special:BookSources/4-88595-226-3"><bdi>4-88595-226-3</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sangi+o+koeta+otoko+%28The+man+who+exceeded+counting+rods%29&rft.place=Tokyo&rft.pub=T%C5%8Dy%C5%8D+Shoten&rft.date=1999&rft.isbn=4-88595-226-3&rft.aulast=W%C3%A1ng&rft.aufirst=Q%C4%ABngxi%C3%A1ng&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=15" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChrisomalis2010" class="citation book cs1">Chrisomalis, Stephen (2010). <i>Numerical Notation: A Comparative History</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-87818-0" title="Special:BookSources/978-0-521-87818-0"><bdi>978-0-521-87818-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numerical+Notation%3A+A+Comparative+History&rft.pub=Cambridge+University+Press&rft.date=2010&rft.isbn=978-0-521-87818-0&rft.aulast=Chrisomalis&rft.aufirst=Stephen&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFlegg1984" class="citation book cs1">Flegg, Graham (1984). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/numberstheirhist0000fleg"><i>Numbers: Their History and Meaning</i></a></span>. Penguin. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-14-022564-8" title="Special:BookSources/978-0-14-022564-8"><bdi>978-0-14-022564-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Numbers%3A+Their+History+and+Meaning&rft.pub=Penguin&rft.date=1984&rft.isbn=978-0-14-022564-8&rft.aulast=Flegg&rft.aufirst=Graham&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnumberstheirhist0000fleg&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson2001" class="citation cs1">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a> (2001). <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/HistTopics/Arabic_numerals.html">"The Arabic numeral system"</a>. <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>. <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Arabic+numeral+system&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.date=2001&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FHistTopics%2FArabic_numerals.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson2000" class="citation cs1">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a> (2000). <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/HistTopics/Indian_numerals.html">"Indian numerals"</a>. <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>. <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Indian+numerals&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.date=2000&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FHistTopics%2FIndian_numerals.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmithKarpinski1911" class="citation book cs1"><a href="/wiki/David_Eugene_Smith" title="David Eugene Smith">Smith, David Eugene</a>; <a href="/wiki/Louis_Charles_Karpinski" title="Louis Charles Karpinski">Karpinski, Louis Charles</a> (1911). <a rel="nofollow" class="external text" href="https://archive.org/details/hinduarabicnumer00smitrich"><i>The Hindu–Arabic Numerals</i></a>. Boston: Ginn.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Hindu%E2%80%93Arabic+Numerals&rft.place=Boston&rft.pub=Ginn&rft.date=1911&rft.aulast=Smith&rft.aufirst=David+Eugene&rft.au=Karpinski%2C+Louis+Charles&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhinduarabicnumer00smitrich&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hindu%E2%80%93Arabic_numeral_system&action=edit&section=16" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMenninger1969" class="citation book cs1">Menninger, Karl W. (1969). <i>Number Words and Number Symbols: A Cultural History of Numbers</i>. MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-13040-8" title="Special:BookSources/0-262-13040-8"><bdi>0-262-13040-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Number+Words+and+Number+Symbols%3A+A+Cultural+History+of+Numbers&rft.pub=MIT+Press&rft.date=1969&rft.isbn=0-262-13040-8&rft.aulast=Menninger&rft.aufirst=Karl+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHindu%E2%80%93Arabic+numeral+system" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://digital.nls.uk/early-gaelic-book-collections/pageturner.cfm?id=77845307">On the genealogy of modern numerals</a> by Edward Clive Bayley</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output 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of writing systems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:List_of_writing_systems" title="Special:EditPage/Template:List of writing systems"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Types_of_writing_systems" style="font-size:114%;margin:0 4em"><a href="/wiki/List_of_writing_systems" title="List of writing systems">Types</a> of <a href="/wiki/Writing_system" title="Writing system">writing systems</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10em">Overview</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/History_of_writing" title="History of writing">History of writing</a></li> <li><a href="/wiki/Grapheme" title="Grapheme">Grapheme</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10em">Lists</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_writing_systems" title="List of writing systems">Writing systems</a> <ul><li><a href="/wiki/Undeciphered_writing_systems" title="Undeciphered writing systems">undeciphered</a></li> <li><a href="/wiki/List_of_creators_of_writing_systems" title="List of creators of writing systems">inventors</a></li> <li><a href="/wiki/List_of_constructed_scripts" title="List of constructed scripts">constructed</a></li></ul></li> <li>Languages by writing system / <a href="/wiki/List_of_languages_by_first_written_accounts" class="mw-redirect" title="List of languages by first written accounts">by first written accounts</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible expanded navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Types" style="font-size:114%;margin:0 4em"><a href="/wiki/List_of_writing_systems" title="List of writing systems">Types</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Abjads" style="font-size:114%;margin:0 4em"><a href="/wiki/Abjad" title="Abjad">Abjads</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Abjad_numerals" title="Abjad numerals">Numerals</a></i></li></ul> <ul><li><a href="/wiki/Aramaic_alphabet" title="Aramaic alphabet">Aramaic</a> <ul><li><a href="/wiki/Hatran_alphabet" class="mw-redirect" title="Hatran alphabet">Hatran</a></li></ul></li> <li><a href="/wiki/Arabic_script" title="Arabic script">Arabic</a> <ul><li><a href="/wiki/Elifba_alphabet" title="Elifba alphabet">Elifba</a></li></ul></li> <li><a href="/wiki/Egyptian_hieroglyphs" title="Egyptian hieroglyphs">Egyptian hieroglyphs</a></li> <li><a href="/wiki/Elymaic" title="Elymaic">Elymaic</a></li> <li><a href="/wiki/Hebrew_alphabet" title="Hebrew alphabet">Hebrew</a> <ul><li><a href="/wiki/Ktav_Ashuri" title="Ktav Ashuri">Ashuri</a></li> <li><a href="/wiki/Cursive_Hebrew" title="Cursive Hebrew">Cursive</a></li> <li><a href="/wiki/Rashi_script" title="Rashi script">Rashi</a></li> <li><a href="/wiki/Solitreo" title="Solitreo">Solitreo</a></li></ul></li> <li><a href="/wiki/Tifinagh" title="Tifinagh">Tifinagh</a></li> <li><a href="/wiki/Mandaic_alphabet" title="Mandaic alphabet">Mandaic</a></li> <li><a href="/wiki/Manichaean_script" title="Manichaean script">Manichaean</a></li> <li><a href="/wiki/Nabataean_script" title="Nabataean script">Nabataean</a></li> <li><a href="/wiki/Ancient_North_Arabian" title="Ancient North Arabian">Ancient North Arabian</a></li> <li><a href="/wiki/Pahlavi_scripts" title="Pahlavi scripts">Pahlavi</a> <ul><li><a href="/wiki/Book_Pahlavi" class="mw-redirect" title="Book Pahlavi">Book</a></li> <li><a href="/wiki/Inscriptional_Pahlavi" title="Inscriptional Pahlavi">Inscriptional</a></li> <li><a href="/wiki/Inscriptional_Parthian" title="Inscriptional Parthian">Inscriptional Parthian</a></li> <li><a href="/wiki/Psalter_Pahlavi" title="Psalter Pahlavi">Psalter</a></li></ul></li> <li><a href="/wiki/Pegon_script" title="Pegon script">Pegon</a></li> <li><a href="/wiki/Phoenician_alphabet" title="Phoenician alphabet">Phoenician</a> <ul><li><a href="/wiki/Paleo-Hebrew_alphabet" title="Paleo-Hebrew alphabet">Paleo-Hebrew</a></li></ul></li> <li><a href="/wiki/Pitman_shorthand" title="Pitman shorthand">Pitman shorthand</a></li> <li><a href="/wiki/Proto-Sinaitic_script" title="Proto-Sinaitic script">Proto-Sinaitic</a></li> <li><a href="/wiki/Punic_alphabet" class="mw-redirect" title="Punic alphabet">Punic</a></li> <li><a href="/wiki/Samaritan_script" title="Samaritan script">Samaritan</a></li> <li><a href="/wiki/Ancient_South_Arabian_script" title="Ancient South Arabian script">South Arabian</a> <ul><li><a href="/wiki/Ancient_South_Arabian_script#Zabur_script" title="Ancient South Arabian script">Zabur</a></li> <li><a href="/wiki/Ancient_South_Arabian_script#Musnad" title="Ancient South Arabian script">Musnad</a></li></ul></li> <li><a href="/wiki/Sogdian_alphabet" title="Sogdian alphabet">Sogdian</a></li> <li><a href="/wiki/Syriac_alphabet" title="Syriac alphabet">Syriac</a> <ul><li><a href="/wiki/Syriac_alphabet#Classical_ʾEsṭrangēlā" title="Syriac alphabet">ʾEsṭrangēlā</a></li> <li><a href="/wiki/Syriac_alphabet#West_Syriac_Serṭā" title="Syriac alphabet">Serṭā</a></li> <li><a href="/wiki/Syriac_alphabet#East_Syriac_Maḏnḥāyā" title="Syriac alphabet">Maḏnḥāyā</a></li></ul></li> <li><a href="/wiki/Teeline_Shorthand" class="mw-redirect" title="Teeline Shorthand">Teeline Shorthand</a></li> <li><a href="/wiki/Ugaritic_alphabet" title="Ugaritic alphabet">Ugaritic</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Abugidas" style="font-size:114%;margin:0 4em"><a href="/wiki/Abugida" title="Abugida">Abugidas</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:5em"><a href="/wiki/Brahmic_scripts" title="Brahmic scripts">Brahmic</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:5em">Northern</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bengali%E2%80%93Assamese_script" title="Bengali–Assamese script">Bengali–Assamese</a></li> <li><a href="/wiki/Bhaiksuki_script" title="Bhaiksuki script">Bhaiksuki</a></li> <li><a href="/wiki/Brahmi_script" title="Brahmi script">Brahmi script</a></li> <li><a href="/wiki/Devanagari" title="Devanagari">Devanagari</a></li> <li><a href="/wiki/Dogri_script" title="Dogri script">Dogri</a></li> <li><a href="/wiki/Gujarati_script" title="Gujarati script">Gujarati</a></li> <li><a href="/wiki/Gupta_script" title="Gupta script">Gupta</a></li> <li><a href="/wiki/Gurmukhi" title="Gurmukhi">Gurmukhi</a></li> <li><a href="/wiki/Kaithi" title="Kaithi">Kaithi</a></li> <li><a href="/wiki/Kalinga_script" title="Kalinga script">Kalinga</a></li> <li><a href="/wiki/Khema_script" title="Khema script">Khema</a></li> <li><a href="/wiki/Khojki_script" title="Khojki script">Khojki</a></li> <li><a href="/wiki/Khudabadi_script" title="Khudabadi script">Khudabadi</a></li> <li><a href="/wiki/La%E1%B9%87%E1%B8%8D%C4%81_scripts" title="Laṇḍā scripts">Laṇḍā</a></li> <li><a href="/wiki/Lepcha_script" title="Lepcha script">Lepcha</a></li> <li><a