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href="#Algebra"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Algebra</span> </div> </a> <ul id="toc-Algebra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Indukcija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Indukcija"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Indukcija</span> </div> </a> <ul id="toc-Indukcija-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Poznate_ličnosti_i_razvoj" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Poznate_ličnosti_i_razvoj"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Poznate ličnosti i razvoj</span> </div> </a> <button aria-controls="toc-Poznate_ličnosti_i_razvoj-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uključi/isključi podsekciju Poznate ličnosti i razvoj</span> </button> <ul id="toc-Poznate_ličnosti_i_razvoj-sublist" class="vector-toc-list"> <li id="toc-Omer_Hajjam" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Omer_Hajjam"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Omer Hajjam</span> </div> </a> <ul id="toc-Omer_Hajjam-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Šaraf_al-Din_al-Tusi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Šaraf_al-Din_al-Tusi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Šaraf al-Din al-Tusi</span> </div> </a> <ul id="toc-Šaraf_al-Din_al-Tusi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ostale_poznate_ličnosti" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ostale_poznate_ličnosti"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Ostale poznate ličnosti</span> </div> </a> <ul id="toc-Ostale_poznate_ličnosti-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Galerija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Galerija"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Galerija</span> </div> </a> <ul id="toc-Galerija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Također_pogledajte" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Također_pogledajte"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Također pogledajte</span> </div> </a> <ul id="toc-Također_pogledajte-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vanjski_linkovi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vanjski_linkovi"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Vanjski linkovi</span> </div> </a> <ul id="toc-Vanjski_linkovi-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="Sadržaj" 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="Uključi/isključi sadržaj" > <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">Uključi/isključi sadržaj</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">Matematika u srednjovjekovnom islamskom svijetu</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="Idi na članak na drugom jeziku. Dostupno na 29 jezika" > <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-29" 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">29 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar badge-Q17437798 badge-goodarticle mw-list-item" title="dobar članak"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA_%D9%81%D9%8A_%D8%B9%D8%B5%D8%B1_%D8%A7%D9%84%D8%AD%D8%B6%D8%A7%D8%B1%D8%A9_%D8%A7%D9%84%D8%A5%D8%B3%D9%84%D8%A7%D9%85%D9%8A%D8%A9" title="الرياضيات في عصر الحضارة الإسلامية – arapski" lang="ar" hreflang="ar" data-title="الرياضيات في عصر الحضارة الإسلامية" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Orta_%C9%99srl%C9%99rd%C9%99_%C4%B0slam_%C3%B6lk%C9%99l%C9%99rind%C9%99_riyaziyyat" title="Orta əsrlərdə İslam ölkələrində riyaziyyat – azerbejdžanski" lang="az" hreflang="az" data-title="Orta əsrlərdə İslam ölkələrində riyaziyyat" data-language-autonym="Azərbaycanca" data-language-local-name="azerbejdžanski" 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%AE%E0%A6%A7%E0%A7%8D%E0%A6%AF%E0%A6%AF%E0%A7%81%E0%A6%97%E0%A7%80%E0%A6%AF%E0%A6%BC_%E0%A6%87%E0%A6%B8%E0%A6%B2%E0%A6%BE%E0%A6%AE%E0%A7%87_%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="মধ্যযুগীয় ইসলামে গণিত – bengalski" lang="bn" hreflang="bn" data-title="মধ্যযুগীয় ইসলামে গণিত" data-language-autonym="বাংলা" data-language-local-name="bengalski" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Matem%C3%A0tiques_a_l%27islam_medieval" title="Matemàtiques a l'islam medieval – katalonski" lang="ca" hreflang="ca" data-title="Matemàtiques a l'islam medieval" data-language-autonym="Català" data-language-local-name="katalonski" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Arabisk_matematik" title="Arabisk matematik – danski" lang="da" hreflang="da" data-title="Arabisk matematik" data-language-autonym="Dansk" data-language-local-name="danski" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437796 