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class="vector-toc-text"> <span class="vector-toc-numb">1.2.2</span> <span>Europe</span> </div> </a> <ul id="toc-Europe-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Russia" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Russia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.3</span> <span>Russia</span> </div> </a> <ul id="toc-Russia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-China" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#China"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.4</span> <span>China</span> </div> </a> <ul id="toc-China-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Encoding" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Encoding"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Encoding</span> </div> </a> <ul id="toc-Encoding-sublist" class="vector-toc-list"> </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">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Footnotes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Footnotes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Footnotes</span> </div> </a> <ul id="toc-Footnotes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-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">6</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-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">Arabic numerals</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 73 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-73" 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">73 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Arabiese_syfers" title="Arabiese syfers – Afrikaans" lang="af" hreflang="af" data-title="Arabiese syfers" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A3%D8%B1%D9%82%D8%A7%D9%85_%D8%B9%D8%B1%D8%A8%D9%8A%D8%A9" title="أرقام عربية – Arabic" lang="ar" hreflang="ar" data-title="أرقام عربية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D4%B1%D6%80%D5%A1%D5%A2%D5%A1%D5%AF%D5%A1%D5%B6_%D4%B9%D5%AB%D6%82%D5%A5%D6%80" title="Արաբական Թիւեր – Western Armenian" lang="hyw" hreflang="hyw" data-title="Արաբական Թիւեր" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/N%C3%BAmberos_ar%C3%A1bigos" title="Númberos arábigos – Asturian" lang="ast" hreflang="ast" data-title="Númberos arábigos" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C6%8Fr%C9%99b_r%C9%99q%C9%99ml%C9%99ri" title="Ərəb rəqəmləri – Azerbaijani" lang="az" hreflang="az" data-title="Ərəb rəqəmləri" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%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" title="আরবি সংখ্যা – Bangla" lang="bn" hreflang="bn" data-title="আরবি সংখ্যা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/A-la-pek_s%C3%B2%CD%98-j%C4%AB" title="A-la-pek sò͘-jī – Minnan" lang="nan" hreflang="nan" data-title="A-la-pek sò͘-jī" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D2%92%D3%99%D1%80%D3%99%D0%BF_%D1%86%D0%B8%D1%84%D1%80%D2%99%D0%B0%D1%80%D1%8B" title="Ғәрәп цифрҙары – Bashkir" lang="ba" hreflang="ba" data-title="Ғәрәп цифрҙары" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%B1%D1%81%D0%BA%D1%96%D1%8F_%D0%BB%D1%96%D1%87%D0%B1%D1%8B" title="Арабскія лічбы – Belarusian" lang="be" hreflang="be" data-title="Арабскія лічбы" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%B1%D1%81%D0%BA%D1%96%D1%8F_%D0%BB%D1%96%D1%87%D0%B1%D1%8B" title="Арабскія лічбы – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Арабскія лічбы" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%B1%D1%81%D0%BA%D0%B8_%D1%86%D0%B8%D1%84%D1%80%D0%B8" title="Арабски цифри – Bulgarian" lang="bg" hreflang="bg" data-title="Арабски цифри" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Arapski_brojevi" title="Arapski brojevi – Bosnian" lang="bs" hreflang="bs" data-title="Arapski brojevi" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Sifro%C3%B9_arabek" title="Sifroù arabek – Breton" lang="br" hreflang="br" data-title="Sifroù arabek" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Nombres_ar%C3%A0bics" title="Nombres aràbics – Catalan" lang="ca" hreflang="ca" data-title="Nombres aràbics" 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/Arabsk%C3%A9_%C4%8D%C3%ADslice" title="Arabské číslice – Czech" lang="cs" hreflang="cs" data-title="Arabské číslice" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Arabische_Zahlschrift" title="Arabische Zahlschrift – German" lang="de" hreflang="de" data-title="Arabische Zahlschrift" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Araabia_numbrid" title="Araabia numbrid – Estonian" lang="et" hreflang="et" data-title="Araabia numbrid" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CF%81%CE%B1%CE%B2%CE%B9%CE%BA%CF%8C_%CF%83%CF%8D%CF%83%CF%84%CE%B7%CE%BC%CE%B1_%CE%B1%CF%81%CE%AF%CE%B8%CE%BC%CE%B7%CF%83%CE%B7%CF%82" title="Αραβικό σύστημα αρίθμησης – Greek" lang="el" hreflang="el" data-title="Αραβικό σύστημα αρίθμησης" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Cifras_ar%C3%A1bigas" title="Cifras arábigas – Spanish" lang="es" hreflang="es" data-title="Cifras arábigas" 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/Arabaj_ciferoj" title="Arabaj ciferoj – Esperanto" lang="eo" hreflang="eo" data-title="Arabaj ciferoj" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Arabiar_zifrak" title="Arabiar zifrak – Basque" lang="eu" hreflang="eu" data-title="Arabiar zifrak" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</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_%D8%B9%D8%B1%D8%A8%DB%8C" title="عددنویسی عربی – Persian" lang="fa" hreflang="fa" data-title="عددنویسی 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/Chiffres_arabes" title="Chiffres arabes – French" lang="fr" hreflang="fr" data-title="Chiffres arabes" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Numeraci%C3%B3n_ar%C3%A1biga" title="Numeración arábiga – Galician" lang="gl" hreflang="gl" data-title="Numeración arábiga" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B9%E0%AA%BF%E0%AA%A8%E0%AB%8D%E0%AA%A6%E0%AB%81-%E0%AA%85%E0%AA%B0%E0%AB%87%E0%AA%AC%E0%AB%80%E0%AA%95_%E0%AA%85%E0%AA%82%E0%AA%95%E0%AB%8B" title="હિન્દુ-અરેબીક અંકો – Gujarati" lang="gu" hreflang="gu" data-title="હિન્દુ-અરેબીક અંકો" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%84%EB%9D%BC%EB%B9%84%EC%95%84_%EC%88%AB%EC%9E%90" title="아라비아 숫자 – Korean" lang="ko" hreflang="ko" data-title="아라비아 숫자" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D6%80%D5%A1%D5%A2%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A9%D5%BE%D5%A5%D6%80" title="Արաբական թվեր – Armenian" lang="hy" hreflang="hy" data-title="Արաբական թվեր" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Arapske_brojke" title="Arapske brojke – Croatian" lang="hr" hreflang="hr" data-title="Arapske brojke" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Angka_Arab" title="Angka Arab – Indonesian" lang="id" hreflang="id" data-title="Angka 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Arab%C3%ADskar_t%C3%B6lur" title="Arabískar tölur – Icelandic" lang="is" hreflang="is" data-title="Arabískar tölur" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%A4%D7%A8%D7%95%D7%AA_%D7%94%D7%95%D7%93%D7%99%D7%95%D7%AA-%D7%A2%D7%A8%D7%91%D7%99%D7%95%D7%AA" title="ספרות הודיות-ערביות – Hebrew" lang="he" hreflang="he" data-title="ספרות הודיות-ערביות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%A0%E1%83%90%E1%83%91%E1%83%A3%E1%83%9A%E1%83%98_%E1%83%AA%E1%83%98%E1%83%A4%E1%83%A0%E1%83%94%E1%83%91%E1%83%98" title="არაბული ციფრები – Georgian" lang="ka" hreflang="ka" data-title="არაბული ციფრები" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%B1_%D1%86%D0%B8%D1%84%D1%80%D0%BB%D0%B0%D1%80%D1%8B" title="Араб цифрлары – Kazakh" lang="kk" hreflang="kk" data-title="Араб цифрлары" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%BF_%D1%81%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%8B" title="Арап сандары – Kyrgyz" lang="ky" hreflang="ky" data-title="Арап сандары" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%95%E0%BA%BB%E0%BA%A7%E0%BB%80%E0%BA%A5%E0%BA%81%E0%BA%AD%E0%BA%B2%E0%BA%AB%E0%BA%A5%E0%BA%B1%E0%BA%9A" title="ຕົວເລກອາຫລັບ – Lao" lang="lo" hreflang="lo" data-title="ຕົວເລກອາຫລັບ" data-language-autonym="ລາວ" data-language-local-name="Lao" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Numeri_Arabici" title="Numeri Arabici – Latin" lang="la" hreflang="la" data-title="Numeri Arabici" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Ar%C4%81bu_skait%C4%BCi" title="Arābu skaitļi – Latvian" lang="lv" hreflang="lv" data-title="Arābu skaitļi" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Arabi%C5%A1kieji_skaitmenys" title="Arabiškieji skaitmenys – Lithuanian" lang="lt" hreflang="lt" data-title="Arabiškieji skaitmenys" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hindu%E2%80%93arab_sz%C3%A1m%C3%ADr%C3%A1s" title="Hindu–arab számírás – Hungarian" lang="hu" hreflang="hu" data-title="Hindu–arab számírás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Tarehimarika_arabo" title="Tarehimarika arabo – Malagasy" lang="mg" hreflang="mg" data-title="Tarehimarika arabo" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%B0%E0%A4%AC%E0%A5%80_%E0%A4%85%E0%A4%82%E0%A4%95" title="अरबी अंक – Marathi" lang="mr" hreflang="mr" data-title="अरबी अंक" 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/Angka_Arab" title="Angka