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class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Lloc"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Somari" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Somari</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mòu a la barra laterala</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">Escondre</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Començament</div> </a> </li> <li id="toc-Evolucion_e_finalitat_dei_matematicas" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Evolucion_e_finalitat_dei_matematicas"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Evolucion e finalitat dei matematicas</span> </div> </a> <ul id="toc-Evolucion_e_finalitat_dei_matematicas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lei_divèrsei_brancas_dei_matematicas" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Lei_divèrsei_brancas_dei_matematicas"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Lei divèrsei brancas dei matematicas</span> </div> </a> <button aria-controls="toc-Lei_divèrsei_brancas_dei_matematicas-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>Commuta la subsecció Lei divèrsei brancas dei matematicas</span> </button> <ul id="toc-Lei_divèrsei_brancas_dei_matematicas-sublist" class="vector-toc-list"> <li id="toc-L'algèbra" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#L'algèbra"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>L'algèbra</span> </div> </a> <ul id="toc-L'algèbra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-L'analisi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#L'analisi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>L'analisi</span> </div> </a> <ul id="toc-L'analisi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-La_geometria" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#La_geometria"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>La geometria</span> </div> </a> <ul id="toc-La_geometria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Matematicas_aplicadas_e_matematicas_puras" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Matematicas_aplicadas_e_matematicas_puras"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Matematicas aplicadas e matematicas puras</span> </div> </a> <ul id="toc-Matematicas_aplicadas_e_matematicas_puras-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Lei_matematicas_e_leis_autrei_sciéncias" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Lei_matematicas_e_leis_autrei_sciéncias"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Lei matematicas e leis autrei sciéncias</span> </div> </a> <button aria-controls="toc-Lei_matematicas_e_leis_autrei_sciéncias-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>Commuta la subsecció Lei matematicas e leis autrei sciéncias</span> </button> <ul id="toc-Lei_matematicas_e_leis_autrei_sciéncias-sublist" class="vector-toc-list"> <li id="toc-Instrument_e_lengatge" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Instrument_e_lengatge"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Instrument e lengatge</span> </div> </a> <ul id="toc-Instrument_e_lengatge-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lo_cas_particular_de_la_fisica" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lo_cas_particular_de_la_fisica"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Lo cas particular de la fisica</span> </div> </a> <ul id="toc-Lo_cas_particular_de_la_fisica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liames_amb_leis_autrei_sciéncias_de_la_natura" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liames_amb_leis_autrei_sciéncias_de_la_natura"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Liames amb leis autrei sciéncias de la natura</span> </div> </a> <ul id="toc-Liames_amb_leis_autrei_sciéncias_de_la_natura-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liames_amb_lei_sciéncias_umanas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liames_amb_lei_sciéncias_umanas"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Liames amb lei sciéncias umanas</span> </div> </a> <ul id="toc-Liames_amb_lei_sciéncias_umanas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-L'àbit_matematic_fa_pas_la_sciéncia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#L'àbit_matematic_fa_pas_la_sciéncia"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>L'àbit matematic fa pas la sciéncia</span> </div> </a> <ul id="toc-L'àbit_matematic_fa_pas_la_sciéncia-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Lei_matematicas_dins_l'Istòria" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Lei_matematicas_dins_l'Istòria"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Lei matematicas dins l'Istòria</span> </div> </a> <ul id="toc-Lei_matematicas_dins_l'Istòria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fondaments,_rigor_e_logica" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Fondaments,_rigor_e_logica"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Fondaments, rigor e logica</span> </div> </a> <button aria-controls="toc-Fondaments,_rigor_e_logica-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>Commuta la subsecció Fondaments, rigor e logica</span> </button> <ul id="toc-Fondaments,_rigor_e_logica-sublist" class="vector-toc-list"> <li id="toc-Lei_fondaments_dei_matematicas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lei_fondaments_dei_matematicas"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Lei