href="/wiki/Mahajani" title="Mahajani">Mahajani</a></li> <li><a href="/wiki/Marchen_script" title="Marchen script">Marchen</a></li> <li><a href="/wiki/Meitei_script" title="Meitei script">Meitei</a></li> <li><a href="/wiki/Modi_script" title="Modi script">Modi</a></li> <li><a href="/wiki/Multani_script" title="Multani script">Multani</a></li> <li><a href="/wiki/N%C4%81gar%C4%AB_script" title="Nāgarī script">Nagari</a></li> <li><a href="/wiki/Nandinagari" title="Nandinagari">Nandinagari</a></li> <li><a href="/wiki/Nepalese_scripts" title="Nepalese scripts">Nepalese scripts</a> <ul><li><a href="/wiki/Bhujimol_script" title="Bhujimol script">Bhujimol</a></li> <li><a href="/w/index.php?title=Golmol_script&action=edit&redlink=1" class="new" title="Golmol script (page does not exist)">Golmol</a></li> <li><a href="/w/index.php?title=Himmol_script&action=edit&redlink=1" class="new" title="Himmol script (page does not exist)">Himmol</a></li> <li><a href="/w/index.php?title=Kummol_script&action=edit&redlink=1" class="new" title="Kummol script (page does not exist)">Kummol</a></li> <li><a href="/w/index.php?title=Kvemmol_script&action=edit&redlink=1" class="new" title="Kvemmol script (page does not exist)">Kvemmol</a></li> <li><a href="/w/index.php?title=Pachumol_script&action=edit&redlink=1" class="new" title="Pachumol script (page does not exist)">Pachumol</a></li> <li><a href="/wiki/Pracalit_script" title="Pracalit script">Pracalit</a></li> <li><a href="/wiki/Ranjana_script" title="Ranjana script">Ranjana</a></li> <li><a href="/wiki/Tamyig_script" class="mw-redirect" title="Tamyig script">Tamyig</a></li> <li><a href="/wiki/Tirhuta_script" title="Tirhuta script">Tirhuta</a></li> <li><a href="/wiki/Limbu_script" title="Limbu script">Limbu</a></li> <li><a href="/wiki/Nepalese_scripts" title="Nepalese scripts">Litumol</a></li></ul></li> <li><a href="/wiki/Odia_script" title="Odia script">Odia</a> <ul><li><a href="/wiki/Karani_script" title="Karani script">Karani</a></li></ul></li> <li><a href="/wiki/%CA%BCPhags-pa_script" title="ʼPhags-pa script">ʼPhags-pa</a></li> <li><a href="/wiki/Sharada_script" title="Sharada script">Sharada</a></li> <li><a href="/wiki/Siddha%E1%B9%83_script" title="Siddhaṃ script">Siddhaṃ</a></li> <li><a href="/wiki/Soyombo_script" title="Soyombo script">Soyombo</a></li> <li><a href="/wiki/Sylheti_Nagri" title="Sylheti Nagri">Sylheti Nagri</a></li> <li><a href="/wiki/Takri_script" title="Takri script">Takri</a></li> <li><a href="/wiki/Tibetan_script" title="Tibetan script">Tibetan</a> <ul><li><a href="/wiki/Uchen_script" title="Uchen script">Uchen</a></li> <li><a href="/wiki/Um%C3%AA_script" title="Umê script">Umê</a></li></ul></li> <li><a href="/wiki/Tocharian_script" title="Tocharian script">Tocharian</a></li> <li><a href="/wiki/Zanabazar_square_script" title="Zanabazar square script">Zanabazar square</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em">Southern</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ahom_script" title="Ahom script">Ahom</a></li> <li><a href="/wiki/Balinese_script" title="Balinese script">Balinese</a></li> <li><a href="/wiki/Batak_script" title="Batak script">Batak</a></li> <li><a href="/wiki/Baybayin" title="Baybayin">Baybayin</a></li> <li><a href="/wiki/Bhattiprolu_script" title="Bhattiprolu script">Bhattiprolu</a></li> <li><a href="/wiki/Buda_script" title="Buda script">Buda</a></li> <li><a href="/wiki/Buhid_script" title="Buhid script">Buhid</a></li> <li><a href="/wiki/Chakma_script" title="Chakma script">Chakma</a></li> <li><a href="/wiki/Cham_script" title="Cham script">Cham</a></li> <li><a href="/wiki/Fakkham_script" title="Fakkham script">Fakkham</a></li> <li><a href="/wiki/Grantha_script" title="Grantha script">Grantha</a></li> <li><a href="/wiki/Goykanadi" title="Goykanadi">Goykanadi</a></li> <li><a href="/wiki/Hanunoo_script" title="Hanunoo script">Hanunoo</a></li> <li><a href="/wiki/Javanese_script" title="Javanese script">Javanese</a></li> <li><a href="/wiki/Kadamba_script" title="Kadamba script">Kadamba</a></li> <li><a href="/wiki/Kannada_script" title="Kannada script">Kannada</a></li> <li><a href="/wiki/S%27gaw_Karen_alphabet" title="S'gaw Karen alphabet">Karen</a></li> <li><a href="/wiki/Kawi_script" title="Kawi script">Kawi</a></li> <li><a href="/wiki/Khmer_script" title="Khmer script">Khmer</a> <ul><li><a href="/wiki/Khom_Thai_script" title="Khom Thai script">Khom Thai</a></li></ul></li> <li><a href="/wiki/Kulitan" title="Kulitan">Kulitan</a></li> <li><a href="/wiki/Tai_Tham_script" title="Tai Tham script">Lanna</a></li> <li><a href="/wiki/Langdi" title="Langdi">Langdi</a></li> <li><a href="/wiki/Lao_script" title="Lao script">Lao</a></li> <li><a href="/wiki/Leke_script" title="Leke script">Leke</a></li> <li><a href="/wiki/Lontara_script" title="Lontara script">Lontara</a> <ul><li><a href="/wiki/Lontara_Bilang-bilang_script" title="Lontara Bilang-bilang script">Bilang-bilang</a></li></ul></li> <li><a href="/wiki/Makasar_script" title="Makasar script">Makasar</a></li> <li><a href="/wiki/Malayalam_script" title="Malayalam script">Malayalam</a></li> <li><a href="/wiki/Maldivian_writing_systems" title="Maldivian writing systems">Old Maldivian</a> <ul><li><a href="/wiki/Dhives_Akuru" title="Dhives Akuru">Dhives Akuru</a></li> <li><a href="/wiki/Eveyla_Akuru" class="mw-redirect" title="Eveyla Akuru">Eveyla Akuru</a></li></ul></li> <li><a href="/wiki/Mon%E2%80%93Burmese_script" title="Mon–Burmese script">Mon–Burmese</a></li> <li><a href="/wiki/Pallava_script" title="Pallava script">Pallava</a></li> <li><a href="/wiki/Pyu_script" title="Pyu script">Pyu</a></li> <li><a href="/wiki/Saurashtra_script" title="Saurashtra script">Saurashtra</a></li> <li><a href="/wiki/Shan_alphabet" title="Shan alphabet">Shan</a></li> <li><a href="/wiki/Sinhala_script" title="Sinhala script">Sinhala</a></li> <li><a href="/wiki/Sukhothai_script" title="Sukhothai script">Sukhothai</a></li> <li><a href="/wiki/Sundanese_script" title="Sundanese script">Sundanese</a> <ul><li><a href="/wiki/Old_Sundanese_script" title="Old Sundanese script">Old Sundanese</a></li></ul></li> <li><a href="/wiki/Tagbanwa_script" title="Tagbanwa script">Tagbanwa</a></li> <li><a href="/wiki/Tai_Le_script" title="Tai Le script">Tai Le</a></li> <li><a href="/wiki/New_Tai_Lue_alphabet" title="New Tai Lue alphabet">New Tai Lue</a></li> <li><a href="/wiki/Tai_Noi_script" title="Tai Noi script">Tai Noi</a></li> <li><a href="/wiki/Tai_Tham_script" title="Tai Tham script">Tai Tham</a></li> <li><a href="/wiki/Tai_Viet_script" title="Tai Viet script">Tai Viet</a></li> <li><a href="/wiki/Lai_Tay_script" title="Lai Tay script">Lai Tay</a></li> <li><a href="/wiki/Tamil_script" title="Tamil script">Tamil</a></li> <li><a href="/wiki/Tamil-Brahmi" title="Tamil-Brahmi">Tamil-Brahmi</a></li> <li><a href="/wiki/Tanchangya_script" title="Tanchangya script">Tanchangya</a></li> <li><a href="/wiki/Telugu_script" title="Telugu script">Telugu</a></li> <li><a href="/wiki/Thai_script" title="Thai script">Thai</a></li> <li><a href="/wiki/Tigalari_script" title="Tigalari script">Tigalari</a></li> <li><a href="/wiki/Ulu_scripts" title="Ulu scripts">Ulu scripts</a> <ul><li><a href="/w/index.php?title=Incung_script&action=edit&redlink=1" class="new" title="Incung script (page does not exist)">Incung</a></li> <li><a href="/wiki/Lampung_script" class="mw-redirect" title="Lampung script">Lampung</a></li> <li><a href="/w/index.php?title=Lembak_script&action=edit&redlink=1" class="new" title="Lembak script (page does not exist)">Lembak</a></li> <li><a href="/w/index.php?title=Ogan_script&action=edit&redlink=1" class="new" title="Ogan script (page does not exist)">Ogan</a></li> <li><a href="/w/index.php?title=Pasemah_script&action=edit&redlink=1" class="new" title="Pasemah script (page does not exist)">Pasemah</a></li> <li><a href="/wiki/Rejang_script" class="mw-redirect" title="Rejang script">Rejang</a></li> <li><a href="/w/index.php?title=Serawai_script&action=edit&redlink=1" class="new" title="Serawai script (page does not exist)">Serawai</a></li></ul></li> <li><a href="/wiki/Vatteluttu" title="Vatteluttu">Vatteluttu</a> <ul><li><a href="/wiki/Kolezhuthu" class="mw-redirect" title="Kolezhuthu">Kolezhuthu</a></li> <li><a href="/wiki/Malayanma" title="Malayanma">Malayanma</a></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:5em">Others</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bharati_script" title="Bharati script">Bharati</a></li> <li><a href="/wiki/Boyd%27s_syllabic_shorthand" title="Boyd's syllabic shorthand">Boyd's syllabic shorthand</a></li> <li><a href="/wiki/Canadian_Aboriginal_syllabics" title="Canadian Aboriginal syllabics">Canadian syllabics</a> <ul><li><a href="/wiki/Blackfoot_language#Writing_system" title="Blackfoot language">Blackfoot</a></li> <li><a href="/wiki/Carrier_syllabics" title="Carrier syllabics">Déné syllabics</a></li></ul></li> <li><a href="/wiki/Dham_script" title="Dham script">Dham</a></li> <li><a href="/wiki/Fox_language#Writing_systems" title="Fox language">Fox I</a></li> <li><a href="/wiki/Ge%CA%BDez_script" title="Geʽez script">Geʽez</a></li> <li><a href="/wiki/Gunjala_Gondi_script" title="Gunjala Gondi script">Gunjala Gondi</a></li> <li><a href="/wiki/Japanese_Braille" title="Japanese Braille">Japanese Braille</a></li> <li><a href="/wiki/Sarati" title="Sarati">Sarati</a></li> <li><a href="/wiki/Sunwar_language#Writing_Systems" title="Sunwar language">Jenticha</a></li> <li><a href="/wiki/Kharosthi" title="Kharosthi">Kharosthi</a></li> <li><a href="/wiki/Mandombe_script" title="Mandombe script">Mandombe</a></li> <li><a href="/wiki/Gondi_writing" title="Gondi writing">Masaram Gondi</a></li> <li><a href="/wiki/Meroitic_script" title="Meroitic script">Meroitic</a></li> <li><a href="/wiki/Pollard_script" title="Pollard script">Miao</a></li> <li><a href="/wiki/Mwangwego_script" title="Mwangwego script">Mwangwego</a></li> <li><a href="/wiki/Pahawh_Hmong" title="Pahawh Hmong">Pahawh Hmong</a></li> <li><a href="/wiki/Sorang_Sompeng_script" title="Sorang Sompeng script">Sorang Sompeng</a></li> <li><a href="/wiki/Tengwar" title="Tengwar">Tengwar</a></li> <li><a href="/wiki/Thaana" title="Thaana">Thaana</a></li> <li><a href="/wiki/Thomas_Natural_Shorthand" title="Thomas Natural Shorthand">Thomas Natural Shorthand</a></li> <li><a href="/wiki/Warang_Citi" title="Warang Citi">Warang Citi</a></li> <li><a href="/wiki/Mwangwego_script" title="Mwangwego script">Mwangwego</a></li> <li><a href="/wiki/Qiang_language" title="Qiang language">Rma</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Alphabets" style="font-size:114%;margin:0 4em"><a href="/wiki/Alphabet" title="Alphabet">Alphabets</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10em">Linear</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adlam_script" title="Adlam script">Adlam</a></li> <li><a href="/wiki/Ariyaka_script" title="Ariyaka script">Ariyaka</a></li> <li><a href="/wiki/Armenian_alphabet" title="Armenian alphabet">Armenian</a></li> <li><a href="/wiki/Avestan_alphabet" title="Avestan alphabet">Avestan</a> <ul><li><a href="/wiki/Pazend" title="Pazend">Pazend</a></li></ul></li> <li><a