Arab – Malay" lang="ms" hreflang="ms" data-title="Angka 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/Algarismos_ando-ar%C3%A1bicos" title="Algarismos ando-arábicos – Mirandese" lang="mwl" hreflang="mwl" data-title="Algarismos ando-arábicos" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%B1_%D1%86%D0%B8%D1%84%D1%80" title="Араб цифр – Mongolian" lang="mn" hreflang="mn" data-title="Араб цифр" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Arabisch-Indische_cijfers" title="Arabisch-Indische cijfers – Dutch" lang="nl" hreflang="nl" data-title="Arabisch-Indische cijfers" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A2%E3%83%A9%E3%83%93%E3%82%A2%E6%95%B0%E5%AD%97" title="アラビア数字 – Japanese" lang="ja" hreflang="ja" data-title="アラビア数字" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Arabiske_tall" title="Arabiske tall – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Arabiske tall" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Arabiske_tal" title="Arabiske tal – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Arabiske tal" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Numeracion_ar%C3%A0bia" title="Numeracion aràbia – Occitan" lang="oc" hreflang="oc" data-title="Numeracion aràbia" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Arab_raqamlari" title="Arab raqamlari – Uzbek" lang="uz" hreflang="uz" data-title="Arab raqamlari" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%B0%E0%A8%AC%E0%A9%80_%E0%A8%85%E0%A9%B0%E0%A8%95" title="ਅਰਬੀ ਅੰਕ – Punjabi" lang="pa" hreflang="pa" data-title="ਅਰਬੀ ਅੰਕ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Cyfry_arabskie" title="Cyfry arabskie – Polish" lang="pl" hreflang="pl" data-title="Cyfry arabskie" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Algarismos_ar%C3%A1bicos" title="Algarismos arábicos – Portuguese" lang="pt" hreflang="pt" data-title="Algarismos arábicos" 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/Cifre_arabe" title="Cifre arabe – Romanian" lang="ro" hreflang="ro" data-title="Cifre arabe" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%B1%D1%81%D0%BA%D0%B8%D0%B5_%D1%86%D0%B8%D1%84%D1%80%D1%8B" title="Арабские цифры – Russian" lang="ru" hreflang="ru" data-title="Арабские цифры" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Numrat_arab%C3%AB" title="Numrat arabë – Albanian" lang="sq" hreflang="sq" data-title="Numrat arabë" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/N%C3%B9mmura_%C3%A0rabbi" title="Nùmmura àrabbi – Sicilian" lang="scn" hreflang="scn" data-title="Nùmmura àrabbi" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Arabsk%C3%A1_%C4%8D%C3%ADslica" title="Arabská číslica – Slovak" lang="sk" hreflang="sk" data-title="Arabská číslica" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Arabske_%C5%A1tevilke" title="Arabske številke – Slovenian" lang="sl" hreflang="sl" data-title="Arabske številke" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%BF%D1%81%D0%BA%D0%B8_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B8" title="Арапски бројеви – Serbian" lang="sr" hreflang="sr" data-title="Арапски бројеви" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Arapski_brojevi" title="Arapski brojevi – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Arapski brojevi" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Arabialaiset_numerot" title="Arabialaiset numerot – Finnish" lang="fi" hreflang="fi" data-title="Arabialaiset numerot" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Arabiska_siffror" title="Arabiska siffror – Swedish" lang="sv" hreflang="sv" data-title="Arabiska siffror" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%B0%E0%AE%BE%E0%AE%AA%E0%AE%BF%E0%AE%AF_%E0%AE%8E%E0%AE%A3%E0%AF%8D%E0%AE%AE%E0%AF%81%E0%AE%B1%E0%AF%88" title="அராபிய எண்முறை – Tamil" lang="ta" hreflang="ta" data-title="அராபிய எண்முறை" 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%95%E0%B8%B1%E0%B8%A7%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B8%AD%E0%B8%B2%E0%B8%AB%E0%B8%A3%E0%B8%B1%E0%B8%9A" title="ตัวเลขอาหรับ – Thai" lang="th" hreflang="th" data-title="ตัวเลขอาหรับ" 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/Arap_rakamlar%C4%B1" title="Arap rakamları – Turkish" lang="tr" hreflang="tr" data-title="Arap rakamları" 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%90%D1%80%D0%B0%D0%B1%D1%81%D1%8C%D0%BA%D1%96_%D1%87%D0%B8%D1%81%D0%BB%D0%B0" title="Арабські числа – Ukrainian" lang="uk" hreflang="uk" data-title="Арабські числа" 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/%D8%B9%D8%B1%D8%A8%DB%8C_%D8%A7%D8%B9%D8%AF%D8%A7%D8%AF" title="عربی اعداد – Urdu" lang="ur" hreflang="ur" data-title="عربی اعداد" 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 href="https://vi.wikipedia.org/wiki/Ch%E1%BB%AF_s%E1%BB%91_%E1%BA%A2_R%E1%BA%ADp" title="Chữ số Ả Rập – Vietnamese" lang="vi" hreflang="vi" data-title="Chữ số Ả Rập" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E9%98%BF%E6%8B%89%E4%BC%AF%E6%95%B8%E5%AD%97" title="阿拉伯數字 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="阿拉伯數字" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E9%98%BF%E6%8B%89%E4%BC%AF%E6%95%B0%E5%AD%97" title="阿拉伯数字 – Wu" lang="wuu" hreflang="wuu" data-title="阿拉伯数字" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%98%BF%E6%8B%89%E4%BC%AF%E6%95%B8%E5%AD%97" title="阿拉伯數字 – Cantonese" lang="yue" hreflang="yue" data-title="阿拉伯數字" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%98%BF%E6%8B%89%E4%BC%AF%E6%95%B0%E5%AD%97" title="阿拉伯数字 – Chinese" lang="zh" hreflang="zh" data-title="阿拉伯数字" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q29961325#sitelinks-wikipedia" 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dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">The symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9</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">This article is about the ten symbols. For the numerical system, see <a href="/wiki/Decimal" title="Decimal">Decimal</a> and <a href="/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system">Hindu–Arabic numeral system</a>. For symbols used in Arabic script, see <a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a>. For other uses, see <a href="/wiki/Arabic_numerals_(disambiguation)" class="mw-disambig" title="Arabic numerals (disambiguation)">Arabic numerals (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hindu%E2%80%93Arabic_numerals.svg" class="mw-file-description"><img alt="Numbers written from 0 to 9" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Hindu%E2%80%93Arabic_numerals.svg/330px-Hindu%E2%80%93Arabic_numerals.svg.png" decoding="async" width="330" height="46" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Hindu%E2%80%93Arabic_numerals.svg/495px-Hindu%E2%80%93Arabic_numerals.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Hindu%E2%80%93Arabic_numerals.svg/660px-Hindu%E2%80%93Arabic_numerals.svg.png 2x" data-file-width="405" data-file-height="57" /></a><figcaption>Arabic numerals set in <a href="/wiki/Source_Sans" title="Source Sans">Source 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.sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .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 mw-collapsed"><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 mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system">Hindu–Arabic numerals</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a class="mw-selflink selflink">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>The ten <b>Arabic numerals</b> 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the most commonly used <a href="/wiki/Numerical_digit" title="Numerical digit">symbols</a> for writing numbers. The term often also implies a <a href="/wiki/Positional_notation" title="Positional notation">positional notation</a> using the numerals, as well as the use of a <a href="/wiki/Decimal" title="Decimal">decimal</a> base, in particular when contrasted with other systems such as <a href="/wiki/Roman_numerals" title="Roman numerals">Roman numerals</a>. However, the symbols are also used to write numbers in other bases such as <a href="/wiki/Octal" title="Octal">octal</a>, as well as for writing non-numerical information such as trademarks or license plate identifiers. </p><p>They are also called <b>Western Arabic numerals</b>, <b>Western digits</b>, <b>European digits</b>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <b>Ghubār numerals</b> or <b>Hindu–Arabic numerals</b>.<sup id="cite_ref-AHB_2-0" class="reference"><a href="#cite_note-AHB-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The <i><a href="/wiki/Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a></i> uses lowercase <i>Arabic numerals</i> for it, while using the fully capitalized term <i>Arabic Numerals</i> for <a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> In contemporary society, the terms <b>digits</b>, <b>numbers</b> and <b>numerals</b> often implies only these symbols, although that can only be inferred from context. </p><p>Europeans first learned of Arabic numerals <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> the 10th century</span>, though their spread was a gradual process. After Italian scholar <a href="/wiki/Fibonacci" title="Fibonacci">Fibonacci</a> of <a href="/wiki/Republic_of_Pisa" title="Republic of Pisa">Pisa</a> encountered the numerals in the Algerian city of <a href="/wiki/B%C3%A9ja%C3%AFa" title="Béjaïa">Béjaïa</a>, his 13th-century work <i><span title="Latin-language text"><i lang="la"><a href="/wiki/Liber_Abaci" title="Liber Abaci">Liber Abaci</a></i></span></i> became crucial in making them known in Europe. However, their use was largely confined to <a href="/wiki/Northern_Italy" title="Northern Italy">Northern Italy</a> until the invention of the <a href="/wiki/Printing_press" title="Printing press">printing press</a> in the 15th century.