fondaments dei matematicas</span> </div> </a> <ul id="toc-Lei_fondaments_dei_matematicas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Logica_e_matematicas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Logica_e_matematicas"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Logica e matematicas</span> </div> </a> <ul id="toc-Logica_e_matematicas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rigor_e_practica_dei_matematicas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rigor_e_practica_dei_matematicas"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Rigor e practica dei matematicas</span> </div> </a> <ul id="toc-Rigor_e_practica_dei_matematicas-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Filosofias_dei_matematicas" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Filosofias_dei_matematicas"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Filosofias dei matematicas</span> </div> </a> <button aria-controls="toc-Filosofias_dei_matematicas-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>Commuta la subsecció Filosofias dei matematicas</span> </button> <ul id="toc-Filosofias_dei_matematicas-sublist" class="vector-toc-list"> <li id="toc-Lo_platonisme" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lo_platonisme"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Lo platonisme</span> </div> </a> <ul id="toc-Lo_platonisme-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-L'aristotelisme" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#L'aristotelisme"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>L'aristotelisme</span> </div> </a> <ul id="toc-L'aristotelisme-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lo_logicisme" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lo_logicisme"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Lo logicisme</span> </div> </a> <ul id="toc-Lo_logicisme-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-L'intuicionisme" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#L'intuicionisme"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>L'intuicionisme</span> </div> </a> <ul id="toc-L'intuicionisme-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lo_constructivisme" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lo_constructivisme"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.5</span> <span>Lo constructivisme</span> </div> </a> <ul id="toc-Lo_constructivisme-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Leis_arts_e_lei_matematicas" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Leis_arts_e_lei_matematicas"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Leis arts e lei matematicas</span> </div> </a> <button aria-controls="toc-Leis_arts_e_lei_matematicas-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>Commuta la subsecció Leis arts e lei matematicas</span> </button> <ul id="toc-Leis_arts_e_lei_matematicas-sublist" class="vector-toc-list"> <li id="toc-Armonia_e_musica" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Armonia_e_musica"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Armonia e musica</span> </div> </a> <ul id="toc-Armonia_e_musica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lei_simetrias" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Lei_simetrias"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>Lei simetrias</span> </div> </a> <ul id="toc-Lei_simetrias-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Annèxas" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Annèxas"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Annèxas</span> </div> </a> <button aria-controls="toc-Annèxas-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>Commuta la subsecció Annèxas</span> </button> <ul id="toc-Annèxas-sublist" class="vector-toc-list"> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Articles_connèxes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Articles_connèxes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Articles connèxes</span> </div> </a> <ul id="toc-Articles_connèxes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Liames_extèrnes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Liames_extèrnes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>Liames extèrnes</span> </div> </a> <ul id="toc-Liames_extèrnes-sublist" class="vector-toc-list"> <li id="toc-Listas_de_liames" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Listas_de_liames"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3.1</span> <span>Listas de liames</span> </div> </a> <ul id="toc-Listas_de_liames-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ressorsas" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ressorsas"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3.2</span> <span>Ressorsas</span> </div> </a> <ul id="toc-Ressorsas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Logiciaus_libres" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Logiciaus_libres"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3.3</span> <span>Logiciaus libres</span> </div> </a> <ul id="toc-Logiciaus_libres-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </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="Somari" 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="Commuta la taula de continguts." > <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">Commuta la taula de continguts.