badge-featuredarticle mw-list-item" title="istaknuti članak"><a href="https://de.wikipedia.org/wiki/Mathematik_in_der_Bl%C3%BCtezeit_des_Islam" title="Mathematik in der Blütezeit des Islam – njemački" lang="de" hreflang="de" data-title="Mathematik in der Blütezeit des Islam" data-language-autonym="Deutsch" data-language-local-name="njemački" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world – engleski" lang="en" hreflang="en" data-title="Mathematics in the medieval Islamic world" data-language-autonym="English" data-language-local-name="engleski" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Matem%C3%A1tica_isl%C3%A1mica" title="Matemática islámica – španski" lang="es" hreflang="es" data-title="Matemática islámica" data-language-autonym="Español" data-language-local-name="španski" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA_%D9%82%D8%AF%DB%8C%D9%85%D9%87_%D8%AF%D8%B1_%D8%AC%D9%87%D8%A7%D9%86_%D8%A7%D8%B3%D9%84%D8%A7%D9%85" title="ریاضیات قدیمه در جهان اسلام – perzijski" lang="fa" hreflang="fa" data-title="ریاضیات قدیمه در جهان اسلام" data-language-autonym="فارسی" data-language-local-name="perzijski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Arabiankielinen_matematiikka_keskiajalla" title="Arabiankielinen matematiikka keskiajalla – finski" lang="fi" hreflang="fi" data-title="Arabiankielinen matematiikka keskiajalla" data-language-autonym="Suomi" data-language-local-name="finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Math%C3%A9matiques_arabes" title="Mathématiques arabes – francuski" lang="fr" hreflang="fr" data-title="Mathématiques arabes" data-language-autonym="Français" data-language-local-name="francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Ilimin_lissafi_a_duniyar_Islama_ta_tsakiya" title="Ilimin lissafi a duniyar Islama ta tsakiya – hausa" lang="ha" hreflang="ha" data-title="Ilimin lissafi a duniyar Islama ta tsakiya" data-language-autonym="Hausa" data-language-local-name="hausa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Matematika_Islam_abad_pertengahan" title="Matematika Islam abad pertengahan – indonezijski" lang="id" hreflang="id" data-title="Matematika Islam abad pertengahan" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Matematica_islamica" title="Matematica islamica – italijanski" lang="it" hreflang="it" data-title="Matematica islamica" data-language-autonym="Italiano" data-language-local-name="italijanski" class="interlanguage-link-target"><span>Italiano</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%A6" title="アラビア数学 – japanski" lang="ja" hreflang="ja" data-title="アラビア数学" data-language-autonym="日本語" data-language-local-name="japanski" class="interlanguage-link-target"><span>日本語</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%98%ED%95%99" title="아라비아 수학 – korejski" lang="ko" hreflang="ko" data-title="아라비아 수학" data-language-autonym="한국어" data-language-local-name="korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Matematik_pada_zaman_pertengahan_Islam" title="Matematik pada zaman pertengahan Islam – malajski" lang="ms" hreflang="ms" data-title="Matematik pada zaman pertengahan Islam" data-language-autonym="Bahasa Melayu" data-language-local-name="malajski" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Arabisk_matematikk" title="Arabisk matematikk – norveški (Nynorsk)" lang="nn" hreflang="nn" data-title="Arabisk matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norveški (Nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Matematikk_i_middelalderens_islam" title="Matematikk i middelalderens islam – norveški (Bokmal)" lang="nb" hreflang="nb" data-title="Matematikk i middelalderens islam" data-language-autonym="Norsk bokmål" data-language-local-name="norveški (Bokmal)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D8%B3%D9%84%D8%A7%D9%85%DB%8C_%D9%82%D8%B1%D9%88%D9%86_%D9%88%D8%B3%D8%B7%DB%8C_%D9%88%DA%86_%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="اسلامی قرون وسطی وچ ریاضی – Western Punjabi" lang="pnb" hreflang="pnb" data-title="اسلامی قرون وسطی وچ ریاضی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Matem%C3%A1tica_isl%C3%A2mica" title="Matemática islâmica – portugalski" lang="pt" hreflang="pt" data-title="Matemática islâmica" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%B8%D1%81%D0%BB%D0%B0%D0%BC%D1%81%D0%BA%D0%BE%D0%B3%D0%BE_%D0%A1%D1%80%D0%B5%D0%B4%D0%BD%D0%B5%D0%B2%D0%B5%D0%BA%D0%BE%D0%B2%D1%8C%D1%8F" title="Математика исламского Средневековья – ruski" lang="ru" hreflang="ru" data-title="Математика исламского Средневековья" data-language-autonym="Русский" data-language-local-name="ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Islamska_matematika" title="Islamska matematika – srpskohrvatski" lang="sh" hreflang="sh" data-title="Islamska matematika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srpskohrvatski" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%98%D1%81%D0%BB%D0%B0%D0%BC%D1%81%D0%BA%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Исламска математика – srpski" lang="sr" hreflang="sr" data-title="Исламска математика" data-language-autonym="Српски / srpski" data-language-local-name="srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Orta_%C3%87a%C4%9F_%C4%B0slam_matemati%C4%9Fi" title="Orta Çağ İslam matematiği – turski" lang="tr" hreflang="tr" 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typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg/220px-Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg" decoding="async" width="220" height="348" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/23/Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg 1.5x" data-file-width="240" data-file-height="380" /></a><figcaption>Stranica iz <i>Sažete knjige o proračunu popunjavanjem i balansiranjem</i> od <a href="/wiki/Abu_Abdullah_Muhammad_bin_Musa_al-Khwarizmi" title="Abu Abdullah Muhammad bin Musa al-Khwarizmi">Al-Kvarizmija</a>.</figcaption></figure> <p>Historija matematičara tokom <a href="/wiki/Zlatno_doba_islama" title="Zlatno doba islama">Zlatnog doba islama</a>, posebno tokom 9. i 10. vijeka, zasnovana na grčkim matematičarima (<a href="/wiki/Euklid" title="Euklid">Euklid</a>, <a href="/wiki/Arhimed" title="Arhimed">Arhimed</a>, Apolonije) i <a href="/wiki/Indijska_matematika" title="Indijska matematika">indijskim matematičarima</a> (<a href="/wiki/Aryabhata" title="Aryabhata">Aryabhata</a>, <a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a>), imala je važan razvoj, kao što je potpuni razvoj decimalnog sistema vrijednosti po mjestu cifre koji uključuje <a href="/wiki/Dekadni_numeri%C4%8Dki_sistem" class="mw-redirect" title="Dekadni numerički sistem">decimalne zareze</a>, prvi sistematizirani studij <a href="/wiki/Algebra" title="Algebra">algebre</a> (nazvan <i>Sažeta knjiga o proračunu popunjavanjem i balansiranjem</i> od učenjaka <a href="/wiki/Abu_Abdullah_Muhammad_bin_Musa_al-Khwarizmi" title="Abu Abdullah Muhammad bin Musa al-Khwarizmi">Al-Kvarizmija</a>) i napretke u <a href="/wiki/Geometrija" title="Geometrija">geometriji</a> i <a href="/wiki/Trigonometrija" title="Trigonometrija">trigonometriji</a>.<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> </p><p>Arapski radovi su također igrali važnu ulogu u prijenosu matematike u Evropu između 10. i 12. vijeka.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historija">Historija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=1" title="Uredi odlomak "Historija"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=1" title="Edit section's source code: Historija"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Algebra">Algebra</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=2" title="Uredi odlomak "Algebra"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=2" title="Edit section's source code: Algebra"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Izučavanje <a href="/wiki/Algebra" title="Algebra">algebre</a>, koja je izvedenica iz <a href="/wiki/Arapski_jezik" title="Arapski jezik">arapske</a> riječi sa značenjem "povezivanje slomljenih dijelova",<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> cvjetalo je tokom islamskog zlatnog perioda. <a href="/wiki/Abu_Abdullah_Muhammad_bin_Musa_al-Khwarizmi" title="Abu Abdullah Muhammad bin Musa al-Khwarizmi">Al-Kvarizmi</a> je, zajedno sa <a href="/wiki/Grci" title="Grci">grčkim</a> matematičarem <a href="/wiki/Diofant" title="Diofant">Diofantom</a>, poznat kao otac algebre.<sup id="cite_ref-fabpedigree.com_4-0" class="reference"><a href="#cite_note-fabpedigree.com-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> U njegovoj knjizi <i>Sažeta knjiga o proračunima<span> popunjavanjem i balansiranjem</span></i> Al-Kvarizmi se suočava sa načinima rješavanja za pozitivne korijene prvog i drugog stepena (linearne i kvadratne) polinomske jednačine.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> On također uvodi metodu redukcije, i za razliku od Diofanta, daje opća rješenja za jednačine kojima se bavio.<sup id="cite_ref-fabpedigree.com_4-1" class="reference"><a href="#cite_note-fabpedigree.com-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Al-Kvarizmijeva algebra je bila retorična, što znači da su jednačine bile zapisivane u pune rečenice. Ovo je bilo različito u odnosu na algebarski rad Diofanta, koji je bio sažet, gdje je nešto simbolizma korišteno. Tranzicija na simboličku algebru, gdje su samo simboli korišteni, može se naći u radovima Ibn al-Banna' al-Marrakushija i Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī.<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> </p> <div class="mw-heading mw-heading3"><h3 id="Indukcija">Indukcija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=3" title="Uredi odlomak "Indukcija"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=3" title="Edit section's source code: Indukcija"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Najraniji implicitni tragovi matematičke indukcije mogu se naći u <a href="/wiki/Euklid" title="Euklid">Euklidovom</a> da je broj prostih brojeva beskonačan (c. 300 p. n. e). Prva eksplicitna formulacija principa indukcije data je od <a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascala</a> u njegovom djelu <i>Traité du triangle arithmétique</i> (1665). </p><p>Između to dvoje, implicitni <a href="/wiki/Matemati%C4%8Dki_dokaz" title="Matematički dokaz">dokaz</a> indukcijom za <a href="/wiki/Aritmeti%C4%8Dka_progresija" title="Aritmetička progresija">aritmetičke nizove</a> uveo je al-Karadži (c. 1000) i nastavio al-Samaw'al, koristeći za specijalne slučajeve <a href="/wiki/Binomni_teorem" class="mw-redirect" title="Binomni teorem">binomne teoreme</a> i svojstva <a href="/wiki/Pascalov_trougao" title="Pascalov trougao">Pascalovog trougla</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Poznate_ličnosti_i_razvoj"><span id="Poznate_li.C4.8Dnosti_i_razvoj"></span>Poznate ličnosti i razvoj</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=4" title="Uredi odlomak "Poznate ličnosti i razvoj"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=4" title="Edit section's source code: Poznate ličnosti i razvoj"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Omer_Hajjam">Omer Hajjam</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=5" title="Uredi odlomak "Omer Hajjam"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=5" title="Edit section's source code: Omer Hajjam"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Omar_Kayy%C3%A1m_-_Geometric_solution_to_cubic_equation.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Omar_Kayy%C3%A1m_-_Geometric_solution_to_cubic_equation.svg/220px-Omar_Kayy%C3%A1m_-_Geometric_solution_to_cubic_equation.svg.png" decoding="async" width="220" height="275" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Omar_Kayy%C3%A1m_-_Geometric_solution_to_cubic_equation.svg/330px-Omar_Kayy%C3%A1m_-_Geometric_solution_to_cubic_equation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Omar_Kayy%C3%A1m_-_Geometric_solution_to_cubic_equation.svg/440px-Omar_Kayy%C3%A1m_-_Geometric_solution_to_cubic_equation.svg.png 2x" data-file-width="360" data-file-height="450" /></a><figcaption>Za rješavanje kubne jednačine <i>x</i><sup>3</sup> + <i>a</i><sup>2</sup><i>x</i> = <i>b</i> Hajjam je konstruisao <a href="/wiki/Parabola_(matematika)" title="Parabola (matematika)">parabolu</a> <i>x</i><sup>2</sup> = <i>ay</i>, <a href="/wiki/Kru%C5%BEnica" title="Kružnica">krug</a> sa prečnikom <i>b</i>/<i>a</i><sup>2</sup>, i vertikalnu liniju kroz presječnu tačku. Rješenje je dato dužinom horizontalnog dijela linije od ishodišta do presjecišta vertikalne linije i <i>x</i>-ose.</figcaption></figure> <p><a href="/wiki/Omar_Hajjam" title="Omar Hajjam">Omer Hajjam</a> (c. 1038/48. u <a href="/wiki/Iran" title="Iran">Iranu</a> – 1123/24)<span class="mw-ref" id="cxcite_ref-FOOTNOTEStruik198796_11-0" data-sourceid="cite_ref-FOOTNOTEStruik198796_11-0"><a href="#cite_note-FOOTNOTEStruik198796-11"><span class="mw-reflink-text">[11]</span></a></span><span class="mw-ref" id="cxcite_ref-FOOTNOTEStruik198796_11-0" data-sourceid="cite_ref-FOOTNOTEStruik198796_11-0"></span> napisao je <i>Raspravu o demonstraciji problema algebre</i> koja sadrži sistematsko rješenje <a href="/wiki/Kubna_funkcija" title="Kubna funkcija">kubnih jednačina</a>, idući van <i>Algebre</i> od <a href="/wiki/Abu_Abdullah_Muhammad_bin_Musa_al-Khwarizmi" title="Abu Abdullah Muhammad bin Musa al-Khwarizmi">Kvarazmija</a>.<sup id="cite_ref-FOOTNOTEBoyer1991241–242_7-0" class="reference"><a href="#cite_note-FOOTNOTEBoyer1991241–242-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Hajjam je našao rješenja ovih jednačina pronalaskom presječnih tačaka dva konusna presjeka. Ovu metodu su koristili Grci,<sup id="cite_ref-FOOTNOTEStruik198797_8-0" class="reference"><a href="#cite_note-FOOTNOTEStruik198797-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> ali nisu generalizirali metodu koja pokriva sve jednačine s pozitivnim <a href="/wiki/Korijen_(matematika)" title="Korijen (matematika)">korijenima</a>.