href="/wiki/Avoiuli" title="Avoiuli">Avoiuli</a></li> <li><a href="/wiki/Bassa_Vah_script" class="mw-redirect" title="Bassa Vah script">Bassa Vah</a></li> <li><a href="/wiki/Carian_alphabets" title="Carian alphabets">Carian</a></li> <li><a href="/wiki/Caucasian_Albanian_script" title="Caucasian Albanian script">Caucasian Albanian</a></li> <li><a href="/wiki/Cirth" title="Cirth">Cirth</a></li> <li><a href="/wiki/Coelbren_y_Beirdd" title="Coelbren y Beirdd">Coelbren</a></li> <li><a href="/wiki/Coorgi%E2%80%93Cox_alphabet" title="Coorgi–Cox alphabet">Coorgi–Cox alphabet</a></li> <li><a href="/wiki/Coptic_alphabet" class="mw-redirect" title="Coptic alphabet">Coptic</a></li> <li><a href="/wiki/Cyrillic_script" title="Cyrillic script">Cyrillic</a> <ul><li><a href="/wiki/Bosnian_Cyrillic" title="Bosnian Cyrillic">Bosnian</a></li> <li><a href="/wiki/Early_Cyrillic_alphabet" title="Early Cyrillic alphabet">Early</a></li></ul></li> <li><a href="/wiki/Deseret_alphabet" title="Deseret alphabet">Deseret</a></li> <li><a href="/wiki/Duployan_shorthand" title="Duployan shorthand">Duployan shorthand</a> <ul><li><a href="/wiki/Duployan_shorthand#Chinook_writing" title="Duployan shorthand">Chinook</a></li></ul></li> <li><a href="/wiki/Eclectic_shorthand" title="Eclectic shorthand">Eclectic shorthand</a></li> <li><a href="/wiki/Elbasan_script" class="mw-redirect" title="Elbasan script">Elbasan</a></li> <li><a href="/wiki/Enochian" title="Enochian">Enochian</a></li> <li><a href="/wiki/Etruscan_alphabet" title="Etruscan alphabet">Etruscan</a></li> <li><a href="/wiki/George_Psalmanazar#Pseudo-lexicographer" title="George Psalmanazar">Formosan</a></li> <li><a href="/wiki/Fox_language#Writing_systems" title="Fox language">Fox II</a></li> <li><a href="/wiki/Fraser_script" title="Fraser script">Fraser</a></li> <li><a href="/wiki/Gabelsberger_shorthand" title="Gabelsberger shorthand">Gabelsberger shorthand</a></li> <li><a href="/wiki/Gadabuursi_Somali_script" class="mw-redirect" title="Gadabuursi Somali script">Gadabuursi</a></li> <li><a href="/wiki/Garay_alphabet" title="Garay alphabet">Garay alphabet</a></li> <li><a href="/wiki/Georgian_scripts" title="Georgian scripts">Georgian</a> <ul><li><a href="/wiki/Asomtavruli" class="mw-redirect" title="Asomtavruli">Asomtavruli</a></li> <li><a href="/wiki/Nuskhuri" class="mw-redirect" title="Nuskhuri">Nuskhuri</a></li> <li><a href="/wiki/Mkhedruli" class="mw-redirect" title="Mkhedruli">Mkhedruli</a></li></ul></li> <li><a href="/wiki/Veso_Bey_alphabet" title="Veso Bey alphabet">Veso Bey</a></li> <li><a href="/wiki/Glagolitic_script" title="Glagolitic script">Glagolitic</a></li> <li><a href="/wiki/Gothic_alphabet" title="Gothic alphabet">Gothic</a></li> <li><a href="/wiki/Gregg_shorthand" title="Gregg shorthand">Gregg shorthand</a></li> <li><a href="/wiki/Greek_alphabet" title="Greek alphabet">Greek</a> (<a href="/wiki/Archaic_Greek_alphabets" title="Archaic Greek alphabets">Archaic</a>)</li> <li><a href="/wiki/Greco-Iberian_alphabet" title="Greco-Iberian alphabet">Greco-Iberian alphabet</a></li> <li><a href="/wiki/Hangul" title="Hangul">Hangul</a></li> <li><a href="/wiki/Hanifi_Rohingya_script" title="Hanifi Rohingya script">Hanifi</a></li> <li><a href="/wiki/Sunwar_language#Writing_Systems" title="Sunwar language">Jenticha</a></li> <li><a href="/wiki/Kaddare_script" class="mw-redirect" title="Kaddare script">Kaddare</a></li> <li><a href="/wiki/Kayah_Li_alphabet" title="Kayah Li alphabet">Kayah Li</a></li> <li><a href="/wiki/Klingon_scripts" title="Klingon scripts">Klingon</a></li> <li><a href="/wiki/Latin_script" title="Latin script">Latin</a> <ul><li><a href="/wiki/Beneventan_script" title="Beneventan script">Beneventan</a></li> <li><a href="/wiki/Blackletter" title="Blackletter">Blackletter</a></li> <li><a href="/wiki/Carolingian_minuscule" title="Carolingian minuscule">Carolingian minuscule</a></li> <li><a href="/wiki/Fraktur" title="Fraktur">Fraktur</a></li> <li><a href="/wiki/Gaelic_type" title="Gaelic type">Gaelic</a></li> <li><a href="/wiki/Insular_script" title="Insular script">Insular</a></li> <li><a href="/wiki/Interlac" class="mw-redirect" title="Interlac">Interlac</a></li> <li><a href="/wiki/International_Phonetic_Alphabet" title="International Phonetic Alphabet">IPA</a></li> <li><a href="/wiki/Kurrent" title="Kurrent">Kurrent</a></li> <li><a href="/wiki/Merovingian_script" title="Merovingian script">Merovingian</a></li> <li><a href="/wiki/Scribal_abbreviation" title="Scribal abbreviation">Sigla</a></li> <li><a href="/wiki/S%C3%BCtterlin" title="Sütterlin">Sütterlin</a></li> <li><a href="/wiki/Tironian_notes" title="Tironian notes">Tironian notes</a></li> <li><a href="/wiki/Visigothic_script" title="Visigothic script">Visigothic</a></li></ul></li> <li><a href="/wiki/Luo_script" title="Luo script">Luo</a></li> <li><a href="/wiki/Lycian_alphabet" title="Lycian alphabet">Lycian</a></li> <li><a href="/wiki/Lydian_alphabet" title="Lydian alphabet">Lydian</a></li> <li><a href="/wiki/Manchu_alphabet" title="Manchu alphabet">Manchu</a></li> <li><a href="/wiki/Medefaidrin" title="Medefaidrin">Medefaidrin</a></li> <li><a href="/wiki/Molodtsov_alphabet" class="mw-redirect" title="Molodtsov alphabet">Molodtsov</a></li> <li><a href="/wiki/Mru_language#Script" title="Mru language">Mru</a></li> <li><a href="/wiki/Mundari_Bani" title="Mundari Bani">Mundari Bani</a></li> <li><a href="/wiki/N%27Ko_script" title="N'Ko script">N'Ko</a></li> <li><a href="/wiki/Ogham" title="Ogham">Ogham</a></li> <li><a href="/wiki/Ol_Chiki_script" title="Ol Chiki script">Ol Chiki</a></li> <li><a href="/wiki/Old_Hungarian_script" title="Old Hungarian script">Old Hungarian</a></li> <li><a href="/wiki/Old_Italic_scripts" title="Old Italic scripts">Old Italic</a></li> <li><a href="/wiki/Old_Permic_script" title="Old Permic script">Old Permic</a></li> <li><a href="/wiki/Old_Turkic_script" title="Old Turkic script">Orkhon</a></li> <li><a href="/wiki/Old_Uyghur_alphabet" title="Old Uyghur alphabet">Old Uyghur</a> <ul><li><a href="/wiki/Mongolian_script" title="Mongolian script">Mongolian</a> <ul><li><a href="/wiki/Evenki_alphabet" class="mw-redirect" title="Evenki alphabet">Evenki</a></li> <li><a href="/wiki/Galik_alphabet" title="Galik alphabet">Galik alphabet</a></li> <li><a href="/wiki/Manchu_alphabet" title="Manchu alphabet">Manchu</a></li> <li><a href="/wiki/Clear_Script" title="Clear Script">Oirat</a></li> <li><a href="/wiki/Vagindra_script" title="Vagindra script">Vagindra</a></li></ul></li></ul></li> <li><a href="/wiki/Ol_Onal" title="Ol Onal">Ol Onal</a></li> <li><a href="/wiki/Osage_script" title="Osage script">Osage</a></li> <li><a href="/wiki/Osmanya_script" class="mw-redirect" title="Osmanya script">Osmanya</a></li> <li><a href="/wiki/Pau_Cin_Hau_script" title="Pau Cin Hau script">Pau Cin Hau</a></li> <li><a href="/wiki/Phrygian_alphabet" title="Phrygian alphabet">Phrygian</a></li> <li><a href="/wiki/Pisidian_language" title="Pisidian language">Pisidian</a></li> <li><a href="/wiki/Runes" class="mw-redirect" title="Runes">Runic</a> <ul><li><a href="/wiki/Anglo-Saxon_runes" title="Anglo-Saxon runes">Anglo-Saxon</a></li> <li><a href="/wiki/Cipher_runes" title="Cipher runes">Cipher</a></li> <li><a href="/wiki/Dalecarlian_runes" title="Dalecarlian runes">Dalecarlian</a></li> <li><a href="/wiki/Elder_Futhark" title="Elder Futhark">Elder Futhark</a></li> <li><a href="/wiki/Younger_Futhark" title="Younger Futhark">Younger Futhark</a></li> <li><a href="/wiki/Gothic_runic_inscriptions" title="Gothic runic inscriptions">Gothic</a></li> <li><a href="/wiki/Marcomannic_runes" class="mw-redirect" title="Marcomannic runes">Marcomannic</a></li> <li><a href="/wiki/Medieval_runes" title="Medieval runes">Medieval</a></li> <li><a href="/wiki/Staveless_runes" title="Staveless runes">Staveless</a></li></ul></li> <li><a href="/wiki/Shavian_alphabet" title="Shavian alphabet">Shavian</a></li> <li><a href="/wiki/Sidetic_language" title="Sidetic language">Sidetic</a></li> <li><a href="/wiki/Sorang_Sompeng_script" title="Sorang Sompeng script">Sorang Sompeng</a></li> <li><a href="/wiki/Sunuwar_alphabet" title="Sunuwar alphabet">Sunuwar</a></li> <li><a href="/wiki/Tifinagh" title="Tifinagh">Tifinagh</a></li> <li><a href="/wiki/Todhri_script" class="mw-redirect" title="Todhri script">Todhri</a></li> <li><a href="/wiki/Kurukh_language#Writing_systems" title="Kurukh language">Tolong Siki</a></li> <li><a href="/wiki/Vellara_alphabet" title="Vellara alphabet">Vellara</a></li> <li><a href="/wiki/Visible_Speech" title="Visible Speech">Visible Speech</a></li> <li><a href="/wiki/Vithkuqi_script" class="mw-redirect" title="Vithkuqi script">Vithkuqi</a></li> <li><a href="/wiki/Wancho_language#Orthography" title="Wancho language">Wancho</a></li> <li><a href="/wiki/Warang_Citi" title="Warang Citi">Warang Citi</a></li> <li><a href="/wiki/Kurdish_alphabets#Yezidi" title="Kurdish alphabets">Yezidi</a></li> <li><a href="/wiki/Zaghawa_script" class="mw-redirect" title="Zaghawa script">Zaghawa</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10em">Non-linear</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Braille" title="Braille">Braille</a></li> <li><a href="/wiki/International_maritime_signal_flags" title="International maritime signal flags">Maritime flags</a></li> <li><a href="/wiki/Telegraph_code" title="Telegraph code">Telegraph code</a></li> <li><a href="/wiki/New_York_Point" title="New York Point">New York Point</a></li> <li><a href="/wiki/Flag_semaphore" title="Flag semaphore">Flag semaphore</a></li> <li><a href="/wiki/Moon_type" title="Moon type">Moon type</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Ideograms" style="font-size:114%;margin:0 4em"><a href="/wiki/Ideogram" title="Ideogram">Ideograms</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adinkra_symbols" title="Adinkra symbols">Adinkra</a></li> <li><a href="/wiki/Aztec_script" title="Aztec script">Aztec</a></li> <li><a href="/wiki/Blissymbols" title="Blissymbols">Blissymbols</a></li> <li><a href="/wiki/Dongba_symbols" title="Dongba symbols">Dongba</a></li> <li><a href="/wiki/Ersu_Shaba_script" title="Ersu Shaba script">Ersu Shaba</a></li> <li><a href="/wiki/Emoji" title="Emoji">Emoji</a></li> <li><a href="/wiki/Isotype_(picture_language)" title="Isotype (picture language)">Isotype</a></li> <li><a href="/wiki/Kaid%C4%81_glyphs" title="Kaidā glyphs">Kaidā</a></li> <li><a href="/wiki/Mi%EA%9E%8Ckmaw_hieroglyphic_writing" class="mw-redirect" title="Miꞌkmaw hieroglyphic writing">Miꞌkmaw</a></li> <li><a href="/wiki/Mixtec_writing" title="Mixtec writing">Mixtec</a></li> <li><a href="/wiki/New_Epoch_Notation_Painting" class="mw-redirect" title="New Epoch Notation Painting">New Epoch Notation Painting</a></li> <li><a href="/wiki/Nsibidi" title="Nsibidi">Nsibidi</a></li> <li><a href="/wiki/Ojibwe_writing_systems#Ojibwe_"hieroglyphs"" title="Ojibwe writing systems">Ojibwe Hieroglyphs</a></li> <li><a href="/wiki/Olmec_hieroglyphs" title="Olmec hieroglyphs">Olmec</a></li> <li><a href="/wiki/Siglas_poveiras" title="Siglas poveiras">Siglas poveiras</a></li> <li><a href="/wiki/Testerian" title="Testerian">Testerian</a></li> <li><a