<sup id="cite_ref-Danna_2021_pp._5–48_4-0" class="reference"><a href="#cite_note-Danna_2021_pp._5–48-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> European trade, books, and <a href="/wiki/Colonialism" title="Colonialism">colonialism</a> subsequently helped popularize the adoption of Arabic numerals around the world. The numerals are used worldwide—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>—and have become common in the writing systems where other numeral systems existed previously, such as <a href="/wiki/Chinese_numerals" title="Chinese numerals">Chinese</a> and <a href="/wiki/Japanese_numerals" title="Japanese numerals">Japanese</a> numerals. </p> <meta property="mw:PageProp/toc" /> <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=Arabic_numerals&action=edit&section=1" 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="Origin">Origin</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=2" title="Edit section: Origin"><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:The_Brahmi_numeral_system_and_its_descendants.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/The_Brahmi_numeral_system_and_its_descendants.png/220px-The_Brahmi_numeral_system_and_its_descendants.png" decoding="async" width="220" height="194" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/The_Brahmi_numeral_system_and_its_descendants.png/330px-The_Brahmi_numeral_system_and_its_descendants.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/The_Brahmi_numeral_system_and_its_descendants.png/440px-The_Brahmi_numeral_system_and_its_descendants.png 2x" data-file-width="627" data-file-height="553" /></a><figcaption>Evolution of Indian numerals into Arabic numerals and their adoption in Europe</figcaption></figure> <p>Positional decimal notation including a zero symbol was <a href="/wiki/History_of_the_Hindu%E2%80%93Arabic_numeral_system" title="History of the Hindu–Arabic numeral system">developed in India</a>, using symbols visually distinct from those that would eventually enter into international use. As the concept spread, the sets of symbols used in different regions diverged over time. </p><p>The immediate ancestors of the digits now commonly called "Arabic numerals" were introduced to Europe in the 10th century by Arabic speakers of Spain and North Africa, with digits at the time in wide use from Libya to Morocco. In the east from Egypt to Iraq and the Arabian Peninsula, the Arabs were using the <a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a> or "Mashriki" numerals: <span dir="ltr" style="unicode-bidi: bidi-override; direction: ltr">٠, ١, ٢, ٣, ٤, ٥, ٦, ٧, ٨, ٩</span>.<sup id="cite_ref-:2_5-0" class="reference"><a href="#cite_note-:2-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Al%C4%AB_ibn_Ahmad_al-Nasaw%C4%AB" class="mw-redirect" title="Alī ibn Ahmad al-Nasawī">Al-Nasawi</a> wrote in the early 11th century that mathematicians had not agreed on the form of the numerals, but most of them had agreed to train themselves with the forms now known as Eastern Arabic numerals.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The oldest specimens of the written numerals available are from Egypt and date to 873–874 AD. They show three forms of the numeral "2" and two forms of the numeral "3", and these variations indicate the divergence between what later became known as the Eastern Arabic numerals and the Western Arabic numerals.<sup id="cite_ref-FOOTNOTEKunitzsch20035_7-0" class="reference"><a href="#cite_note-FOOTNOTEKunitzsch20035-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The Western Arabic numerals came to be used in the <a href="/wiki/Maghreb" title="Maghreb">Maghreb</a> and <a href="/wiki/Al-Andalus" title="Al-Andalus">Al-Andalus</a> from the 10th century onward.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Some amount of consistency in the Western Arabic numeral forms endured from the 10th century, found in a Latin manuscript of <a href="/wiki/Isidore_of_Seville" title="Isidore of Seville">Isidore of Seville</a>'s <i><span title="Latin-language text"><i lang="la"><a href="/wiki/Etymologiae" title="Etymologiae">Etymologiae</a></i></span></i> from 976 and the Gerbertian abacus, into the 12th and 13th centuries, in early manuscripts of translations from the city of <a href="/wiki/Toledo,_Spain" title="Toledo, Spain">Toledo</a>.<sup id="cite_ref-:2_5-1" class="reference"><a href="#cite_note-:2-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Calculations were originally performed using a dust board (<span title="Arabic-language romanization"><i lang="ar-Latn">takht</i></span>, Latin: <span title="Latin-language text"><i lang="la">tabula</i></span>), which involved writing symbols with a stylus and erasing them. The use of the dust board appears to have introduced a divergence in terminology as well: whereas the Hindu reckoning was called <span title="Arabic-language romanization"><i lang="ar-Latn">ḥisāb al-hindī</i></span> in the east, it was called <span title="Arabic-language romanization"><i lang="ar-Latn">ḥisāb al-ghubār</i></span> 'calculation with dust' in the west.<sup id="cite_ref-FOOTNOTEKunitzsch20038_9-0" class="reference"><a href="#cite_note-FOOTNOTEKunitzsch20038-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The numerals themselves were referred to in the west as <span title="Arabic-language romanization"><i lang="ar-Latn">ashkāl al‐ghubār</i></span> 'dust figures' or <span title="Arabic-language romanization"><i lang="ar-Latn">qalam al-ghubår</i></span> 'dust letters'.<sup id="cite_ref-FOOTNOTEKunitzsch200310_10-0" class="reference"><a href="#cite_note-FOOTNOTEKunitzsch200310-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Abu%27l-Hasan_al-Uqlidisi" title="Abu'l-Hasan al-Uqlidisi">Al-Uqlidisi</a> later invented a system of calculations with ink and paper 'without board and erasing' (<span title="Arabic-language romanization"><i lang="ar-Latn">bi-ghayr takht wa-lā maḥw bal bi-dawāt wa-qirṭās</i></span>).<sup id="cite_ref-FOOTNOTEKunitzsch20037–8_11-0" class="reference"><a href="#cite_note-FOOTNOTEKunitzsch20037–8-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>A popular myth claims that the symbols were designed to indicate their numeric value through the number of angles they contained, but there is no contemporary evidence of this, and the myth is difficult to reconcile with any digits past 4.<sup id="cite_ref-ifrah_12-0" class="reference"><a href="#cite_note-ifrah-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Gregor_Reisch,_Margarita_Philosophica,_1508_(1230x1615).png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png/220px-Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png" decoding="async" width="220" height="290" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png/330px-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/440px-Gregor_Reisch%2C_Margarita_Philosophica%2C_1508_%281230x1615%29.png 2x" data-file-width="1205" data-file-height="1591" /></a><figcaption>Etching from 1503 (or earlier) showing usage of Arabic numerals.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Adoption_and_spread">Adoption and spread</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=3" title="Edit section: Adoption and spread"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></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 first Arabic numerals in the West appeared in the <i><span title="Latin-language text"><i lang="la"><a href="/wiki/Codex_Albeldensis" class="mw-redirect" title="Codex Albeldensis">Codex Albeldensis</a></i></span></i> in Spain.</figcaption></figure> <p>The first mentions of the numerals from 1 to 9 in the West are found in the 976 <i><span title="Latin-language text"><i lang="la"><a href="/wiki/Codex_Vigilanus" title="Codex Vigilanus">Codex Vigilanus</a></i></span></i>, an <a href="/wiki/Illuminated_manuscript" title="Illuminated manuscript">illuminated</a> collection of various historical documents covering a period from antiquity to the 10th century in <a href="/wiki/Hispania" title="Hispania">Hispania</a>.