<sup id="cite_ref-FOOTNOTEBoyer19991241–242_9-0" class="reference"><a href="#cite_note-FOOTNOTEBoyer19991241–242-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Šaraf_al-Din_al-Tusi"><span id=".C5.A0araf_al-Din_al-Tusi"></span>Šaraf al-Din al-Tusi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=6" title="Uredi odlomak "Šaraf al-Din al-Tusi"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=6" title="Edit section's source code: Šaraf al-Din al-Tusi"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Šaraf al-Din al-Tusi (?, Tus, Iran – 1213/4) razvio je novi pristup istraživanja <a href="/wiki/Kubna_funkcija" title="Kubna funkcija">kubnih jednačina</a> – pristup koji podrazumijeva pronalaženje tačke pri kojoj kubni polinom ima svoju najveću vrijednost. Naprimjer, za rješavanje jednačine <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ x^{3}+a=bx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mi>a</mi> <mo>=</mo> <mi>b</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x^{3}+a=bx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8439ca6b6f3b09acef7ebe9a4847b8c46851493d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.46ex; height:2.843ex;" alt="{\displaystyle \ x^{3}+a=bx}"></span>, sa pozitivnim varijablama <i>a</i> i <i>b</i>, on bi napisao da se maksimum krivulje <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ y=bx-x^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>y</mi> <mo>=</mo> <mi>b</mi> <mi>x</mi> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ y=bx-x^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acdb80478512625029a75c486101c07f7b8e80f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.386ex; height:3.009ex;" alt="{\displaystyle \ y=bx-x^{3}}"></span> nalazi na <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=\textstyle {\sqrt {\frac {b}{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mi>b</mi> <mn>3</mn> </mfrac> </msqrt> </mrow> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=\textstyle {\sqrt {\frac {b}{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe82906d7defb92c33260ccbd26607dfe8e70c86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:8.41ex; height:4.843ex;" alt="{\displaystyle x=\textstyle {\sqrt {\frac {b}{3}}}}"></span> i da jednačina: nema rješenja, ima jedno rješenje ili ima dva rješenja, zavisno od toga da li je visina krivulje u toj tački manja od, jednaka, ili veća od <i>a</i>. Njegovi preživjeli radovi ne daju predstavu o tome kako je otkrio svoju formulu za maksimum ovih krivulja. Postoje razna nagađanja vezana za ovo njegovo otkriće.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ostale_poznate_ličnosti"><span id="Ostale_poznate_li.C4.8Dnosti"></span>Ostale poznate ličnosti</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=7" title="Uredi odlomak "Ostale poznate ličnosti"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=7" title="Edit section's source code: Ostale poznate ličnosti"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>'Abd al-Hamīd ibn Turk (fl. 830) (kvadratne jednačine)</li> <li>Thabit ibn Qurra (826–901)</li> <li>Abū Kāmil Shujā ibn Aslam (c. 850 – 930) (iracionalni brojevi)</li> <li>Sind ibn Ali</li> <li>Abū Sahl al-Qūhī (c. 940–1000) (centri gravitacije)</li> <li>Abu'l-Hasan al-Uqlidisi (952 – 953) (aritmetika)</li> <li>'Abd al-'Aziz al-Qabisi</li> <li>Abū al-Wafā' Būzjānī (940 – 998) (sferna trigonometrija)</li> <li>Al-Karaji (c. 953 – c. 1029) (algebra, matematička indukcija)</li> <li>Abu Nasr Mansur (c. 960 – 1036) (sferna trigonometrija)</li> <li>Ibn Tahir al-Baghdadi (c. 980–1037) (iracionalni brojevi)</li> <li><a href="/wiki/Ibn_al-Haitam" class="mw-redirect" title="Ibn al-Haitam">Ibn al-Haytham</a> (ca. 965–1040)</li> <li><a href="/wiki/El-Biruni" title="El-Biruni">Abū al-Rayḥān al-Bīrūnī</a> (973 – 1048) (trigonometrija)</li> <li>Ibn Yaḥyā al-Maghribī al-Samawʾal (c. 1130 – c. 1180)</li> <li>Ibn Maḍāʾ (c. 1116 - 1196)</li> <li>Naṣīr al-Dīn al-Ṭūsī (1201–1274) (paralelni postulat)</li> <li>Jamshīd al-Kāshī (c. 1380–1429) (decimale i procjena konstante kruga)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Galerija">Galerija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=8" title="Uredi odlomak "Galerija"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=8" title="Edit section's source code: Galerija"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Datoteka:Gravure_originale_du_compas_parfait_par_Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB.jpg" class="mw-file-description" title="Graviranje Abū Sahl al-Qūhījevog savršenog kompasa za crtanje koničnih dijelova."><img alt="Graviranje Abū Sahl al-Qūhījevog savršenog kompasa za crtanje koničnih dijelova." 