href="/wiki/Yerkish" title="Yerkish">Yerkish</a></li> <li><a href="/wiki/Zapotec_script" title="Zapotec script">Zapotec</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Logograms" style="font-size:114%;margin:0 4em"><a href="/wiki/Logogram" title="Logogram">Logograms</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10em"><a href="/wiki/Chinese_family_of_scripts" title="Chinese family of scripts">Chinese family of scripts</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10em"><a href="/wiki/Chinese_characters" title="Chinese characters">Chinese characters</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Simplified_Chinese_characters" title="Simplified Chinese characters">Simplified</a></li> <li><a href="/wiki/Traditional_Chinese_characters" title="Traditional Chinese characters">Traditional</a></li> <li><a href="/wiki/Oracle_bone_script" title="Oracle bone script">Oracle bone script</a></li> <li><a href="/wiki/Chinese_bronze_inscriptions" title="Chinese bronze inscriptions">Bronze scripts</a></li> <li><a href="/wiki/Seal_script" title="Seal script">Seal script</a> <ul><li><a href="/wiki/Large_seal_script" title="Large seal script">large</a></li> <li><a href="/wiki/Small_seal_script" title="Small seal script">small</a></li> <li><a href="/wiki/Bird-worm_seal_script" title="Bird-worm seal script">bird-worm</a></li></ul></li> <li><a href="/wiki/Hanja" title="Hanja">Hanja</a></li> <li><a href="/wiki/Kanji" title="Kanji">Kanji</a></li> <li><a href="/wiki/Ch%E1%BB%AF_N%C3%B4m" title="Chữ Nôm">Chữ Nôm</a></li> <li><a href="/wiki/Sawndip" title="Sawndip">Sawndip</a></li> <li><a href="/wiki/Bowen_script" class="mw-redirect" title="Bowen script">Bowen</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10em">Chinese-influenced</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jurchen_script" title="Jurchen script">Jurchen</a></li> <li><a href="/wiki/Khitan_large_script" title="Khitan large script">Khitan large script</a></li> <li><a href="/wiki/Sui_script" title="Sui script">Sui</a></li> <li><a href="/wiki/Tangut_script" title="Tangut script">Tangut</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:10em"><a href="/wiki/Cuneiform" title="Cuneiform">Cuneiform</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Akkadian_cuneiform" class="mw-redirect" title="Akkadian cuneiform">Akkadian</a></li> <li><a href="/wiki/Assyrian_cuneiform" class="mw-redirect" title="Assyrian cuneiform">Assyrian</a></li> <li><a href="/wiki/Elamite_cuneiform" title="Elamite cuneiform">Elamite</a></li> <li><a href="/wiki/Hittite_cuneiform" title="Hittite cuneiform">Hittite</a></li> <li><a href="/wiki/Cuneiform_Luwian" class="mw-redirect" title="Cuneiform Luwian">Luwian</a></li> <li><a href="/wiki/Cuneiform" title="Cuneiform">Sumerian</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10em">Other logosyllabic</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anatolian_hieroglyphs" title="Anatolian hieroglyphs">Anatolian</a></li> <li><a href="/wiki/Bagam_script" title="Bagam script">Bagam</a></li> <li><a href="/wiki/Cretan_hieroglyphs" title="Cretan hieroglyphs">Cretan</a></li> <li><a href="/wiki/Isthmian_script" title="Isthmian script">Isthmian</a></li> <li><a href="/wiki/Maya_script" title="Maya script">Maya</a></li> <li><a href="/wiki/Proto-Elamite_script" title="Proto-Elamite script">Proto-Elamite</a></li> <li><a href="/wiki/Tenevil" title="Tenevil">Tenevil</a></li> <li><a href="/wiki/Yi_script#Classical_Yi" title="Yi script">Yi (Classical)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10em">Logoconsonantal</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Demotic_(Egyptian)" title="Demotic (Egyptian)">Demotic</a></li> <li><a href="/wiki/Hieratic" title="Hieratic">Hieratic</a></li> <li><a href="/wiki/Egyptian_hieroglyphs" title="Egyptian hieroglyphs">Hieroglyphs</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10em">Numerals</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Hindu-Arabic</a></li> <li><a href="/wiki/Abjad_numerals" title="Abjad numerals">Abjad</a></li> <li><a href="/wiki/Attic_numerals" title="Attic numerals">Attic (Greek)</a></li> <li><a href="/wiki/Muisca_numerals" title="Muisca numerals">Muisca</a></li> <li><a href="/wiki/Roman_numerals" title="Roman numerals">Roman</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10em">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Sitelen_Pona" title="Sitelen Pona">Sitelen Pona</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Semi-syllabaries" style="font-size:114%;margin:0 4em"><a href="/wiki/Semi-syllabaries" class="mw-redirect" title="Semi-syllabaries">Semi-syllabaries</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10em">Full</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Linear_Elamite" title="Linear Elamite">Linear Elamite</a></li> <li><a href="/wiki/Celtiberian_script" title="Celtiberian script">Celtiberian</a></li> <li><a href="/wiki/Northeastern_Iberian_script" title="Northeastern Iberian script">Northeastern Iberian</a></li> <li><a href="/wiki/Southeastern_Iberian_script" title="Southeastern Iberian script">Southeastern Iberian</a></li> <li><a href="/wiki/Khom_script_(Ong_Kommadam)" title="Khom script (Ong Kommadam)">Khom</a></li> <li><a href="/wiki/Dunging_script" title="Dunging script">Dunging</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10em">Redundant</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Espanca_script" title="Espanca script">Espanca script</a></li> <li><a href="/wiki/Pahawh_Hmong" title="Pahawh Hmong">Pahawh Hmong</a></li> <li><a href="/wiki/Khitan_small_script" title="Khitan small script">Khitan small script</a></li> <li><a href="/wiki/Southwest_Paleohispanic_script" title="Southwest Paleohispanic script">Southwest Paleohispanic</a></li> <li><a href="/wiki/Bopomofo" title="Bopomofo">Bopomofo</a></li> <li><a href="/wiki/History_of_writing_in_Vietnam#Quốc_Âm_Tân_Tự" title="History of writing in Vietnam">Quốc Âm Tân Tự</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Sign_languages" style="font-size:114%;margin:0 4em"><a href="/wiki/Sign_language" title="Sign language">Sign languages</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/ASLwrite" title="ASLwrite">ASLwrite</a></li> <li><a href="/wiki/SignWriting" title="SignWriting">SignWriting</a></li> <li><a href="/wiki/Si5s" title="Si5s">si5s</a></li> <li><a href="/wiki/Stokoe_notation" title="Stokoe notation">Stokoe notation</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Syllabaries" style="font-size:114%;margin:0 4em"><a href="/wiki/Syllabary" title="Syllabary">Syllabaries</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Afaka_syllabary" title="Afaka syllabary">Afaka</a></li> <li><a href="/wiki/Bamum_script" title="Bamum script">Bamum</a></li> <li><a href="/wiki/B%C3%A9t%C3%A9_syllabary" title="Bété syllabary">Bété</a></li> <li><a href="/wiki/Byblos_syllabary" title="Byblos syllabary">Byblos</a></li> <li><a href="/wiki/Canadian_Aboriginal_syllabics" title="Canadian Aboriginal syllabics">Canadian Aboriginal</a></li> <li><a href="/wiki/Cherokee_syllabary" title="Cherokee syllabary">Cherokee</a></li> <li><a href="/wiki/Cypriot_syllabary" title="Cypriot syllabary">Cypriot</a></li> <li><a href="/wiki/Cypro-Minoan_syllabary" title="Cypro-Minoan syllabary">Cypro-Minoan</a></li> <li><a href="/wiki/Ditema_tsa_Dinoko" title="Ditema tsa Dinoko">Ditema tsa Dinoko</a></li> <li><a href="/wiki/Eskayan_script" title="Eskayan script">Eskayan</a></li> <li><a href="/wiki/Geba_syllabary" title="Geba syllabary">Geba</a></li> <li><a href="/wiki/Great_Lakes_Algonquian_syllabics" title="Great Lakes Algonquian syllabics">Great Lakes Algonquian</a></li> <li><a href="/wiki/Iban_language#Alphabet" title="Iban language">Iban</a></li> <li><a href="/wiki/Idu_script" title="Idu script">Idu</a></li> <li><a href="/wiki/Kana" title="Kana">Kana</a> <ul><li><a href="/wiki/Hiragana" title="Hiragana">Hiragana</a></li> <li><a href="/wiki/Katakana" title="Katakana">Katakana</a></li> <li><a href="/wiki/Man%27y%C5%8Dgana" title="Man'yōgana">Man'yōgana</a></li> <li><a href="/wiki/Hentaigana" title="Hentaigana">Hentaigana</a></li> <li><a href="/wiki/S%C5%8Dgana" title="Sōgana">Sōgana</a></li> <li><a href="/wiki/Jindai_moji" title="Jindai moji">Jindai moji</a></li></ul></li> <li><a href="/wiki/Mende_Kikakui_script" title="Mende Kikakui script">Kikakui</a></li> <li><a href="/wiki/Kpelle_syllabary" title="Kpelle syllabary">Kpelle</a></li> <li><a href="/wiki/Linear_B" title="Linear B">Linear B</a></li> <li><a href="/wiki/Linear_Elamite" title="Linear Elamite">Linear Elamite</a></li> <li><a href="/wiki/Lisu_language#Lisu_syllabary" title="Lisu language">Lisu</a></li> <li><a href="/wiki/Loma_language#writing_systems" title="Loma language">Loma</a></li> <li><a href="/wiki/N%C3%BCshu" title="Nüshu">Nüshu</a></li> <li><a href="/wiki/Nwagu_Aneke_script" title="Nwagu Aneke script">Nwagu Aneke script</a></li> <li><a href="/wiki/Old_Persian_cuneiform" title="Old Persian cuneiform">Old Persian cuneiform</a></li> <li><a href="/wiki/Cuneiform" title="Cuneiform">Sumerian</a></li> <li><a href="/wiki/Vai_syllabary" title="Vai syllabary">Vai</a></li> <li><a href="/wiki/Woleai_script" title="Woleai script">Woleai</a></li> <li><a href="/wiki/Yi_script#Modern_Yi" title="Yi script">Yi</a></li> <li><a href="/wiki/Yugtun_script" title="Yugtun script">Yugtun</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible autocollapse navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Braille" title="Template:Braille"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Braille" title="Template talk:Braille"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Braille" title="Special:EditPage/Template:Braille"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Braille_⠃⠗⠁⠊⠇⠇⠑" style="font-size:114%;margin:0 4em"><a href="/wiki/Braille" title="Braille">Braille</a><span style="padding-left:0.5em;"> </span>⠃⠗⠁⠊⠇⠇⠑</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Braille cell</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/1829_braille" title="1829 braille">1829 braille</a></span></li> <li><span class="nowrap"><a href="/wiki/International_uniformity_of_braille_alphabets" title="International uniformity of braille alphabets">International uniformity</a></span></li> <li><span class="nowrap"><a href="/wiki/Braille_ASCII" title="Braille ASCII">ASCII braille</a></span></li> <li><span class="nowrap"><a href="/wiki/Braille_Patterns" title="Braille Patterns">Unicode braille patterns</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Braille scripts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:French-ordered_braille_alphabets" title="Category:French-ordered braille alphabets">French-ordered</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Albanian_Braille" title="Albanian Braille">Albanian</a></span></li> <li><span class="nowrap"><a href="/wiki/Azeri_Braille" class="mw-redirect" title="Azeri Braille">Azerbaijani</a></span></li> <li><span class="nowrap"><a href="/wiki/Cantonese_Braille" title="Cantonese Braille">Cantonese</a></span></li> <li><span class="nowrap"><a href="/wiki/Catalan_Braille" title="Catalan