<sup id="cite_ref-:1_13-0" class="reference"><a href="#cite_note-:1-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Other texts show that numbers from 1 to 9 were occasionally supplemented by a placeholder known as <a href="/wiki/Names_for_the_number_0_in_English" title="Names for the number 0 in English"><span title="Arabic-language romanization"><i lang="ar-Latn">sipos</i></span></a>, represented as a circle or wheel, reminiscent of the eventual symbol for <a href="/wiki/0" title="0">zero</a>. The Arabic term for zero is <span title="Arabic-language romanization"><i lang="ar-Latn">ṣifr</i></span> (<span title="Arabic-language text"><span lang="ar" dir="rtl">صفر</span></span>), transliterated into Latin as <span title="Latin-language text"><i lang="la">cifra</i></span>, which became the English word <i><a href="/wiki/Cipher" title="Cipher">cipher</a></i>. </p><p>From the 980s, Gerbert of <a href="/wiki/Aurillac" title="Aurillac">Aurillac</a> (later <a href="/wiki/Pope_Sylvester_II" title="Pope Sylvester II">Pope Sylvester II</a>) used his position to spread knowledge of the numerals in Europe. Gerbert studied in <a href="/wiki/Barcelona" title="Barcelona">Barcelona</a> in his youth. He was known to have requested mathematical treatises concerning the <a href="/wiki/Astrolabe" title="Astrolabe">astrolabe</a> from <a href="/wiki/Lupitus_of_Barcelona" title="Lupitus of Barcelona">Lupitus of Barcelona</a> after he had returned to France.<sup id="cite_ref-:1_13-1" class="reference"><a href="#cite_note-:1-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>The reception of Arabic numerals in the West was gradual and lukewarm, as other numeral systems circulated in addition to the older Roman numbers. As a discipline, the first to adopt Arabic numerals as part of their own writings were astronomers and astrologists, evidenced from manuscripts surviving from mid-12th-century Bavaria. Reinher of Paderborn (1140–1190) used the numerals in his calendrical tables to calculate the dates of <a href="/wiki/Easter" title="Easter">Easter</a> more easily in his text <i><span title="Latin-language text"><i lang="la">Computus emendatus</i></span></i>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Italy">Italy</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=4" title="Edit section: Italy"><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:Liber_abbaci_magliab_f124r.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Liber_abbaci_magliab_f124r.jpg/220px-Liber_abbaci_magliab_f124r.jpg" decoding="async" width="220" height="336" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Liber_abbaci_magliab_f124r.jpg/330px-Liber_abbaci_magliab_f124r.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Liber_abbaci_magliab_f124r.jpg/440px-Liber_abbaci_magliab_f124r.jpg 2x" data-file-width="744" data-file-height="1137" /></a><figcaption>A page of the <i>Liber Abaci</i>. The list on the right shows the <a href="/wiki/Fibonacci_sequence" title="Fibonacci sequence">Fibonacci sequence</a>: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377. The 2, 8, and 9 resemble Arabic numerals more than <a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a> or <a href="/wiki/Indian_numerals" class="mw-redirect" title="Indian numerals">Indian numerals</a></figcaption></figure> <p><a href="/wiki/Leonardo_Fibonacci" class="mw-redirect" title="Leonardo Fibonacci">Leonardo Fibonacci</a> was a <a href="/wiki/Republic_of_Pisa" title="Republic of Pisa">Pisan</a> mathematician who had studied in the Pisan trading colony of <a href="/wiki/B%C3%A9ja%C3%AFa" title="Béjaïa">Bugia</a>, in what is now <a href="/wiki/Algeria" title="Algeria">Algeria</a>,<sup id="cite_ref-K._K._Tung_15-0" class="reference"><a href="#cite_note-K._K._Tung-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> and he endeavored to promote the numeral system in Europe with his 1202 book <i><span title="Latin-language text"><i lang="la"><a href="/wiki/Liber_Abaci" title="Liber Abaci">Liber Abaci</a></i></span></i>: </p> <blockquote><p>When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it.</p></blockquote> <p>The <i><span title="Latin-language text"><i lang="la">Liber Abaci</i></span></i><span class="nowrap" style="padding-left:0.1em;">'</span>s analysis highlighting the advantages of positional notation was widely influential. Likewise, Fibonacci's use of the Béjaïa digits in his exposition ultimately led to their widespread adoption in Europe.<sup id="cite_ref-:0_16-0" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> Fibonacci's work coincided with the European <a href="/wiki/Commercial_revolution" title="Commercial revolution">commercial revolution</a> of the 12th and 13th centuries centered in Italy. Positional notation facilitated complex calculations (such as currency conversion) to be completed more quickly than was possible with the Roman system. In addition, the system could handle larger numbers, did not require a separate reckoning tool, and allowed the user to check their work without repeating the entire procedure. Late medieval Italian merchants did not stop using Roman numerals or other reckoning tools: instead, Arabic numerals were adopted for use in addition to their preexisting methods.<sup id="cite_ref-:0_16-1" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Europe">Europe</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=5" title="Edit section: Europe"><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:Ms.Thott.290.2%C2%BA_150v.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Ms.Thott.290.2%C2%BA_150v.jpg/220px-Ms.Thott.290.2%C2%BA_150v.jpg" decoding="async" width="220" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Ms.Thott.290.2%C2%BA_150v.jpg/330px-Ms.Thott.290.2%C2%BA_150v.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Ms.Thott.290.2%C2%BA_150v.jpg/440px-Ms.Thott.290.2%C2%BA_150v.jpg 2x" data-file-width="1334" data-file-height="2000" /></a><figcaption>A German manuscript page teaching use of Arabic numerals (<a href="/wiki/Hans_Talhoffer" title="Hans Talhoffer">Talhoffer</a> Thott, 1459), presented together with the <a href="/wiki/Hebrew_alphabet" title="Hebrew alphabet">Hebrew alphabet</a> and <a href="/wiki/Astrology" title="Astrology">astrology</a>.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:EuropeanFormOfArabianDigits.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/EuropeanFormOfArabianDigits.png/330px-EuropeanFormOfArabianDigits.png" decoding="async" width="330" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/EuropeanFormOfArabianDigits.png/495px-EuropeanFormOfArabianDigits.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/EuropeanFormOfArabianDigits.png/660px-EuropeanFormOfArabianDigits.png 2x" data-file-width="1486" data-file-height="917" /></a><figcaption>Table of numerals in many variants, 1757, by <a href="/wiki/Jean-%C3%89tienne_Montucla" title="Jean-Étienne Montucla">Jean-Étienne Montucla</a></figcaption></figure> <p>By the late 14th century, only a few texts using Arabic numerals appeared outside of Italy. This suggests that the use of Arabic numerals in commercial practice, and the significant advantage they conferred, remained a virtual Italian monopoly until the late 15th century.<sup id="cite_ref-:0_16-2" class="reference"><a href="#cite_note-:0-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> This may in part have been due to language barriers: although Fibonacci's <i><span title="Latin-language text"><i lang="la">Liber Abaci</i></span></i> was written in Latin, the Italian abacus traditions were predominantly written in Italian vernaculars that circulated in the private collections of abacus schools or individuals. </p><p>The European acceptance of the numerals was accelerated by the invention of the <a href="/wiki/Printing_press" title="Printing press">printing press</a>, and they became widely known during the 15th century. Their use grew steadily in other centers of finance and trade such as Lyon.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Early evidence of their use in <a href="/wiki/Great_Britain_in_the_Middle_Ages" class="mw-redirect" title="Great Britain in the Middle Ages">Britain</a> includes: an equal hour horary <a href="/wiki/Quadrant_(instrument)" title="Quadrant (instrument)">quadrant</a> from 1396,<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> in England, a 1445 inscription on the tower of <a href="/wiki/Heathfield_and_Waldron" title="Heathfield and Waldron">Heathfield</a> Church, <a href="/wiki/Sussex" title="Sussex">Sussex</a>; a 1448 inscription on a wooden lych-gate of <a href="/wiki/Bray,_Berkshire" title="Bray, Berkshire">Bray</a> Church, <a href="/wiki/Berkshire" title="Berkshire">Berkshire</a>; and a 1487 inscription on the belfry door at <a href="/wiki/Piddletrenthide" title="Piddletrenthide">Piddletrenthide</a> church, <a href="/wiki/Dorset" title="Dorset">Dorset</a>; and in <a href="/wiki/Scotland" title="Scotland">Scotland</a> a 1470 inscription on the tomb of the first Earl of Huntly in <a href="/wiki/Elgin,_Moray" title="Elgin, Moray">Elgin</a> Cathedral.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> In central Europe, the <a href="/wiki/King_of_Hungary" title="King of Hungary">King of Hungary</a> <a href="/wiki/Ladislaus_the_Posthumous" title="Ladislaus the Posthumous">Ladislaus the Posthumous</a>, started the use of Arabic numerals, which appear for the first time in a royal document of 1456.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p>By the mid-16th century, they had been widely adopted in Europe, and by 1800 had almost completely replaced the use of counting boards and Roman numerals in accounting. Roman numerals were mostly relegated to niche uses such as years and numbers on clock faces. </p> <div class="mw-heading mw-heading4"><h4 id="Russia">Russia</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=6" title="Edit section: Russia"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Prior to the introduction of Arabic numerals, <a href="/wiki/Cyrillic_numerals" title="Cyrillic numerals">Cyrillic numerals</a>, derived from the <a href="/wiki/Early_Cyrillic_alphabet" title="Early Cyrillic alphabet">Cyrillic alphabet</a>, were used by <a href="/wiki/South_Slavs" title="South Slavs">South</a> and <a href="/wiki/East_Slavs" title="East Slavs">East Slavs</a>. The system was used in Russia as late as the early 18th century, although it was formally replaced in official use by <a href="/wiki/Peter_the_Great" title="Peter the Great">Peter the Great</a> in 1699.