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/90px-Gravure_originale_du_compas_parfait_par_Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB.jpg" decoding="async" width="90" height="120" 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/135px-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/179px-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> <div class="gallerytext">Graviranje <a href="/w/index.php?title=Ab%C5%AB_Sahl_al-Q%C5%ABh%C4%AB&action=edit&redlink=1" class="new" title="Abū Sahl al-Qūhī (stranica ne postoji)">Abū Sahl al-Qūhījevog</a> savršenog kompasa za crtanje koničnih dijelova.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Datoteka:Theorem_of_al-Haitham.JPG" class="mw-file-description" title="Ibn Haythamova teorema."><img alt="Ibn Haythamova teorema." src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Theorem_of_al-Haitham.JPG/120px-Theorem_of_al-Haitham.JPG" decoding="async" width="120" height="60" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Theorem_of_al-Haitham.JPG/180px-Theorem_of_al-Haitham.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Theorem_of_al-Haitham.JPG/240px-Theorem_of_al-Haitham.JPG 2x" data-file-width="833" data-file-height="415" /></a></span></div> <div class="gallerytext"><a href="/wiki/Krug#Teoreme" title="Krug">Ibn Haythamova teorema</a>.</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Također_pogledajte"><span id="Tako.C4.91er_pogledajte"></span>Također pogledajte</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=9" title="Uredi odlomak "Također pogledajte"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=9" title="Edit section's source code: Također pogledajte"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Arapski_brojevi" title="Arapski brojevi">Arapski brojevi</a></li> <li><a href="/wiki/Zlatno_doba_islama" title="Zlatno doba islama">Zlatno doba islama</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Reference">Reference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=10" title="Uredi odlomak "Reference"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=10" title="Edit section's source code: Reference"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r3312388">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">Katz (1993): "A complete history of mathematics of medieval Islam cannot yet be written, since so many of these Arabic manuscripts lie unstudied.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Adolph P. Yushkevich <style data-mw-deduplicate="TemplateStyles:r3303350">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),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 a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFSertima1992" class="citation cs2"><a href="/w/index.php?title=Ivan_van_Sertima&action=edit&redlink=1" class="new" title="Ivan van Sertima (stranica ne postoji)">Sertima, Ivan Van</a> (1992), <a rel="nofollow" class="external text" href="https://archive.org/details/goldenageofmoor00vans/page/394"><i>Golden age of the Moor, Volume 11</i></a>, Transaction Publishers, str. <a rel="nofollow" class="external text" href="https://archive.org/details/goldenageofmoor00vans/page/394">394</a>, <a href="/wiki/ISBN_(identifikator)" class="mw-redirect" title="ISBN (identifikator)">ISBN</a> <a href="/wiki/Posebno:Knji%C5%BEni_izvori/1-56000-581-5" title="Posebno:Knjižni izvori/1-56000-581-5"><bdi>1-56000-581-5</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Golden+age+of+the+Moor%2C+Volume+11&rft.pages=394&rft.pub=Transaction+Publishers&rft.date=1992&rft.isbn=1-56000-581-5&rft.aulast=Sertima&rft.aufirst=Ivan+Van&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgoldenageofmoor00vans%2Fpage%2F394&rfr_id=info%3Asid%2Fbs.wikipedia.org%3AMatematika+u+srednjovjekovnom+islamskom+svijetu" class="Z3988"></span> <span class="cs1-maint citation-comment">CS1 održavanje: nepreporučeni parametar (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_nepreporu%C4%8Deni_parametar" title="Kategorija:CS1 održavanje: nepreporučeni parametar">link</a>)</span> "The Islamic mathematicians exercised a prolific influence on the development of science in Europe, enriched as much by their own discoveries as those they had inherited by the Greeks, the Indians, the Syrians, the Babylonians, etc."