Braille">Catalan</a></span></li> <li><span class="nowrap"><a href="/wiki/Mainland_Chinese_Braille" title="Mainland Chinese Braille">Chinese (mainland Mandarin)</a> (largely reassigned)</span></li> <li><span class="nowrap"><a href="/wiki/Czech_Braille" title="Czech Braille">Czech</a></span></li> <li><span class="nowrap"><a href="/wiki/Dutch_Braille" title="Dutch Braille">Dutch</a></span></li> <li><span class="nowrap"><a href="/wiki/English_Braille" title="English Braille">English</a> (<a href="/wiki/Unified_English_Braille" title="Unified English Braille">Unified English</a>)</span></li> <li><span class="nowrap"><a href="/wiki/Esperanto_Braille" title="Esperanto Braille">Esperanto</a></span></li> <li><span class="nowrap"><a href="/wiki/French_Braille" title="French Braille">French</a></span></li> <li><span class="nowrap"><a href="/wiki/German_Braille" title="German Braille">German</a></span></li> <li><span class="nowrap"><a href="/wiki/Ghanaian_braille" title="Ghanaian braille">Ghanaian</a></span></li> <li><span class="nowrap"><a href="/wiki/Guarani_Braille" title="Guarani Braille">Guarani</a></span></li> <li><span class="nowrap"><a href="/wiki/Hawaiian_Braille" title="Hawaiian Braille">Hawaiian</a></span></li> <li><span class="nowrap"><a href="/wiki/Hungarian_Braille" title="Hungarian Braille">Hungarian</a></span></li> <li><span class="nowrap"><a href="/wiki/I%C3%B1upiaq_Braille" title="Iñupiaq Braille">Iñupiaq</a></span></li> <li><span class="nowrap"><a href="/wiki/IPA_Braille" title="IPA Braille">IPA</a></span></li> <li><span class="nowrap"><a href="/wiki/Irish_Braille" title="Irish Braille">Irish</a></span></li> <li><span class="nowrap"><a href="/wiki/Italian_Braille" title="Italian Braille">Italian</a></span></li> <li><span class="nowrap"><a href="/wiki/Latvian_Braille" title="Latvian Braille">Latvian</a></span></li> <li><span class="nowrap"><a href="/wiki/Lithuanian_Braille" title="Lithuanian Braille">Lithuanian</a></span></li> <li><span class="nowrap"><a href="/wiki/Luxembourgish_Braille" title="Luxembourgish Braille">Luxembourgish</a> (extended to 8-dot)</span></li> <li><span class="nowrap"><a href="/wiki/Maltese_Braille" title="Maltese Braille">Maltese</a></span></li> <li><span class="nowrap"><a href="/wiki/M%C4%81ori_Braille" title="Māori Braille">Māori</a></span></li> <li><span class="nowrap"><a href="/wiki/Navajo_Braille" title="Navajo Braille">Navajo</a></span></li> <li><span class="nowrap"><a href="/wiki/Nigerian_braille" title="Nigerian braille">Nigerian</a></span></li> <li><span class="nowrap"><a href="/wiki/Philippine_Braille" title="Philippine Braille">Philippine</a></span></li> <li><span class="nowrap"><a href="/wiki/Polish_Braille" title="Polish Braille">Polish</a></span></li> <li><span class="nowrap"><a href="/wiki/Portuguese_Braille" title="Portuguese Braille">Portuguese</a></span></li> <li><span class="nowrap"><a href="/wiki/Romanian_Braille" title="Romanian Braille">Romanian</a></span></li> <li><span class="nowrap"><a href="/wiki/Samoan_Braille" title="Samoan Braille">Samoan</a></span></li> <li><span class="nowrap"><a href="/wiki/Slovak_Braille" title="Slovak Braille">Slovak</a></span></li> <li><span class="nowrap"><a href="/wiki/South_African_braille" title="South African braille">South African</a></span></li> <li><span class="nowrap"><a href="/wiki/Spanish_Braille" title="Spanish Braille">Spanish</a></span></li> <li><span class="nowrap"><a href="/wiki/Taiwanese_Braille" title="Taiwanese Braille">Taiwanese Mandarin</a> (largely reassigned)</span></li> <li><span class="nowrap"><a href="/wiki/Turkish_Braille" title="Turkish Braille">Turkish</a></span></li> <li><span class="nowrap"><a href="/wiki/Vietnamese_Braille" title="Vietnamese Braille">Vietnamese</a></span></li> <li><span class="nowrap"><a href="/wiki/Welsh_Braille" title="Welsh Braille">Welsh</a></span></li> <li><span class="nowrap"><a href="/wiki/Yugoslav_Braille" title="Yugoslav Braille">Yugoslav</a></span></li> <li><span class="nowrap"><a href="/wiki/Zambian_Braille" title="Zambian Braille">Zambian</a></span></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Nordic family</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Estonian_Braille" title="Estonian Braille">Estonian</a></span></li> <li><span class="nowrap"><a href="/wiki/Faroese_Braille" title="Faroese Braille">Faroese</a></span></li> <li><span class="nowrap"><a href="/wiki/Icelandic_Braille" title="Icelandic Braille">Icelandic</a></span></li> <li><span class="nowrap"><a href="/wiki/Scandinavian_Braille" title="Scandinavian Braille">Scandinavian</a></span> <ul><li><span class="nowrap">Danish</span></li> <li><span class="nowrap">Finnish</span></li> <li><span class="nowrap">Greenlandic</span></li> <li><span class="nowrap"><a href="/wiki/Northern_S%C3%A1mi_Braille" title="Northern Sámi Braille">Northern Sámi</a></span></li> <li><span class="nowrap">Norwegian</span></li> <li><span class="nowrap">Swedish</span></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Russian lineage family<br />i.e. <a href="/wiki/Cyrillic_alphabets" title="Cyrillic alphabets">Cyrillic</a>-mediated scripts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Belarusian_Braille" title="Belarusian Braille">Belarusian</a></span></li> <li><span class="nowrap"><a href="/wiki/Bulgarian_Braille" title="Bulgarian Braille">Bulgarian</a></span></li> <li><span class="nowrap"><a href="/wiki/Kazakh_Braille" title="Kazakh Braille">Kazakh</a></span></li> <li><span class="nowrap"><a href="/wiki/Kyrgyz_Braille" title="Kyrgyz Braille">Kyrgyz</a></span></li> <li><span class="nowrap"><a href="/wiki/Mongolian_Braille" title="Mongolian Braille">Mongolian</a></span></li> <li><span class="nowrap"><a href="/wiki/Russian_Braille" title="Russian Braille">Russian</a></span></li> <li><span class="nowrap"><a href="/wiki/Tatar_Braille" title="Tatar Braille">Tatar</a></span></li> <li><span class="nowrap"><a href="/wiki/Ukrainian_Braille" title="Ukrainian Braille">Ukrainian</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Egyptian lineage family<br />i.e. <a href="/wiki/Arabic_script" title="Arabic script">Arabic</a>-mediated scripts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Arabic_Braille" title="Arabic Braille">Arabic</a></span></li> <li><span class="nowrap"><a href="/wiki/Persian_Braille" title="Persian Braille">Persian</a></span></li> <li><span class="nowrap"><a href="/wiki/Urdu_Braille" title="Urdu Braille">Urdu</a> (Pakistan)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Indian lineage family<br />i.e. <a href="/wiki/Bharati_Braille" title="Bharati Braille">Bharati Braille</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Devanagari_Braille" title="Devanagari Braille">Devanagari (Hindi / Marathi / Nepali)</a></span></li> <li><span class="nowrap"><a href="/wiki/Bengali_Braille" title="Bengali Braille">Bengali (Bangla / Assamese)</a></span></li> <li><span class="nowrap"><a href="/wiki/Gujarati_Braille" title="Gujarati Braille">Gujarati</a></span></li> <li><span class="nowrap"><a href="/wiki/Kannada_Braille" title="Kannada Braille">Kannada</a></span></li> <li><span class="nowrap"><a href="/wiki/Malayalam_Braille" title="Malayalam Braille">Malayalam</a></span></li> <li><span class="nowrap"><a href="/wiki/Odia_Braille" title="Odia Braille">Odia</a></span></li> <li><span class="nowrap"><a href="/wiki/Punjabi_Braille" title="Punjabi Braille">Punjabi</a></span></li> <li><span class="nowrap"><a href="/wiki/Sinhala_Braille" title="Sinhala Braille">Sinhala</a></span></li> <li><span class="nowrap"><a href="/wiki/Tamil_Braille" title="Tamil Braille">Tamil</a></span></li> <li><span class="nowrap"><a href="/wiki/Telugu_Braille" title="Telugu Braille">Telugu</a></span></li> <li><span class="nowrap"><a href="/wiki/Urdu_Braille" title="Urdu Braille">Urdu</a> (India)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other scripts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Ge%27ez_Braille" class="mw-redirect" title="Ge'ez Braille">Amharic</a></span></li> <li><span class="nowrap"><a href="/wiki/Armenian_Braille" title="Armenian Braille">Armenian</a></span></li> <li><span class="nowrap"><a href="/wiki/Burmese_Braille" title="Burmese Braille">Burmese</a></span></li> <li><span class="nowrap"><a href="/wiki/Dzongkha_Braille" title="Dzongkha Braille">Dzongkha</a> (Bhutanese)</span></li> <li><span class="nowrap"><a href="/wiki/Georgian_Braille" title="Georgian Braille">Georgian</a></span></li> <li><span class="nowrap"><a href="/wiki/Greek_Braille" title="Greek Braille">Greek</a></span></li> <li><span class="nowrap"><a href="/wiki/Hebrew_Braille" title="Hebrew Braille">Hebrew</a></span></li> <li><span class="nowrap"><a href="/wiki/Inuktitut_Braille" title="Inuktitut Braille">Inuktitut</a> (reassigned vowels)</span></li> <li><span class="nowrap"><a href="/wiki/Khmer_Braille" title="Khmer Braille">Khmer</a></span></li> <li><span class="nowrap"><a href="/wiki/Thai_and_Lao_Braille" title="Thai and Lao Braille">Thai and Lao</a> (Japanese vowels)</span></li> <li><span class="nowrap"><a href="/wiki/Tibetan_Braille" title="Tibetan Braille">Tibetan</a></span></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Reordered</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Algerian_Braille" title="Algerian Braille">Algerian Braille</a> (obsolete)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Frequency-based</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/American_Braille" title="American Braille">American Braille</a> (obsolete)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Independent</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap">Chinese semi-syllabaries</span> <ul><li><span class="nowrap"><a href="/wiki/Cantonese_Braille" title="Cantonese Braille">Cantonese</a></span></li> <li><span class="nowrap"><a href="/wiki/Mainland_Chinese_Braille" title="Mainland Chinese Braille">Mainland Chinese Mandarin</a></span></li> <li><span class="nowrap"><a href="/wiki/Taiwanese_Braille" title="Taiwanese Braille">Taiwanese Mandarin</a></span></li> <li><span class="nowrap"><a href="/wiki/Two-cell_Chinese_Braille" title="Two-cell Chinese Braille">Two-cell Chinese (Shuangpin)</a></span></li></ul></li> <li><span class="nowrap"><a href="/wiki/Japanese_Braille" title="Japanese Braille">Japanese</a></span></li> <li><span class="nowrap"><a href="/wiki/Korean_Braille" title="Korean Braille">Korean</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Eight-dot</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Luxembourgish_Braille" title="Luxembourgish Braille">Luxembourgish</a></span></li> <li><span class="nowrap"><a href="/wiki/Braille_kanji" title="Braille kanji">Kanji</a></span></li> <li><span class="nowrap"><a href="/wiki/Gardner%E2%80%93Salinas_braille_codes" title="Gardner–Salinas braille codes">Gardner–Salinas braille codes</a> (GS8)</span></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Symbols in braille</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Braille_music" title="Braille music">Braille music</a></span></li> <li><span class="nowrap"><a href="/wiki/Canadian_currency_tactile_feature" title="Canadian currency