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Reasons for Peter's switch from the alphanumerical system are believed to go beyond a surface-level desire to imitate the West. Historian Peter Brown makes arguments for sociological, militaristic, and pedagogical reasons for the change. At a broad, societal level, Russian merchants, soldiers, and officials increasingly came into contact with counterparts from the West and became familiar with the communal use of Arabic numerals. Peter also covertly travelled throughout Northern Europe from 1697 to 1698 <a href="/wiki/Grand_Embassy_of_Peter_the_Great" title="Grand Embassy of Peter the Great">during his Grand Embassy</a> and was likely informally exposed to Western mathematics during this time.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> The Cyrillic system was found to be inferior for calculating practical <a href="/wiki/Kinematic" class="mw-redirect" title="Kinematic">kinematic</a> values, such as the trajectories and parabolic flight patterns of artillery. With its use, it was difficult to keep pace with Arabic numerals in the growing field of <a href="/wiki/Ballistics" title="Ballistics">ballistics</a>, whereas Western mathematicians such as <a href="/wiki/John_Napier" title="John Napier">John Napier</a> had been publishing on the topic since 1614.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="China">China</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=7" title="Edit section: China"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Shang_numerals_to_brahmi.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Shang_numerals_to_brahmi.jpg/250px-Shang_numerals_to_brahmi.jpg" decoding="async" width="250" height="117" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/06/Shang_numerals_to_brahmi.jpg/375px-Shang_numerals_to_brahmi.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/0/06/Shang_numerals_to_brahmi.jpg 2x" data-file-width="453" data-file-height="212" /></a><figcaption>Chinese <a href="/wiki/Shang_dynasty" title="Shang dynasty">Shang dynasty</a> oracle bone numerals of 14th century B.C.<sup id="cite_ref-Taylor_&_Francis_24-0" class="reference"><a href="#cite_note-Taylor_&_Francis-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-The_Shorter_Science_p._6_25-0" class="reference"><a href="#cite_note-The_Shorter_Science_p._6-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The Chinese <a href="/wiki/Shang_dynasty" title="Shang dynasty">Shang dynasty</a> numerals from the 14th century B.C. predates the Indian Brahmi numerals by over 1000 years and shows substantial similarity to the Brahmi numerals. Similar to the modern Arabic numerals, the Shang dynasty numeral system was also decimal based and <a href="/wiki/Positional_notation" title="Positional notation">positional</a>.<sup id="cite_ref-Taylor_&_Francis_24-1" class="reference"><a href="#cite_note-Taylor_&_Francis-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-The_Shorter_Science_p._6_25-1" class="reference"><a href="#cite_note-The_Shorter_Science_p._6-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>While positional Chinese numeral systems such as the <a href="/wiki/Counting_rods" title="Counting rods">counting rod system</a> and <a href="/wiki/Suzhou_numerals" title="Suzhou numerals">Suzhou numerals</a> had been in use prior to the introduction of modern Arabic numerals,<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> the externally-developed system was eventually introduced to medieval China by the <a href="/wiki/Hui_people" title="Hui people">Hui people</a>. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese <a href="/wiki/Jesuits" title="Jesuits">Jesuits</a>.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Encoding">Encoding</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=8" title="Edit section: Encoding"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The ten Arabic numerals are encoded in virtually every character set designed for electric, radio, and digital communication, such as <a href="/wiki/Morse_code" title="Morse code">Morse code</a>. They are encoded in <a href="/wiki/ASCII" title="ASCII">ASCII</a> (and therefore in <a href="/wiki/Unicode" title="Unicode">Unicode</a> encodings<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup>) at positions 0x30 to 0x39. <a href="/wiki/Mask_(computing)" title="Mask (computing)">Masking</a> all but the four least-significant binary digits gives the value of the decimal digit, a design decision facilitating the digitization of text onto early computers. <a href="/wiki/EBCDIC" title="EBCDIC">EBCDIC</a> used a different offset, but also possessed the aforementioned masking property. </p> <table class="wikitable"> <tbody><tr> <th rowspan="2"> </th> <th colspan="4">ASCII </th> <th rowspan="2">Unicode </th> <th rowspan="2">EBCDIC<br />hex </th></tr> <tr> <th>binary </th> <th>octal </th> <th>decimal </th> <th>hex </th></tr> <tr> <th>0 </th> <td>0011 0000 </td> <td>060 </td> <td>48 </td> <td>30 </td> <td>U+0030 DIGIT ZERO </td> <td>F0 </td></tr> <tr> <th>1 </th> <td>0011 0001 </td> <td>061 </td> <td>49 </td> <td>31 </td> <td>U+0031 DIGIT ONE </td> <td>F1 </td></tr> <tr> <th>2 </th> <td>0011 0010 </td> <td>062 </td> <td>50 </td> <td>32 </td> <td>U+0032 DIGIT TWO </td> <td>F2 </td></tr> <tr> <th>3 </th> <td>0011 0011 </td> <td>063 </td> <td>51 </td> <td>33 </td> <td>U+0033 DIGIT THREE </td> <td>F3 </td></tr> <tr> <th>4 </th> <td>0011 0100 </td> <td>064 </td> <td>52 </td> <td>34 </td> <td>U+0034 DIGIT FOUR </td> <td>F4 </td></tr> <tr> <th>5 </th> <td>0011 0101 </td> <td>065 </td> <td>53 </td> <td>35 </td> <td>U+0035 DIGIT FIVE </td> <td>F5 </td></tr> <tr> <th>6 </th> <td>0011 0110 </td> <td>066 </td> <td>54 </td> <td>36 </td> <td>U+0036 DIGIT SIX </td> <td>F6 </td></tr> <tr> <th>7 </th> <td>0011 0111 </td> <td>067 </td> <td>55 </td> <td>37 </td> <td>U+0037 DIGIT SEVEN </td> <td>F7 </td></tr> <tr> <th>8 </th> <td>0011 1000 </td> <td>070 </td> <td>56 </td> <td>38 </td> <td>U+0038 DIGIT EIGHT </td> <td>F8 </td></tr> <tr> <th>9 </th> <td>0011 1001 </td> <td>071 </td> <td>57 </td> <td>39 </td> <td>U+0039 DIGIT NINE </td> <td>F9 </td></tr></tbody></table> <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=Arabic_numerals&action=edit&section=9" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Arabic_numeral_variations" title="Arabic numeral variations">Arabic numeral variations</a></li> <li><a href="/wiki/Regional_handwriting_variation#Arabic_numerals" title="Regional handwriting variation">Regional variations in modern handwritten Arabic numerals</a></li> <li><a href="/wiki/Seven-segment_display" title="Seven-segment display">Seven-segment display</a></li> <li><a href="/wiki/Text_figures" title="Text figures">Text figures</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=10" title="Edit section: Footnotes"><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 reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.unicode.org/terminology/digits.html">Terminology for Digits</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20211026112524/https://www.unicode.org/terminology/digits.html">Archived</a> 26 October 2021 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. Unicode Consortium.</span> </li> <li id="cite_note-AHB-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-AHB_2-0">^</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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ahdictionary.com/word/search.html?id=A5414100">"Arabic numeral"</a>. <i><a href="/wiki/American_Heritage_Dictionary" class="mw-redirect" title="American Heritage Dictionary">American Heritage Dictionary</a></i>. Houghton Mifflin Harcourt. 2020. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20211121235943/https://www.ahdictionary.com/word/search.html?id=A5414100">Archived</a> from the original on 21 November 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">21 November</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=American+Heritage+Dictionary&rft.atitle=Arabic+numeral&rft.date=2020&rft_id=https%3A%2F%2Fwww.ahdictionary.com%2Fword%2Fsearch.html%3Fid%3DA5414100&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">"Arabic", <i>Oxford English Dictionary</i>, 2nd edition</span> </li> <li id="cite_note-Danna_2021_pp._5–48-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Danna_2021_pp._5–48_4-0">^</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 January 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%E2%80%93Arabic+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%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-:2-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_5-1"><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="CITEREFBurnett2002" class="citation book cs1">Burnett, Charles (2002). Dold-Samplonius, Yvonne; Van Dalen, Benno; Dauben, Joseph; Folkerts, Menso (eds.). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=AG2XBCmxYcUC"><i>From China to Paris: 2000 Years Transmission of Mathematical Ideas</i></a>. Franz Steiner Verlag. pp. 237–288. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-515-08223-5" title="Special:BookSources/978-3-515-08223-5"><bdi>978-3-515-08223-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=From+China+to+Paris%3A+2000+Years+Transmission+of+Mathematical+Ideas&rft.pages=237-288&rft.pub=Franz+Steiner+Verlag&rft.date=2002&rft.isbn=978-3-515-08223-5&rft.aulast=Burnett&rft.aufirst=Charles&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DAG2XBCmxYcUC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a href="#CITEREFKunitzsch2003">Kunitzsch 2003</a>, p. 7: <span title="French-language text"><i lang="fr">"Les personnes qui se sont occupées de la science du calcul n'ont pas été d'accord sur une partie des formes de ces neuf signes; mais la plupart d'entre elles sont convenues de les former comme il suit."</i></span></span> </li> <li id="cite_note-FOOTNOTEKunitzsch20035-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKunitzsch20035_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKunitzsch2003">Kunitzsch 2003</a>, p. 5.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a href="#CITEREFKunitzsch2003">Kunitzsch 2003</a>, pp. 12–13: "While specimens of Western Arabic numerals from the early period—the tenth to thirteenth centuries—are still not available, we know at least that Hindu reckoning (called <i>ḥisāb al-ghubār</i>) was known in the West from the 10th century onward..."</span> </li> <li id="cite_note-FOOTNOTEKunitzsch20038-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKunitzsch20038_9-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKunitzsch2003">Kunitzsch 2003</a>, p. 8.</span> </li> <li id="cite_note-FOOTNOTEKunitzsch200310-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKunitzsch200310_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKunitzsch2003">Kunitzsch 2003</a>, p. 10.</span> </li> <li id="cite_note-FOOTNOTEKunitzsch20037–8-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEKunitzsch20037–8_11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFKunitzsch2003">Kunitzsch 2003</a>, pp. 7–8.</span> </li> <li id="cite_note-ifrah-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-ifrah_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIfrah1998" class="citation book cs1">Ifrah, Georges (1998). <i>The universal history of numbers: from prehistory to the invention of the computer</i>. Translated by Bellos, David. London: Harvill. pp. 356–357. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-860-46324-2" title="Special:BookSources/978-1-860-46324-2"><bdi>978-1-860-46324-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+universal+history+of+numbers%3A+from+prehistory+to+the+invention+of+the+computer&rft.place=London&rft.pages=356-357&rft.pub=Harvill&rft.date=1998&rft.isbn=978-1-860-46324-2&rft.aulast=Ifrah&rft.aufirst=Georges&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-:1-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_13-1"><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="CITEREFNothaft2020" class="citation journal cs1">Nothaft, C. Philipp E. (3 May 2020). <a rel="nofollow" class="external text" href="https://doi.org/10.1080/26375451.2020.1726050">"Medieval Europe's satanic ciphers: on the genesis of a modern myth"</a>. <i>British Journal for the History of Mathematics</i>. <b>35</b> (2): 107–136. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F26375451.2020.1726050">10.1080/26375451.2020.1726050</a>. <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/2637-5451">2637-5451</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:213113566">213113566</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=British+Journal+for+the+History+of+Mathematics&rft.atitle=Medieval+Europe%27s+satanic+ciphers%3A+on+the+genesis+of+a+modern+myth&rft.volume=35&rft.issue=2&rft.pages=107-136&rft.date=2020-05-03&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A213113566%23id-name%3DS2CID&rft.issn=2637-5451&rft_id=info%3Adoi%2F10.1080%2F26375451.2020.1726050&rft.aulast=Nothaft&rft.aufirst=C.+Philipp+E.&rft_id=https%3A%2F%2Fdoi.org%2F10.1080%2F26375451.2020.1726050&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></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="CITEREFHerold2005" class="citation web cs1 cs1-prop-foreign-lang-source">Herold, Werner (2005). <a rel="nofollow" class="external text" href="https://ixtheo.de/Record/164418110X">"Der "computus emendatus" des Reinher von Paderborn"</a>. <i>ixtheo.de</i> (in German). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220730020351/https://ixtheo.de/Record/164418110X">Archived</a> from the original on 30 July 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">29 July</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ixtheo.de&rft.atitle=Der+%22computus+emendatus%22+des+Reinher+von+Paderborn&rft.date=2005&rft.aulast=Herold&rft.aufirst=Werner&rft_id=https%3A%2F%2Fixtheo.de%2FRecord%2F164418110X&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-K._K._Tung-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-K._K._Tung_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTung2016" class="citation book cs1">Tung, K. K. (2016). <i>Topics in Mathematical Modeling</i>. Princeton University Press. p. 1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4008-8405-6" title="Special:BookSources/978-1-4008-8405-6"><bdi>978-1-4008-8405-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Topics+in+Mathematical+Modeling&rft.pages=1&rft.pub=Princeton+University+Press&rft.date=2016&rft.isbn=978-1-4008-8405-6&rft.aulast=Tung&rft.aufirst=K.+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-:0-16"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_16-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_16-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:0_16-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDanna2021" class="citation thesis cs1">Danna, Raffaele (12 July 2021). <a rel="nofollow" class="external text" href="https://www.repository.cam.ac.uk/handle/1810/325042"><i>The Spread of Hindu–Arabic Numerals in the European Tradition of Practical Arithmetic: a Socio-Economic Perspective (13th–16th centuries)</i></a> (PhD thesis). University of Cambridge. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.17863%2Fcam.72497">10.17863/cam.72497</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210727110444/https://www.repository.cam.ac.uk/handle/1810/325042">Archived</a> from the original on 27 July 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">29 July</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=The+Spread+of+Hindu%E2%80%93Arabic+Numerals+in+the+European+Tradition+of+Practical+Arithmetic%3A+a+Socio-Economic+Perspective+%2813th%E2%80%9316th+centuries%29&rft.degree=PhD&rft.inst=University+of+Cambridge&rft.date=2021-07-12&rft_id=info%3Adoi%2F10.17863%2Fcam.72497&rft.aulast=Danna&rft.aufirst=Raffaele&rft_id=https%3A%2F%2Fwww.repository.cam.ac.uk%2Fhandle%2F1810%2F325042&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDannaIoriMina2022" class="citation ssrn cs1">Danna, Raffaele; Iori, Martina; Mina, Andrea (22 June 2022). "A Numerical Revolution: The Diffusion of Practical Mathematics and the Growth of Pre-modern European Economies". <a href="/wiki/SSRN_(identifier)" class="mw-redirect" title="SSRN (identifier)">SSRN</a> <a rel="nofollow" class="external text" href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4143442">4143442</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=Social+Science+Research+Network&rft.atitle=A+Numerical+Revolution%3A+The+Diffusion+of+Practical+Mathematics+and+the+Growth+of+Pre-modern+European+Economies&rft.date=2022-06-22&rft_id=https%3A%2F%2Fpapers.ssrn.com%2Fsol3%2Fpapers.cfm%3Fabstract_id%3D4143442%23id-name%3DSSRN&rft.aulast=Danna&rft.aufirst=Raffaele&rft.au=Iori%2C+Martina&rft.au=Mina%2C+Andrea&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="http://www.abc.net.au/news/2011-11-09/one-man27s-trash-is-another27s-centuries-old-treasure/3654974">"14th century timepiece unearthed in Qld farm shed"</a>. <i>ABC News</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120229232807/http://www.abc.net.au/news/2011-11-09/one-man27s-trash-is-another27s-centuries-old-treasure/3654974">Archived</a> from the original on 29 February 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">10 November</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ABC+News&rft.atitle=14th+century+timepiece+unearthed+in+Qld+farm+shed&rft_id=http%3A%2F%2Fwww.abc.net.au%2Fnews%2F2011-11-09%2Fone-man27s-trash-is-another27s-centuries-old-treasure%2F3654974&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" 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">See G. F. Hill, <i>The Development of Arabic Numerals in Europe</i>, for more examples.</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text">Erdélyi: Magyar művelődéstörténet 1-2. kötet. Kolozsvár, 1913, 1918.</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="CITEREFConatser_Segura2020" class="citation thesis cs1">Conatser Segura, Sylvia (26 May 2020). <a rel="nofollow" class="external text" href="https://baylor-ir.tdl.org/handle/2104/10914"><i>Orthographic Reform and Language Planning in Russian History</i></a> (Honors thesis). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220730020351/https://baylor-ir.tdl.org/handle/2104/10914">Archived</a> from the original on 30 July 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">29 July</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Orthographic+Reform+and+Language+Planning+in+Russian+History&rft.degree=Honors&rft.date=2020-05-26&rft.aulast=Conatser+Segura&rft.aufirst=Sylvia&rft_id=https%3A%2F%2Fbaylor-ir.tdl.org%2Fhandle%2F2104%2F10914&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" 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 id="CITEREFBrown2012" class="citation journal cs1">Brown, Peter B. (2012). <a rel="nofollow" class="external text" href="https://brill.com/view/journals/ruhi/39/4/article-p393_1.xml">"Muscovite Arithmetic in Seventeenth-Century Russian Civilization: Is It Not Time to Discard the "Backwardness" Label?"</a>. <i>Russian History</i>. <b>39</b> (4): 393–459. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1163%2F48763316-03904001">10.1163/48763316-03904001</a>. <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/0094-288X">0094-288X</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220730020352/https://brill.com/view/journals/ruhi/39/4/article-p393_1.xml">Archived</a> from the original on 30 July 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">29 July</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Russian+History&rft.atitle=Muscovite+Arithmetic+in+Seventeenth-Century+Russian+Civilization%3A+Is+It+Not+Time+to+Discard+the+%22Backwardness%22+Label%3F&rft.volume=39&rft.issue=4&rft.pages=393-459&rft.date=2012&rft_id=info%3Adoi%2F10.1163%2F48763316-03904001&rft.issn=0094-288X&rft.aulast=Brown&rft.aufirst=Peter+B.&rft_id=https%3A%2F%2Fbrill.com%2Fview%2Fjournals%2Fruhi%2F39%2F4%2Farticle-p393_1.xml&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLockwood1978" class="citation journal cs1">Lockwood, E. H. (October 1978). <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/mathematical-discoveries-16001750-by-p-l-griffiths-pp-121-275-1977-sbn-0-7223-1006-4-stockwell/444F9C9ADA0D2634DDA7C34EF5F08F66">"Mathematical discoveries 1600-1750, by P. L. Griffiths. Pp 121. £2·75. 1977. ISBN 0 7223 1006 4 (Stockwell)"</a>. <i>The Mathematical Gazette</i>. <b>62</b> (421): 219. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F3616704">10.2307/3616704</a>. <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/0025-5572">0025-5572</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/3616704">3616704</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220730020352/https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/mathematical-discoveries-16001750-by-p-l-griffiths-pp-121-275-1977-sbn-0-7223-1006-4-stockwell/444F9C9ADA0D2634DDA7C34EF5F08F66">Archived</a> from the original on 30 July 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">29 July</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Mathematical+Gazette&rft.atitle=Mathematical+discoveries+1600-1750%2C+by+P.+L.+Griffiths.+Pp+121.+%C2%A32%C2%B775.+1977.+ISBN+0+7223+1006+4+%28Stockwell%29&rft.volume=62&rft.issue=421&rft.pages=219&rft.date=1978-10&rft.issn=0025-5572&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F3616704%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F3616704&rft.aulast=Lockwood&rft.aufirst=E.+H.&rft_id=https%3A%2F%2Fwww.cambridge.org%2Fcore%2Fjournals%2Fmathematical-gazette%2Farticle%2Fabs%2Fmathematical-discoveries-16001750-by-p-l-griffiths-pp-121-275-1977-sbn-0-7223-1006-4-stockwell%2F444F9C9ADA0D2634DDA7C34EF5F08F66&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-Taylor_&_Francis-24"><span class="mw-cite-backlink">^ <a href="#cite_ref-Taylor_&_Francis_24-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Taylor_&_Francis_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="CITEREFCampbellHiggins1984" class="citation book cs1">Campbell, Douglas M.; Higgins, John C. (1984). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=PFNsm_IaymYC&dq=shang+numerals+brahmi&pg=PA31"><i>Mathematics: People, Problems, Results</i></a>. 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=book&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=Campbell&rft.aufirst=Douglas+M.&rft.au=Higgins%2C+John+C.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DPFNsm_IaymYC%26dq%3Dshang%2Bnumerals%2Bbrahmi%26pg%3DPA31&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-The_Shorter_Science_p._6-25"><span class="mw-cite-backlink">^ <a href="#cite_ref-The_Shorter_Science_p._6_25-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-The_Shorter_Science_p._6_25-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">The Shorter Science & Civilisation in China Vol 2, An abridgement by Colin Ronan of Joseph Needham's original text, Table 20, p. 6, Cambridge University Press <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-23582-0" title="Special:BookSources/0-521-23582-0">0-521-23582-0</a></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShell-Gellasch2015" class="citation book cs1">Shell-Gellasch, Amy (2015). <i>Algebra in context : introductory algebra from origins to applications</i>. J. B. Thoo. Baltimore. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4214-1728-8" title="Special:BookSources/978-1-4214-1728-8"><bdi>978-1-4214-1728-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Algebra+in+context+%3A+introductory+algebra+from+origins+to+applications&rft.place=Baltimore&rft.date=2015&rft.isbn=978-1-4214-1728-8&rft.aulast=Shell-Gellasch&rft.aufirst=Amy&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUy2003" class="citation journal cs1">Uy, Frederick L. (January 2003). "The Chinese Numeration System and Place Value". <i>Teaching Children Mathematics</i>. <b>9</b> (5): 243–247. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5951%2Ftcm.9.5.0243">10.5951/tcm.9.5.0243</a>. <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/1073-5836">1073-5836</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Teaching+Children+Mathematics&rft.atitle=The+Chinese+Numeration+System+and+Place+Value&rft.volume=9&rft.issue=5&rft.pages=243-247&rft.date=2003-01&rft_id=info%3Adoi%2F10.5951%2Ftcm.9.5.0243&rft.issn=1073-5836&rft.aulast=Uy&rft.aufirst=Frederick+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSelin1997" class="citation book cs1"><a href="/wiki/Helaine_Selin" title="Helaine Selin">Selin, Helaine</a>, ed. (1997). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=raKRY3KQspsC&pg=PA198"><i>Encyclopaedia of the history of science, technology, and medicine in non-western cultures</i></a>. Springer. p. 198. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7923-4066-9" title="Special:BookSources/978-0-7923-4066-9"><bdi>978-0-7923-4066-9</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151027201326/https://books.google.com/books?id=raKRY3KQspsC&pg=PA198">Archived</a> from the original on 27 October 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">18 October</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Encyclopaedia+of+the+history+of+science%2C+technology%2C+and+medicine+in+non-western+cultures&rft.pages=198&rft.pub=Springer&rft.date=1997&rft.isbn=978-0-7923-4066-9&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DraKRY3KQspsC%26pg%3DPA198&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMeuleman2002" class="citation book cs1">Meuleman, Johan H. (2002). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=YNArhqy4emwC&pg=PA272"><i>Islam in the era of globalization: Muslim attitudes towards modernity and identity</i></a>. Psychology Press. p. 272. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7007-1691-3" title="Special:BookSources/978-0-7007-1691-3"><bdi>978-0-7007-1691-3</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151027201326/https://books.google.com/books?id=YNArhqy4emwC&pg=PA272">Archived</a> from the original on 27 October 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">18 October</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Islam+in+the+era+of+globalization%3A+Muslim+attitudes+towards+modernity+and+identity&rft.pages=272&rft.pub=Psychology+Press&rft.date=2002&rft.isbn=978-0-7007-1691-3&rft.aulast=Meuleman&rft.aufirst=Johan+H.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DYNArhqy4emwC%26pg%3DPA272&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeng_Yoke_Ho2000" class="citation book cs1">Peng Yoke Ho (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=_P6C4JO4JCUC&pg=PA106"><i>Li, Qi and Shu: An Introduction to Science and Civilization in China</i></a>. Mineola, NY: Courier Dover Publications. p. 106. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-486-41445-4" title="Special:BookSources/978-0-486-41445-4"><bdi>978-0-486-41445-4</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151027201326/https://books.google.com/books?id=_P6C4JO4JCUC&pg=PA106">Archived</a> from the original on 27 October 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">18 October</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Li%2C+Qi+and+Shu%3A+An+Introduction+to+Science+and+Civilization+in+China&rft.place=Mineola%2C+NY&rft.pages=106&rft.pub=Courier+Dover+Publications&rft.date=2000&rft.isbn=978-0-486-41445-4&rft.au=Peng+Yoke+Ho&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D_P6C4JO4JCUC%26pg%3DPA106&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</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="https://www.unicode.org/charts/PDF/U0000.pdf">"The Unicode Standard, Version 13.0"</a> <span class="cs1-format">(PDF)</span>. <i>unicode.org</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20010602232829/http://www.unicode.org:80/charts/PDF/U0000.