</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r3303350"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.etymonline.com/index.php?term=algebra&allowed_in_frame=0">"algebra"</a>. <i><a href="/w/index.php?title=Online_Etymology_Dictionary&action=edit&redlink=1" class="new" title="Online Etymology Dictionary (stranica ne postoji)">Online Etymology Dictionary</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Online+Etymology+Dictionary&rft.atitle=algebra&rft_id=http%3A%2F%2Fwww.etymonline.com%2Findex.php%3Fterm%3Dalgebra%26allowed_in_frame%3D0&rfr_id=info%3Asid%2Fbs.wikipedia.org%3AMatematika+u+srednjovjekovnom+islamskom+svijetu" class="Z3988"></span></span> </li> <li id="cite_note-fabpedigree.com-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-fabpedigree.com_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-fabpedigree.com_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a rel="nofollow" class="external free" href="http://fabpedigree.com/james/mathmen.htm#Khowarizmi">http://fabpedigree.com/james/mathmen.htm#Khowarizmi</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r3303350"><cite id="CITEREFBoyer1991" class="citation book cs1"><a href="/w/index.php?title=Carl_Benjamin_Boyer&action=edit&redlink=1" class="new" title="Carl Benjamin Boyer (stranica ne postoji)">Boyer, Carl B.</a> (1991). "The Arabic Hegemony". <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema00boye/page/228"><i>A History of Mathematics</i></a> (Second izd.). John Wiley & Sons. str. <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema00boye/page/228">228</a>. <a href="/wiki/ISBN_(identifikator)" class="mw-redirect" title="ISBN (identifikator)">ISBN</a> <a href="/wiki/Posebno:Knji%C5%BEni_izvori/0-471-54397-7" title="Posebno:Knjižni izvori/0-471-54397-7"><bdi>0-471-54397-7</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+Arabic+Hegemony&rft.btitle=A+History+of+Mathematics&rft.pages=228&rft.edition=Second&rft.pub=John+Wiley+%26+Sons&rft.date=1991&rft.isbn=0-471-54397-7&rft.aulast=Boyer&rft.aufirst=Carl+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryofmathema00boye%2Fpage%2F228&rfr_id=info%3Asid%2Fbs.wikipedia.org%3AMatematika+u+srednjovjekovnom+islamskom+svijetu" class="Z3988"></span> <span class="cs1-maint citation-comment">CS1 održavanje: nepreporučeni parametar (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_nepreporu%C4%8Deni_parametar" title="Kategorija:CS1 održavanje: nepreporučeni parametar">link</a>)</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r3303350"><cite class="citation cs2"><a href="/w/index.php?title=John_J._O%27Connor_(mathematician)&action=edit&redlink=1" class="new" title="John J. O'Connor (mathematician) (stranica ne postoji)">O'Connor, John J.</a>; <a href="/w/index.php?title=Edmund_F._Robertson&action=edit&redlink=1" class="new" title="Edmund F. Robertson (stranica ne postoji)">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Al-Banna.html">"al-Marrakushi ibn Al-Banna"</a>, <i><a href="/w/index.php?title=MacTutor_History_of_Mathematics_archive&action=edit&redlink=1" class="new" title="MacTutor History of Mathematics archive (stranica ne postoji)">MacTutor History of Mathematics archive</a></i>, <a href="/w/index.php?title=University_of_St_Andrews&action=edit&redlink=1" class="new" title="University of St Andrews (stranica ne postoji)">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=al-Marrakushi+ibn+Al-Banna&rft.btitle=MacTutor+History+of+Mathematics+archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=http%3A%2F%2Fwww-history.mcs.st-andrews.ac.uk%2FBiographies%2FAl-Banna.html&rfr_id=info%3Asid%2Fbs.wikipedia.org%3AMatematika+u+srednjovjekovnom+islamskom+svijetu" class="Z3988"></span> <span class="cs1-maint citation-comment">CS1 održavanje: nepreporučeni parametar (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_nepreporu%C4%8Deni_parametar" title="Kategorija:CS1 održavanje: nepreporučeni parametar">link</a>)</span>.</span> </li> <li id="cite_note-FOOTNOTEBoyer1991241–242-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBoyer1991241–242_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBoyer1991">Boyer 1991</a>, str. 241–242.</span> </li> <li id="cite_note-FOOTNOTEStruik198797-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEStruik198797_8-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFStruik1987">Struik 1987</a>, str. 97.<span class="error harv-error" style="display: none; font-size:100%"> harv error: no target: CITEREFStruik1987 (<a href="/wiki/Kategorija:Harv_and_Sfn_template_errors" title="Kategorija:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-FOOTNOTEBoyer19991241–242-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBoyer19991241–242_9-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBoyer19991">Boyer i 19991</a>, str. 241–242.