tactile feature">Canadian currency marks</a></span></li> <li><span class="nowrap"><a href="/wiki/Computer_Braille_Code" title="Computer Braille Code">Computer Braille Code</a></span></li> <li><span class="nowrap"><a href="/wiki/Gardner%E2%80%93Salinas_braille_codes" title="Gardner–Salinas braille codes">Gardner–Salinas braille codes</a> (science; GS8/GS6)</span></li> <li><span class="nowrap"><a href="/wiki/IPA_Braille" title="IPA Braille">International Phonetic Alphabet (IPA)</a></span></li> <li><span class="nowrap"><a href="/wiki/Nemeth_Braille" title="Nemeth Braille">Nemeth braille code</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Braille_technology" title="Braille technology">Braille technology</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Braille_e-book" title="Braille e-book">Braille e-book</a></span></li> <li><span class="nowrap"><a href="/wiki/Braille_embosser" title="Braille embosser">Braille embosser</a></span></li> <li><span class="nowrap"><a href="/wiki/Braille_translator" title="Braille translator">Braille translator</a></span></li> <li><span class="nowrap"><a href="/wiki/Braille_watch" title="Braille watch">Braille watch</a></span></li> <li><span class="nowrap"><a href="/wiki/Mountbatten_Brailler" title="Mountbatten Brailler">Mountbatten Brailler</a></span></li> <li><span class="nowrap"><a href="/wiki/Optical_braille_recognition" title="Optical braille recognition">Optical braille recognition</a></span></li> <li><span class="nowrap"><a href="/wiki/Perforation" title="Perforation">Perforation</a></span></li> <li><span class="nowrap"><a href="/wiki/Perkins_Brailler" title="Perkins Brailler">Perkins Brailler</a></span></li> <li><span class="nowrap"><a href="/wiki/Refreshable_braille_display" title="Refreshable braille display">Refreshable braille display</a></span></li> <li><span class="nowrap"><a href="/wiki/Slate_and_stylus" title="Slate and stylus">Slate and stylus</a></span></li> <li><span class="nowrap"><a href="/wiki/Braigo" title="Braigo">Braigo</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Louis_Braille" title="Louis Braille">Louis Braille</a></span></li> <li><span class="nowrap"><a href="/wiki/Charles_Barbier" title="Charles Barbier">Charles Barbier</a></span></li> <li><span class="nowrap"><a href="/wiki/R%C3%B3%C5%BCa_Czacka" title="Róża Czacka">Róża Czacka</a></span></li> <li><span class="nowrap"><a href="/wiki/Valentin_Ha%C3%BCy" title="Valentin Haüy">Valentin Haüy</a></span></li> <li><span class="nowrap"><a href="/wiki/Harris_Mowbray" title="Harris Mowbray">Harris Mowbray</a></span></li> <li><span class="nowrap"><a href="/wiki/Thakur_Vishva_Narain_Singh" title="Thakur Vishva Narain Singh">Thakur Vishva Narain Singh</a></span></li> <li><span class="nowrap"><a href="/wiki/Sabriye_Tenberken" title="Sabriye Tenberken">Sabriye Tenberken</a></span></li> <li><span class="nowrap"><a href="/wiki/William_Bell_Wait" title="William Bell Wait">William Bell Wait</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Organisations</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Braille_Institute_of_America" title="Braille Institute of America">Braille Institute of America</a></span></li> <li><span class="nowrap"><a href="/wiki/Braille_Without_Borders" title="Braille Without Borders">Braille Without Borders</a></span></li> <li><span class="nowrap"><a href="/wiki/Japan_Braille_Library" title="Japan Braille Library">Japan Braille Library</a></span></li> <li><span class="nowrap"><a href="/wiki/National_Braille_Association" title="National Braille Association">National Braille Association</a></span></li> <li><span class="nowrap"><a href="/wiki/Category:Blindness_organizations" title="Category:Blindness organizations">Blindness organizations</a></span></li> <li><span class="nowrap"><a href="/wiki/Category:Schools_for_the_blind" title="Category:Schools for the blind">Schools for the blind</a></span></li> <li><span class="nowrap"><a href="/wiki/American_Printing_House_for_the_Blind" title="American Printing House for the Blind">American Printing House for the Blind</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other <a href="/wiki/Tactile_alphabet" title="Tactile alphabet">tactile alphabets</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Decapoint" title="Decapoint">Decapoint</a></span></li> <li><span class="nowrap"><a href="/wiki/Moon_type" title="Moon type">Moon type</a></span></li> <li><span class="nowrap"><a href="/wiki/New_York_Point" title="New York Point">New York Point</a></span></li> <li><span class="nowrap"><a href="/wiki/Night_writing" title="Night writing">Night writing</a></span></li> <li><span class="nowrap"><a href="/wiki/Vibratese" title="Vibratese">Vibratese</a></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Accessible_publishing" title="Accessible publishing">Accessible publishing</a></span></li> <li><span class="nowrap"><a href="/wiki/Braille_literacy" title="Braille literacy">Braille literacy</a></span></li> <li><span class="nowrap"><a href="/wiki/RoboBraille" title="RoboBraille">RoboBraille</a></span></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Indian_mathematics" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Indian_mathematics" title="Template:Indian mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Indian_mathematics" title="Template talk:Indian mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Indian_mathematics" title="Special:EditPage/Template:Indian mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Indian_mathematics" style="font-size:114%;margin:0 4em"><a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian mathematics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_Indian_mathematicians" title="List of Indian mathematicians">Mathematicians</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Ancient</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Apastamba_Dharmasutra" title="Apastamba Dharmasutra">Apastamba</a></li> <li><a href="/wiki/Baudhayana_sutras" title="Baudhayana sutras">Baudhayana</a></li> <li><a href="/wiki/K%C4%81ty%C4%81yana" title="Kātyāyana">Katyayana</a></li> <li><a href="/wiki/Manava" title="Manava">Manava</a></li> <li><a href="/wiki/P%C4%81%E1%B9%87ini" title="Pāṇini">Pāṇini</a></li> <li><a href="/wiki/Pingala" title="Pingala">Pingala</a></li> <li><a href="/wiki/Yajnavalkya" title="Yajnavalkya">Yajnavalkya</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Classical</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aryabhata" title="Aryabhata">Āryabhaṭa I</a></li> <li><a href="/wiki/Aryabhata_II" title="Aryabhata II">Āryabhaṭa II</a></li> <li><a href="/wiki/Bh%C4%81skara_I" title="Bhāskara I">Bhāskara I</a></li> <li><a href="/wiki/Bh%C4%81skara_II" title="Bhāskara II">Bhāskara II</a></li> <li><a href="/wiki/Melpathur_Narayana_Bhattathiri" title="Melpathur Narayana Bhattathiri">Melpathur Narayana Bhattathiri</a></li> <li><a href="/wiki/Brahmadeva" title="Brahmadeva">Brahmadeva</a></li> <li><a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a></li> <li><a href="/wiki/Govindasv%C4%81mi" title="Govindasvāmi">Govindasvāmi</a></li> <li><a href="/wiki/Halayudha" title="Halayudha">Halayudha</a></li> <li><a href="/wiki/Jye%E1%B9%A3%E1%B9%ADhadeva" title="Jyeṣṭhadeva">Jyeṣṭhadeva</a></li> <li><a href="/wiki/Kamalakara" title="Kamalakara">Kamalakara</a></li> <li><a href="/wiki/Madhava_of_Sangamagrama" title="Madhava of Sangamagrama">Mādhava of Saṅgamagrāma</a></li> <li><a href="/wiki/Mah%C4%81v%C4%ABra_(mathematician)" title="Mahāvīra (mathematician)">Mahāvīra</a></li> <li><a href="/wiki/Mahendra_S%C5%ABri" title="Mahendra Sūri">Mahendra Sūri</a></li> <li><a href="/wiki/Munishvara" title="Munishvara">Munishvara</a></li> <li><a href="/wiki/Narayana_Pandit" class="mw-redirect" title="Narayana Pandit">Narayana</a></li> <li><a href="/wiki/Parameshvara" class="mw-redirect" title="Parameshvara">Parameshvara</a></li> <li><a href="/wiki/Achyuta_Pisharati" class="mw-redirect" title="Achyuta Pisharati">Achyuta Pisharati</a></li> <li><a href="/wiki/Jagannatha_Samrat" title="Jagannatha Samrat">Jagannatha Samrat</a></li> <li><a href="/wiki/Nilakantha_Somayaji" title="Nilakantha Somayaji">Nilakantha Somayaji</a></li> <li><a href="/wiki/%C5%9Ar%C4%ABpati" title="Śrīpati">Śrīpati</a></li> <li><a href="/wiki/Sridhara" title="Sridhara">Sridhara</a></li> <li><a href="/wiki/Gangesha_Upadhyaya" class="mw-redirect" title="Gangesha Upadhyaya">Gangesha Upadhyaya</a></li> <li><a href="/wiki/Var%C4%81hamihira" title="Varāhamihira">Varāhamihira</a></li> <li><a href="/wiki/Sankara_Variar" title="Sankara Variar">Sankara Variar</a></li> <li><a href="/wiki/Virasena" title="Virasena">Virasena</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modern</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Srinivasa_Ramanujan" title="Srinivasa Ramanujan">Srinivasa Ramanujan</a></li> <li><a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Satyendra Nath Bose</a></li> <li><a href="/wiki/P.C._Mahalanobis" class="mw-redirect" title="P.C. Mahalanobis">P.C. Mahalanobis</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Subrahmanyan Chandrasekhar</a></li> <li><a href="/wiki/C.R._Rao" class="mw-redirect" title="C.R. Rao">C.R. Rao</a></li> <li><a href="/wiki/Veeravalli_S._Varadarajan" title="Veeravalli S. Varadarajan">Veeravalli S. Varadarajan</a></li> <li><a href="/wiki/S._R._Srinivasa_Varadhan" title="S. R. Srinivasa Varadhan">S. R. Srinivasa Varadhan</a></li> <li><a href="/wiki/K._R._Parthasarathy_(probabilist)" title="K. R. Parthasarathy (probabilist)">K. R. Parthasarathy (probabilist)</a></li> <li><a href="/wiki/M._S._Narasimhan" title="M. S. Narasimhan">M. S. Narasimhan</a></li> <li><a href="/wiki/C._S._Seshadri" title="C. S. Seshadri">C. S. Seshadri</a></li> <li><a href="/wiki/Harish-Chandra" title="Harish-Chandra">Harish-Chandra</a></li> <li><a href="/wiki/Subbayya_Sivasankaranarayana_Pillai" title="Subbayya Sivasankaranarayana Pillai">Subbayya Sivasankaranarayana Pillai</a></li> <li><a href="/wiki/Tilak_Raj_Prabhakar" title="Tilak Raj Prabhakar">Tilak Raj Prabhakar</a></li> <li><a href="/wiki/Manjul_Bhargava" title="Manjul Bhargava">Manjul Bhargava</a></li> <li><a href="/wiki/Akshay_Venkatesh" title="Akshay Venkatesh">Akshay Venkatesh</a></li> <li><a href="/wiki/Ravi_Vakil" title="Ravi Vakil">Ravi Vakil</a></li> <li><a href="/wiki/Kannan_Soundararajan" title="Kannan Soundararajan">Kannan Soundararajan</a></li> <li><a href="/wiki/Template:SSBPST_recipients_in_Mathematical_Science" title="Template:SSBPST recipients in Mathematical Science">Shanti Swarup Bhatnagar Prize recipients in Mathematical Science</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Treatises</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Aryabhatiya" title="Aryabhatiya">Aryabhatiya</a></i></li> <li><a href="/wiki/Bakhshali_manuscript" title="Bakhshali manuscript">Bakhshali manuscript</a></li> <li><i><a href="/wiki/Bijaganita" title="Bijaganita">Bijaganita</a></i></li> <li><i><a href="/wiki/Br%C4%81hmasphu%E1%B9%ADasiddh%C4%81nta" title="Brāhmasphuṭasiddhānta">Brāhmasphuṭasiddhānta</a></i></li> <li><i><a href="/wiki/Ganita_Kaumudi" title="Ganita Kaumudi">Ganita