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2 June 2001<span class="reference-accessdate">. Retrieved <span class="nowrap">1 September</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=unicode.org&rft.atitle=The+Unicode+Standard%2C+Version+13.0&rft_id=https%3A%2F%2Fwww.unicode.org%2Fcharts%2FPDF%2FU0000.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=11" title="Edit section: Sources"><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="CITEREFKunitzsch2003" class="citation book cs1">Kunitzsch, Paul (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=_AUtLNtg3nsC&pg=PA3">"The Transmission of Hindu–Arabic Numerals Reconsidered"</a>. In J. P. Hogendijk; A. I. Sabra (eds.). <i>The Enterprise of Science in Islam: New Perspectives</i>. MIT Press. pp. 3–22. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-262-19482-2" title="Special:BookSources/978-0-262-19482-2"><bdi>978-0-262-19482-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Transmission+of+Hindu%E2%80%93Arabic+Numerals+Reconsidered&rft.btitle=The+Enterprise+of+Science+in+Islam%3A+New+Perspectives&rft.pages=3-22&rft.pub=MIT+Press&rft.date=2003&rft.isbn=978-0-262-19482-2&rft.aulast=Kunitzsch&rft.aufirst=Paul&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D_AUtLNtg3nsC%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" 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=Arabic_numerals&action=edit&section=12" 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="CITEREFBurnett2006" class="citation journal cs1">Burnett, Charles (2006). "The Semantics of Indian Numerals in Arabic, Greek and Latin". <i>Journal of Indian Philosophy</i>. <b>34</b> (1–2). Springer-Netherlands: 15–30. <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%2Fs10781-005-8153-z">10.1007/s10781-005-8153-z</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:170783929">170783929</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Indian+Philosophy&rft.atitle=The+Semantics+of+Indian+Numerals+in+Arabic%2C+Greek+and+Latin&rft.volume=34&rft.issue=1%E2%80%932&rft.pages=15-30&rft.date=2006&rft_id=info%3Adoi%2F10.1007%2Fs10781-005-8153-z&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A170783929%23id-name%3DS2CID&rft.aulast=Burnett&rft.aufirst=Charles&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHayashi1995" class="citation book cs1">Hayashi, Takao (1995). <i>The Bakhshālī Manuscript: An Ancient Indian Mathematical Treatise</i>. Groningen, Netherlands: Egbert Forsten. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/906980087X" title="Special:BookSources/906980087X"><bdi>906980087X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Bakhsh%C4%81l%C4%AB+Manuscript%3A+An+Ancient+Indian+Mathematical+Treatise&rft.place=Groningen%2C+Netherlands&rft.pub=Egbert+Forsten&rft.date=1995&rft.isbn=906980087X&rft.aulast=Hayashi&rft.aufirst=Takao&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIfrah2000" class="citation book cs1"><a href="/wiki/Georges_Ifrah" title="Georges Ifrah">Ifrah, Georges</a> (2000). <i>A Universal History of Numbers: From Prehistory to Computers</i>. New York: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0471393401" title="Special:BookSources/0471393401"><bdi>0471393401</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Universal+History+of+Numbers%3A+From+Prehistory+to+Computers&rft.place=New+York&rft.pub=Wiley&rft.date=2000&rft.isbn=0471393401&rft.aulast=Ifrah&rft.aufirst=Georges&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKatz2007" class="citation book cs1">Katz, Victor J., ed. (20 July 2007). <i>The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook</i>. Princeton, New Jersey: Princeton University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0691114859" title="Special:BookSources/978-0691114859"><bdi>978-0691114859</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematics+of+Egypt%2C+Mesopotamia%2C+China%2C+India%2C+and+Islam%3A+A+Sourcebook&rft.place=Princeton%2C+New+Jersey&rft.pub=Princeton+University+Press&rft.date=2007-07-20&rft.isbn=978-0691114859&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F189273c0">"Mathematics in South Asia"</a>. <i>Nature</i>. <b>189</b> (4761): 273. 1961. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1961Natur.189S.273.">1961Natur.189S.273.</a>. <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/10.1038%2F189273c0">10.1038/189273c0</a></span>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4288165">4288165</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Mathematics+in+South+Asia&rft.volume=189&rft.issue=4761&rft.pages=273&rft.date=1961&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4288165%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1038%2F189273c0&rft_id=info%3Abibcode%2F1961Natur.189S.273.&rft_id=https%3A%2F%2Fdoi.org%2F10.1038%252F189273c0&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOre1988" class="citation book cs1">Ore, Oystein (1988). <a rel="nofollow" class="external text" href="https://archive.org/details/numbertheoryitsh0000orey/page/19">"Hindu–Arabic numerals"</a>. <i>Number Theory and Its History</i>. Dover. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/numbertheoryitsh0000orey/page/19">19–24</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0486656209" title="Special:BookSources/0486656209"><bdi>0486656209</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Hindu%E2%80%93Arabic+numerals&rft.btitle=Number+Theory+and+Its+History&rft.pages=19-24&rft.pub=Dover&rft.date=1988&rft.isbn=0486656209&rft.aulast=Ore&rft.aufirst=Oystein&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fnumbertheoryitsh0000orey%2Fpage%2F19&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArabic+numerals" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Arabic_numerals&action=edit&section=13" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist"><a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a> has media related to:<br /> <a href="https://commons.wikimedia.org/wiki/Arabic_numerals" class="extiw" title="commons:Arabic numerals"><span style="font-style:italic; font-weight:bold;">Arabic numerals</span></a> (<a href="https://commons.wikimedia.org/wiki/Category:Arabic_numerals" class="extiw" title="commons:Category:Arabic numerals">category</a>)</div></div> </div> <ul><li>Lam Lay Yong, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120321111930/http://sciences.aum.edu/~sbrown/Hindu%20Arabic%20and%20Chinese.pdf">"Development of Hindu Arabic and Traditional Chinese Arithmetic"</a>, <i>Chinese Science</i> 13 (1996): 35–54.</li> <li><a rel="nofollow" class="external text" href="http://www.historyworld.net/wrldhis/PlainTextHistories.asp?historyid=ab34">"Counting Systems and Numerals"</a>, <i>Historyworld</i>. Retrieved 11 December 2005.</li> <li><a rel="nofollow" class="external text" href="http://www.laputanlogic.com/articles/2003/06/01-95210802.html">The Evolution of Numbers</a>. 16 April 2005.</li> <li>O'Connor, J. J., and E. F. Robertson, <a rel="nofollow" class="external text" href="http://www-gap.dcs.st-and.ac.uk/%7Ehistory/HistTopics/Indian_numerals.html">Indian numerals</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150706140353/http://www-gap.dcs.st-and.ac.uk/%7Ehistory/HistTopics/Indian_numerals.html">Archived</a> 6 July 2015 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. November 2000.</li> <li>History of the numerals <ul><li><a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/HistTopics/Arabic_numerals/">Arabic numerals</a></li> <li><a rel="nofollow" class="external text" href="http://www.scit.wlv.ac.uk/~cm1993/maths/mm2217/han.htm">Hindu–Arabic numerals</a></li> <li><a rel="nofollow" class="external text" href="http://www.archimedes-lab.org/numeral.html">Numeral & Numbers' history and curiosities</a></li> <li><a rel="nofollow" class="external text" href="http://www.maa.org/publications/periodicals/convergence/gerbert-daurillac-and-the-march-of-spain-a-convergence-of-cultures-hindu-arabic-numerals">Gerbert d'Aurillac's early use of Hindu–Arabic numerals</a> at <a rel="nofollow" class="external text" href="http://www.maa.org/publications/periodicals/convergence">Convergence</a></li></ul></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style 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.navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></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 href="/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system">Hindu–Arabic numeral system</a></li> <li><a class="mw-selflink selflink">Arabic numerals</a> (<a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic numerals</a>, <a class="mw-selflink selflink">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 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"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q29961325#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div 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