<span class="error harv-error" style="display: none; font-size:100%"> harv error: no target: CITEREFBoyer19991 (<a href="/wiki/Kategorija:Harv_and_Sfn_template_errors" title="Kategorija:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r3303350"><cite id="CITEREFBerggrenAl-TūsīRashedAl-Tusi1990" class="citation cs2">Berggren, J. Lennart; Al-Tūsī, Sharaf Al-Dīn; Rashed, Roshdi; Al-Tusi, Sharaf Al-Din (1990), "Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's <i>al-Muʿādalāt", </i>Journal of the American Oriental Society<i>, <b>110</b> (2): 304–309, <a href="/wiki/Doi_(identifikator)" class="mw-redirect" title="Doi (identifikator)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F604533">10.2307/604533</a>, <a href="/wiki/JSTOR_(identifikator)" class="mw-redirect" title="JSTOR (identifikator)">JSTOR</a> <a rel="nofollow" class="external text" href="//www.jstor.org/stable/604533">604533</a></i></cite><i><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+American+Oriental+Society&rft.atitle=Innovation+and+Tradition+in+Sharaf+al-D%C4%ABn+al-%E1%B9%AC%C5%ABs%C4%AB%27s+al-Mu%CA%BF%C4%81dal%C4%81t&rft.volume=110&rft.issue=2&rft.pages=304-309&rft.date=1990&rft_id=info%3Adoi%2F10.2307%2F604533&rft_id=%2F%2Fwww.jstor.org%2Fstable%2F604533%23id-name%3DJSTOR&rft.aulast=Berggren&rft.aufirst=J.+Lennart&rft.au=Al-T%C5%ABs%C4%AB%2C+Sharaf+Al-D%C4%ABn&rft.au=Rashed%2C+Roshdi&rft.au=Al-Tusi%2C+Sharaf+Al-Din&rfr_id=info%3Asid%2Fbs.wikipedia.org%3AMatematika+u+srednjovjekovnom+islamskom+svijetu" class="Z3988"></span></i></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Vanjski_linkovi">Vanjski linkovi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&veaction=edit&section=11" title="Uredi odlomak "Vanjski linkovi"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika_u_srednjovjekovnom_islamskom_svijetu&action=edit&section=11" title="Edit section's source code: Vanjski linkovi"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r3303350"><cite id="CITEREFHogendijk1999" class="citation web cs1">Hogendijk, Jan P. (januar 1999). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20181224211852/http://www.jphogendijk.nl/publ/Islamath.html">"Bibliography of Mathematics in Medieval Islamic Civilization"</a>. Arhivirano s <a rel="nofollow" class="external text" href="http://www.jphogendijk.nl/publ/Islamath.html">originala</a>, 24. 12. 2018<span class="reference-accessdate">. Pristupljeno 18. 3. 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Bibliography+of+Mathematics+in+Medieval+Islamic+Civilization&rft.date=1999-01&rft.aulast=Hogendijk&rft.aufirst=Jan+P.&rft_id=http%3A%2F%2Fwww.jphogendijk.nl%2Fpubl%2FIslamath.html&rfr_id=info%3Asid%2Fbs.wikipedia.org%3AMatematika+u+srednjovjekovnom+islamskom+svijetu" class="Z3988"></span><span class="cs1-maint citation-comment">CS1 održavanje: ref=harv (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_ref%3Dharv" title="Kategorija:CS1 održavanje: ref=harv">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r3303350"><cite class="citation cs2"><a href="/w/index.php?title=John_J._O%27Connor_(mathematician)&action=edit&redlink=1" class="new" title="John J. O'Connor (mathematician) (stranica ne postoji)">O'Connor, John J.</a>; <a href="/w/index.php?title=Edmund_F._Robertson&action=edit&redlink=1" class="new" title="Edmund F. Robertson (stranica ne postoji)">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/HistTopics/Arabic_mathematics.html">"Arabic mathematics: forgotten brilliance?"</a>, <i><a href="/w/index.php?title=MacTutor_History_of_Mathematics_archive&action=edit&redlink=1" class="new" title="MacTutor History of Mathematics archive (stranica ne postoji)">MacTutor History of Mathematics archive</a></i>, <a href="/w/index.php?title=University_of_St_Andrews&action=edit&redlink=1" class="new" title="University of St Andrews (stranica ne postoji)">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Arabic+mathematics%3A+forgotten+brilliance%3F&rft.btitle=MacTutor+History+of+Mathematics+archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=http%3A%2F%2Fwww-history.mcs.st-andrews.ac.uk%2FHistTopics%2FArabic_mathematics.html&rfr_id=info%3Asid%2Fbs.wikipedia.org%3AMatematika+u+srednjovjekovnom+islamskom+svijetu" class="Z3988"></span> <span class="cs1-maint citation-comment">CS1 održavanje: nepreporučeni parametar (<a href="/wiki/Kategorija:CS1_odr%C5%BEavanje:_nepreporu%C4%8Deni_parametar" title="Kategorija:CS1 održavanje: nepreporučeni parametar">link</a>)</span>.</li> <li><a rel="nofollow" class="external text" href="http://www.saudiaramcoworld.com/issue/200703/rediscovering.arabic.science.htm">Richard Covington, <i>Rediscovering Arabic Science</i>, 2007, Saudi Aramco World</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141030100805/http://www.saudiaramcoworld.com/issue/200703/rediscovering.arabic.science.htm">Arhivirano</a> 30. 10. 2014. na <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li></ul> <div role="navigation" class="navbox" aria-labelledby="Islamske_nauke" 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"><style data-mw-deduplicate="TemplateStyles:r3312386">.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 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