Kaumudi</a></i></li> <li><i><a href="/wiki/Kanakkusaram" title="Kanakkusaram">Kanakkusaram</a></i></li> <li><i><a href="/wiki/Karanapaddhati" title="Karanapaddhati">Karanapaddhati</a></i></li> <li><i><a href="/wiki/L%C4%ABl%C4%81vat%C4%AB" title="Līlāvatī">Līlāvatī</a></i></li> <li><i><a href="/wiki/Lokavibhaga" title="Lokavibhaga">Lokavibhaga</a></i></li> <li><i><a href="/wiki/P%C4%81t%C4%ABga%E1%B9%87ita" title="Pātīgaṇita">Pātīgaṇita</a></i></li> <li><i><a href="/wiki/Paulisa_Siddhanta" title="Paulisa Siddhanta">Paulisa Siddhanta</a></i></li> <li><i><a href="/wiki/Var%C4%81hamihira#Pancha-Siddhantika" title="Varāhamihira">Paitamaha Siddhanta</a></i></li> <li><i><a href="/wiki/Romaka_Siddhanta" title="Romaka Siddhanta">Romaka Siddhanta</a></i></li> <li><i><a href="/wiki/Sadratnamala" title="Sadratnamala">Sadratnamala</a></i></li> <li><i><a href="/wiki/Siddh%C4%81nta_Shiromani" title="Siddhānta Shiromani">Siddhānta Shiromani</a></i></li> <li><i><a href="/wiki/Shulba_Sutras" title="Shulba Sutras">Śulba Sūtras</a></i></li> <li><i><a href="/wiki/Surya_Siddhanta" title="Surya Siddhanta">Surya Siddhanta</a></i></li> <li><i><a href="/wiki/Tantrasamgraha" title="Tantrasamgraha">Tantrasamgraha</a></i></li> <li><i><a href="/wiki/Vasishtha_Siddhanta" title="Vasishtha Siddhanta">Vasishtha Siddhanta</a></i></li> <li><i><a href="/wiki/Venvaroha" title="Venvaroha">Veṇvāroha</a></i></li> <li><i><a href="/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81" title="Yuktibhāṣā">Yuktibhāṣā</a></i></li> <li><i><a href="/wiki/Yavanajataka" title="Yavanajataka">Yavanajataka</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Pioneering<br /> innovations</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brahmi numerals</a></li> <li><a class="mw-selflink selflink">Hindu–Arabic numeral system</a></li> <li>Symbol for <a href="/wiki/0" title="0">zero (0)</a></li> <li><a href="/wiki/Madhava_series" title="Madhava series">Infinite series expansions for the trigonometric functions</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Centres</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kerala_school_of_astronomy_and_mathematics" title="Kerala school of astronomy and mathematics">Kerala school of astronomy and mathematics</a></li> <li><a href="/wiki/Jantar_Mantar" title="Jantar Mantar">Jantar Mantar</a> (<a href="/wiki/Jantar_Mantar,_Jaipur" title="Jantar Mantar, Jaipur">Jaipur</a>, <a href="/wiki/Jantar_Mantar,_New_Delhi" title="Jantar Mantar, New Delhi">New Delhi</a>, <a href="/wiki/Jantar_Mantar,_Ujjain" title="Jantar Mantar, Ujjain">Ujjain</a>, <a href="/wiki/Jantar_Mantar,_Varanasi" title="Jantar Mantar, Varanasi">Varanasi</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Historians of<br /> mathematics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bapudeva_Sastri" title="Bapudeva Sastri">Bapudeva Sastri</a> (1821–1900)</li> <li><a href="/w/index.php?title=Shankar_Balakrishna_Dikshit&action=edit&redlink=1" class="new" title="Shankar Balakrishna Dikshit (page does not exist)">Shankar Balakrishna Dikshit</a> (1853–1898)</li> <li><a href="/wiki/Sudhakara_Dvivedi" title="Sudhakara Dvivedi">Sudhakara Dvivedi</a> (1855–1910)</li> <li><a href="/w/index.php?title=M._Rangacarya&action=edit&redlink=1" class="new" title="M. Rangacarya (page does not exist)">M. Rangacarya</a> (1861–1916)</li> <li><a href="/wiki/P._C._Sengupta" class="mw-redirect" title="P. C. Sengupta">P. C. Sengupta</a> (1876–1962)</li> <li><a href="/wiki/B._B._Datta" class="mw-redirect" title="B. B. Datta">B. B. Datta</a> (1888–1958)</li> <li><a href="/wiki/Takao_Hayashi" title="Takao Hayashi">T. Hayashi</a></li> <li><a href="/w/index.php?title=A._A._Krishnaswamy_Ayyangar&action=edit&redlink=1" class="new" title="A. A. Krishnaswamy Ayyangar (page does not exist)">A. A. Krishnaswamy Ayyangar</a> (1892– 1953)</li> <li><a href="/wiki/Avadhesh_Narayan_Singh" title="Avadhesh Narayan Singh">A. N. Singh</a> (1901–1954)</li> <li><a href="/wiki/C._T._Rajagopal" class="mw-redirect" title="C. T. Rajagopal">C. T. Rajagopal</a> (1903–1978)</li> <li><a href="/wiki/T._A._Saraswati_Amma" class="mw-redirect" title="T. A. Saraswati Amma">T. A. Saraswati Amma</a> (1918–2000)</li> <li><a href="/w/index.php?title=S._N._Sen&action=edit&redlink=1" class="new" title="S. N. Sen (page does not exist)">S. N. Sen</a> (1918–1992)</li> <li><a href="/wiki/K._S._Shukla" class="mw-redirect" title="K. S. Shukla">K. S. Shukla</a> (1918–2007)</li> <li><a href="/wiki/K._V._Sarma" title="K. V. Sarma">K. V. Sarma</a> (1919–2005)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Translators</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Walter_Eugene_Clark" title="Walter Eugene Clark">Walter Eugene Clark</a></li> <li><a href="/wiki/Henry_Thomas_Colebrooke" title="Henry Thomas Colebrooke">Henry Thomas Colebrooke </a></li> <li><a href="/wiki/David_Pingree" title="David Pingree">David Pingree</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other regions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Babylonian_mathematics" title="Babylonian mathematics">Babylon</a></li> <li><a href="/wiki/Chinese_mathematics" title="Chinese mathematics">China</a></li> <li><a href="/wiki/Greek_mathematics" title="Greek mathematics">Greece</a></li> <li><a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Islamic mathematics</a></li> <li><a href="/wiki/History_of_mathematics#Medieval_European_mathematics" title="History of mathematics">Europe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modern<br /> institutions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Indian_Statistical_Institute" title="Indian Statistical Institute">Indian Statistical Institute</a></li> <li><a href="/wiki/Bhaskaracharya_Pratishthana" title="Bhaskaracharya Pratishthana">Bhaskaracharya Pratishthana</a></li> <li><a href="/wiki/Chennai_Mathematical_Institute" title="Chennai Mathematical Institute">Chennai Mathematical Institute</a></li> <li><a href="/wiki/Institute_of_Mathematical_Sciences,_Chennai" title="Institute of Mathematical Sciences, Chennai">Institute of Mathematical Sciences</a></li> <li><a href="/wiki/Indian_Institute_of_Science" title="Indian Institute of Science">Indian Institute of Science</a></li> <li><a href="/wiki/Harish-Chandra_Research_Institute" title="Harish-Chandra Research Institute">Harish-Chandra Research Institute</a></li> <li><a href="/wiki/Homi_Bhabha_Centre_for_Science_Education" title="Homi Bhabha Centre for Science Education">Homi Bhabha Centre for Science Education</a></li> <li><a href="/wiki/Ramanujan_Institute_for_Advanced_Study_in_Mathematics" title="Ramanujan Institute for Advanced Study in Mathematics">Ramanujan Institute for Advanced Study in Mathematics</a></li> <li><a href="/wiki/Tata_Institute_of_Fundamental_Research" title="Tata Institute of Fundamental Research">TIFR</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Mathematics_in_the_medieval_Islamic_world" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Islamic_mathematics" title="Template:Islamic mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Islamic_mathematics" title="Template talk:Islamic mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Islamic_mathematics" title="Special:EditPage/Template:Islamic mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Mathematics_in_the_medieval_Islamic_world" style="font-size:114%;margin:0 4em"><a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Mathematics in the medieval Islamic world</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Mathematicians_of_the_medieval_Islamic_world" title="Category:Mathematicians of the medieval Islamic world">Mathematicians</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">9th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%27Abd_al-Ham%C4%ABd_ibn_Turk" class="mw-redirect" title="'Abd al-Hamīd ibn Turk">'Abd al-Hamīd ibn Turk</a></li> <li><a href="/wiki/Sanad_ibn_Ali" title="Sanad ibn Ali">Sanad ibn Ali</a></li> <li><a href="/wiki/Al-Abb%C4%81s_ibn_Said_al-Jawhar%C4%AB" title="Al-Abbās ibn Said al-Jawharī">al-Jawharī</a></li> <li><a href="/wiki/Al-%E1%B8%A4ajj%C4%81j_ibn_Y%C5%ABsuf_ibn_Ma%E1%B9%ADar" title="Al-Ḥajjāj ibn Yūsuf ibn Maṭar">Al-Ḥajjāj ibn Yūsuf</a></li> <li><a href="/wiki/Al-Kindi" title="Al-Kindi">Al-Kindi</a></li> <li><a href="/wiki/Qusta_ibn_Luqa" title="Qusta ibn Luqa">Qusta ibn Luqa</a></li> <li><a href="/wiki/Al-Mahani" title="Al-Mahani">Al-Mahani</a></li> <li><a href="/wiki/Abu_Hanifa_Dinawari" title="Abu Hanifa Dinawari">al-Dinawari</a></li> <li><a href="/wiki/Ban%C5%AB_M%C5%ABs%C4%81_brothers" title="Banū Mūsā brothers">Banū Mūsā brothers</a></li> <li><a href="/wiki/Hunayn_ibn_Ishaq" title="Hunayn ibn Ishaq">Hunayn ibn Ishaq</a></li> <li><a href="/wiki/Al-Khwarizmi" title="Al-Khwarizmi">Al-Khwarizmi</a></li> <li><a href="/wiki/Yusuf_al-Khuri" title="Yusuf al-Khuri">Yusuf al-Khuri</a></li> <li><a href="/wiki/Ishaq_ibn_Hunayn" title="Ishaq ibn Hunayn">Ishaq ibn Hunayn</a></li> <li><a href="/wiki/Na%27im_ibn_Musa" title="Na'im ibn Musa">Na'im ibn Musa</a></li> <li><a href="/wiki/Th%C4%81bit_ibn_Qurra" title="Thābit ibn Qurra">Thābit ibn Qurra</a></li> <li><a href="/wiki/Habash_al-Hasib_al-Marwazi" class="mw-redirect" title="Habash al-Hasib al-Marwazi">al-Marwazi</a></li> <li><a href="/wiki/Abu_Said_Gorgani" title="Abu Said Gorgani">Abu Said Gorgani</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">10th century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abu_al-Wafa%27_Buzjani" class="mw-redirect" title="Abu al-Wafa' Buzjani">Abu al-Wafa</a></li> <li><a href="/wiki/Abu_Ja%27far_al-Khazin" title="Abu Ja'far al-Khazin">al-Khazin</a></li> <li><a href="/wiki/Al-Qabisi" title="Al-Qabisi">Al-Qabisi</a></li> <li><a href="/wiki/Abu_Kamil" title="Abu Kamil">Abu Kamil</a></li> <li><a href="/wiki/Ahmad_ibn_Yusuf" title="Ahmad ibn Yusuf">Ahmad ibn Yusuf</a></li> <li><a href="/wiki/A%E1%B9%A3-%E1%B9%A2aidan%C4%81n%C4%AB" title="Aṣ-Ṣaidanānī">Aṣ-Ṣaidanānī</a></li> <li><a href="/wiki/Sin%C4%81n_ibn_al-Fat%E1%B8%A5" title="Sinān ibn al-Fatḥ">Sinān ibn al-Fatḥ</a></li> <li><a href="/wiki/Abu-Mahmud_Khojandi" class="mw-redirect" title="Abu-Mahmud Khojandi">al-Khojandi</a></li> <li><a href="/wiki/Al-Nayrizi" title="Al-Nayrizi">Al-Nayrizi</a></li> <li><a href="/wiki/Al-Saghani" class="mw-redirect" title="Al-Saghani">Al-Saghani</a></li> <li><a href="/wiki/Brethren_of_Purity" title="Brethren of Purity">Brethren of Purity</a></li> <li><a href="/wiki/Ibn_Sahl_(mathematician)" title="Ibn Sahl (mathematician)">Ibn Sahl</a></li> <li><a href="/wiki/Ibn_Yunus" title="Ibn Yunus">Ibn Yunus</a></li> <li><a href="/wiki/Abu%27l-Hasan_al-Uqlidisi" title="Abu'l-Hasan al-Uqlidisi">al-Uqlidisi</a></li> <li><a href="/wiki/Al-Battani" title="Al-Battani">Al-Battani</a></li> <li><a href="/wiki/Sinan_ibn_Thabit" title="Sinan ibn Thabit">Sinan ibn Thabit</a></li> <li><a href="/wiki/Ibrahim_ibn_Sinan" title="Ibrahim ibn Sinan">Ibrahim ibn Sinan</a></li> <li><a href="/wiki/Al-Isfahani" title="Al-Isfahani">Al-Isfahani</a></li> <li><a href="/wiki/Nazif_ibn_Yumn" title="Nazif ibn Yumn">Nazif ibn Yumn</a></li> <li><a href="/wiki/Abu_Sahl_al-Quhi" title="Abu Sahl al-Quhi">al-Qūhī</a></li> <li><a href="/wiki/Abu_al-Jud" title="Abu al-Jud">Abu al-Jud</a></li> <li><a href="/wiki/Al-Sijzi" title="Al-Sijzi">Al-Sijzi</a></li> <li><a href="/wiki/Al-Karaji" title="Al-Karaji">Al-Karaji</a></li> <li><a href="/wiki/Maslama_al-Majriti" title="Maslama al-Majriti">al-Majriti</a></li> <li><a href="/wiki/Mohammed_ibn_Abdun_al-Jabali" title="Mohammed ibn Abdun al-Jabali">al-Jabali</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">11th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abu_Nasr_Mansur" title="Abu Nasr Mansur">Abu Nasr Mansur</a></li> <li><a href="/wiki/Ibn_al-Haytham" title="Ibn al-Haytham">Alhazen</a></li> <li><a href="/wiki/Kushyar_Gilani" title="Kushyar Gilani">Kushyar Gilani</a></li> <li><a href="/wiki/Al-Biruni" title="Al-Biruni">Al-Biruni</a></li> <li><a href="/wiki/Ibn_al-Samh" title="Ibn al-Samh">Ibn al-Samh</a></li> <li><a href="/wiki/Abu_Mansur_al-Baghdadi" title="Abu Mansur al-Baghdadi">Abu Mansur al-Baghdadi</a></li> <li><a href="/wiki/Avicenna" title="Avicenna">Avicenna</a></li> <li><a href="/wiki/Ibn_Mu%27adh_al-Jayyani" title="Ibn Mu'adh al-Jayyani">al-Jayyānī</a></li> <li><a href="/wiki/Al%C4%AB_ibn_Ahmad_al-Nasaw%C4%AB" class="mw-redirect" title="Alī ibn Ahmad al-Nasawī"> al-Nasawī</a></li> <li><a href="/wiki/Ab%C5%AB_Is%E1%B8%A5%C4%81q_Ibr%C4%81h%C4%ABm_al-Zarq%C4%81l%C4%AB" class="mw-redirect" title="Abū Isḥāq Ibrāhīm al-Zarqālī">al-Zarqālī</a></li> <li><a href="/wiki/Yusuf_al-Mu%27taman_ibn_Hud" title="Yusuf al-Mu'taman ibn Hud"> ibn Hud</a></li> <li><a href="/wiki/Al-Isfizari" title="Al-Isfizari">Al-Isfizari</a></li> <li><a href="/wiki/Omar_Khayyam" title="Omar Khayyam">Omar Khayyam</a></li> <li><a href="/wiki/Muhammad_al-Baghdadi" title="Muhammad al-Baghdadi">Muhammad al-Baghdadi</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">12th century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jabir_ibn_Aflah" title="Jabir ibn Aflah">Jabir ibn Aflah</a></li> <li><a href="/wiki/Al-Kharaq%C4%AB" title="Al-Kharaqī">Al-Kharaqī</a></li> <li><a href="/wiki/Al-Khazini" title="Al-Khazini">Al-Khazini</a></li> <li><a href="/wiki/Al-Samawal_al-Maghribi" title="Al-Samawal al-Maghribi">Al-Samawal al-Maghribi</a></li> <li><a href="/wiki/Abu_Bakr_al-Hassar" title="Abu Bakr al-Hassar">al-Hassar</a></li> <li><a href="/wiki/Sharaf_al-Din_al-Tusi" title="Sharaf al-Din al-Tusi">Sharaf al-Din al-Tusi</a></li> <li><a href="/wiki/Ibn_al-Yasamin" title="Ibn al-Yasamin">Ibn al-Yasamin</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">13th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ibn_al%E2%80%90Ha%27im_al%E2%80%90Ishbili" class="mw-redirect" title="Ibn al‐Ha'im al‐Ishbili">Ibn al‐Ha'im al‐Ishbili</a></li> <li><a href="/wiki/Ahmad_al-Buni" title="Ahmad al-Buni">Ahmad al-Buni</a></li> <li><a href="/wiki/Ahmad_ibn_Munim_al-Abdari" title="Ahmad ibn Munim al-Abdari">Ibn Munim</a></li> <li><a href="/wiki/Alam_al-Din_al-Hanafi" title="Alam al-Din al-Hanafi">Alam al-Din al-Hanafi</a></li> <li><a href="/wiki/Ibn_Adlan" title="Ibn Adlan">Ibn Adlan</a></li> <li><a href="/wiki/Mu%27ayyad_al-Din_al-Urdi" title="Mu'ayyad al-Din al-Urdi">al-Urdi</a></li> <li><a href="/wiki/Nasir_al-Din_al-Tusi" title="Nasir al-Din al-Tusi">Nasir al-Din al-Tusi</a></li> <li><a href="/wiki/Athir_al-Din_al-Abhari" title="Athir al-Din al-Abhari">al-Abhari</a></li> <li><a href="/wiki/Muhyi_al-Din_al-Maghribi" title="Muhyi al-Din al-Maghribi">Muhyi al-Din al-Maghribi</a></li> <li><a href="/wiki/Abu_Ali_al-Hasan_al-Marrakushi" title="Abu Ali al-Hasan al-Marrakushi">al-Hasan al-Marrakushi</a></li> <li><a href="/wiki/Qutb_al-Din_al-Shirazi" title="Qutb al-Din al-Shirazi">Qutb al-Din al-Shirazi</a></li> <li><a href="/wiki/Shams_al-Din_al-Samarqandi" title="Shams al-Din al-Samarqandi">Shams al-Din al-Samarqandi</a></li> <li><a href="/wiki/Ibn_al-Banna%27_al-Marrakushi" title="Ibn al-Banna' al-Marrakushi">Ibn al-Banna'</a></li> <li><a href="/wiki/Kam%C4%81l_al-D%C4%ABn_al-F%C4%81ris%C4%AB" title="Kamāl al-Dīn al-Fārisī">Kamāl al-Dīn al-Fārisī</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">14th century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nizam_al-Din_al-Nisapuri" class="mw-redirect" title="Nizam al-Din al-Nisapuri">Nizam al-Din al-Nisapuri</a></li> <li><a href="/wiki/Ibn_al-Shatir" title="Ibn al-Shatir">Ibn al-Shatir</a></li> <li><a href="/wiki/Ibn_al-Durayhim" title="Ibn al-Durayhim">Ibn al-Durayhim</a></li> <li><a href="/wiki/Shams_al-Din_Abu_Abd_Allah_al-Khalili" title="Shams al-Din Abu Abd Allah al-Khalili">Al-Khalili</a></li> <li><a href="/wiki/Ya%27ish_ibn_Ibrahim_al-Umawi" title="Ya'ish ibn Ibrahim al-Umawi">al-Umawi</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">15th century</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ibn_al-Majdi" title="Ibn al-Majdi">Ibn al-Majdi</a></li> <li><a href="/wiki/Q%C4%81%E1%B8%8D%C4%AB_Z%C4%81da_al-R%C5%ABm%C4%AB" title="Qāḍī Zāda al-Rūmī">al-Rūmī</a></li> <li><a href="/wiki/Jamshid_al-Kashi" title="Jamshid al-Kashi">al-Kāshī</a></li> <li><a href="/wiki/Ulugh_Beg" title="Ulugh Beg">Ulugh Beg</a></li> <li><a href="/wiki/Ali_Qushji" title="Ali Qushji">Ali Qushji</a></li> <li><a href="/wiki/%27Abd_al-%27Aziz_al-Wafa%27i" title="'Abd al-'Aziz al-Wafa'i">al-Wafa'i</a></li> <li><a href="/wiki/Abu%27l-Hasan_ibn_Ali_al-Qalasadi" title="Abu'l-Hasan ibn Ali al-Qalasadi">al-Qalaṣādī</a></li> <li><a href="/wiki/Sibt_al-Maridini" title="Sibt al-Maridini">Sibt al-Maridini</a></li> <li><a href="/wiki/Ibn_Ghazi_al-Miknasi" title="Ibn Ghazi al-Miknasi">Ibn Ghazi al-Miknasi</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">16th century</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Al-Birjandi" title="Al-Birjandi">Al-Birjandi</a></li> <li><a href="/wiki/Muhammad_Baqir_Yazdi" title="Muhammad Baqir Yazdi">Muhammad Baqir Yazdi</a></li> <li><a href="/wiki/Taqi_ad-Din_Muhammad_ibn_Ma%27ruf" title="Taqi ad-Din Muhammad ibn Ma'ruf">Taqi ad-Din</a></li> <li><a href="/wiki/Ibn_Hamza_al-Maghribi" title="Ibn Hamza al-Maghribi">Ibn Hamza al-Maghribi</a></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="7" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Gravure_originale_du_compas_parfait_par_Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Gravure_originale_du_compas_parfait_par_Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB.jpg/80px-Gravure_originale_du_compas_parfait_par_Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB.jpg" decoding="async" width="80" height="107" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Gravure_originale_du_compas_parfait_par_Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB.jpg/120px-Gravure_originale_du_compas_parfait_par_Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Gravure_originale_du_compas_parfait_par_Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB.jpg/160px-Gravure_originale_du_compas_parfait_par_Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB.jpg 2x" data-file-width="458" data-file-height="612" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Mathematical_works_of_the_medieval_Islamic_world" title="Category:Mathematical works of the medieval Islamic world">Mathematical<br />works</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/The_Compendious_Book_on_Calculation_by_Completion_and_Balancing" class="mw-redirect" title="The Compendious Book on Calculation by Completion and Balancing">The Compendious Book on Calculation by Completion and Balancing</a></i></li> <li><i><a href="/wiki/De_Gradibus" title="De Gradibus">De Gradibus</a></i></li> <li><i><a href="/wiki/Principles_of_Hindu_Reckoning" title="Principles of Hindu Reckoning">Principles of Hindu Reckoning</a></i></li> <li><i><a href="/wiki/Book_of_Optics" title="Book of Optics">Book of Optics</a></i></li> <li><i><a href="/wiki/The_Book_of_Healing" title="The Book of Healing">The Book of Healing</a></i></li> <li><i><a href="/wiki/Book_on_the_Measurement_of_Plane_and_Spherical_Figures" title="Book on the Measurement of Plane and Spherical Figures">Book on the Measurement of Plane and Spherical Figures</a></i></li> <li><i><a href="/wiki/Encyclopedia_of_the_Brethren_of_Purity" title="Encyclopedia of the Brethren of Purity">Encyclopedia of the Brethren of Purity</a></i></li> <li><i><a href="/wiki/Toledan_Tables" title="Toledan Tables">Toledan Tables</a></i></li> <li><i><a href="/wiki/Tabula_Rogeriana" title="Tabula Rogeriana">Tabula Rogeriana</a></i></li> <li><i><a href="/wiki/Zij" title="Zij">Zij</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alhazen%27s_problem" title="Alhazen's problem">Alhazen's problem</a></li> <li><a href="/wiki/Islamic_geometric_patterns" title="Islamic geometric patterns">Islamic geometric patterns</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Centers</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Al-Azhar_University" title="Al-Azhar University">Al-Azhar University</a></li> <li><a href="/wiki/Al-Mustansiriya_University" title="Al-Mustansiriya University">Al-Mustansiriya University</a></li> <li><a href="/wiki/House_of_Knowledge" title="House of Knowledge">House of Knowledge</a></li> <li><a href="/wiki/House_of_Wisdom" title="House of Wisdom">House of Wisdom</a></li> <li><a href="/wiki/Constantinople_observatory_of_Taqi_ad-Din" title="Constantinople observatory of Taqi ad-Din">Constantinople observatory of Taqi ad-Din</a></li> <li><a href="/wiki/Madrasa" title="Madrasa">Madrasa</a></li> <li><a href="/wiki/Maragheh_observatory" title="Maragheh observatory">Maragheh observatory</a></li> <li><a href="/wiki/University_of_al-Qarawiyyin" title="University of al-Qarawiyyin">University of al-Qarawiyyin</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Influences</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Babylonian_mathematics" title="Babylonian mathematics">Babylonian mathematics</a></li> <li><a href="/wiki/Greek_mathematics" title="Greek mathematics">Greek mathematics</a></li> <li><a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian mathematics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Influenced</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Byzantine_science" title="Byzantine science">Byzantine mathematics</a></li> <li><a href="/wiki/History_of_mathematics#Medieval_European_mathematics" title="History of mathematics">European mathematics</a></li> <li><a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian mathematics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Hindu–Arabic numeral system</a></li> <li><a href="/wiki/Arabic_numerals" title="Arabic numerals">Arabic numerals</a> (<a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a>, <a href="/wiki/Arabic_numerals" title="Arabic numerals">Western Arabic numerals</a>)</li> <li><a href="/wiki/Trigonometric_functions" title="Trigonometric functions">Trigonometric functions</a></li> <li><a href="/wiki/History_of_trigonometry" title="History of trigonometry">History of trigonometry</a></li> <li><a href="/wiki/History_of_algebra" title="History of algebra">History of algebra</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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