</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">Matematicas</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="Vés a un article en una altra llengua. Disponible en 254 llengües" > <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-254" 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">254 lengas</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/Wiskunde" title="Wiskunde - afrikaans" lang="af" hreflang="af" data-title="Wiskunde" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Mathematik" title="Mathematik - aleman de Soïssa" lang="gsw" hreflang="gsw" data-title="Mathematik" data-language-autonym="Alemannisch" data-language-local-name="aleman de Soïssa" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%89%B5%E1%88%9D%E1%88%85%E1%88%AD%E1%89%B0_%E1%88%82%E1%88%B3%E1%89%A5" title="ትምህርተ ሂሳብ - amaric" lang="am" hreflang="am" data-title="ትምህርተ ሂሳብ" data-language-autonym="አማርኛ" data-language-local-name="amaric" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Matematicas" title="Matematicas - aragonés" lang="an" hreflang="an" data-title="Matematicas" data-language-autonym="Aragonés" data-language-local-name="aragonés" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/R%C4%ABmcr%C3%A6ft" title="Rīmcræft - anglès antic" lang="ang" hreflang="ang" data-title="Rīmcræft" data-language-autonym="Ænglisc" data-language-local-name="anglès antic" class="interlanguage-link-target"><span>Ænglisc</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित - angika" lang="anp" hreflang="anp" data-title="गणित" data-language-autonym="अंगिका" data-language-local-name="angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar badge-Q17437798 badge-goodarticle mw-list-item" title="bons articles"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA" title="رياضيات - arabi" lang="ar" hreflang="ar" data-title="رياضيات" data-language-autonym="العربية" data-language-local-name="arabi" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%84%D9%85%D8%A7%D8%B7" title="لماط - arabe marocain" lang="ary" hreflang="ary" data-title="لماط" data-language-autonym="الدارجة" data-language-local-name="arabe marocain" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA" title="رياضيات - àrab egipci" lang="arz" hreflang="arz" data-title="رياضيات" data-language-autonym="مصرى" data-language-local-name="àrab egipci" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="গণিত - assamès" lang="as" hreflang="as" data-title="গণিত" data-language-autonym="অসমীয়া" data-language-local-name="assamès" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Matem%C3%A1tiques" title="Matemátiques - asturian" lang="ast" hreflang="ast" data-title="Matemátiques" data-language-autonym="Asturianu" data-language-local-name="asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-avk mw-list-item"><a href="https://avk.wikipedia.org/wiki/Solokseropa" title="Solokseropa - kotava" lang="avk" hreflang="avk" data-title="Solokseropa" data-language-autonym="Kotava" data-language-local-name="kotava" class="interlanguage-link-target"><span>Kotava</span></a></li><li class="interlanguage-link interwiki-awa mw-list-item"><a href="https://awa.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित - awadhi" lang="awa" hreflang="awa" data-title="गणित" data-language-autonym="अवधी" data-language-local-name="awadhi" class="interlanguage-link-target"><span>अवधी</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Jakhu" title="Jakhu - aimara" lang="ay" hreflang="ay" data-title="Jakhu" data-language-autonym="Aymar aru" data-language-local-name="aimara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Riyaziyyat" title="Riyaziyyat - azerbaijani" lang="az" hreflang="az" data-title="Riyaziyyat" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA" title="ریاضیات - South Azerbaijani" lang="azb" hreflang="azb" data-title="ریاضیات" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - baixkir" lang="ba" hreflang="ba" data-title="Математика" data-language-autonym="Башҡортса" data-language-local-name="baixkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Mathematik" title="Mathematik - bavarès" lang="bar" hreflang="bar" data-title="Mathematik" data-language-autonym="Boarisch" data-language-local-name="bavarès" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Matemat%C4%97ka" title="Matematėka - samogitien" lang="sgs" hreflang="sgs" data-title="Matematėka" data-language-autonym="Žemaitėška" data-language-local-name="samogitien" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Matematika" title="Matematika - Central Bikol" lang="bcl" hreflang="bcl" data-title="Matematika" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Матэматыка - belarús" lang="be" hreflang="be" data-title="Матэматыка" data-language-autonym="Беларуская" data-language-local-name="belarús" 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%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Матэматыка - Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Матэматыка" 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%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - bulgar" lang="bg" hreflang="bg" data-title="Математика" data-language-autonym="Български" data-language-local-name="bulgar" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित - Bhojpuri" lang="bh" hreflang="bh" data-title="गणित" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Matematikis" title="Matematikis - bislama" lang="bi" hreflang="bi" data-title="Matematikis" data-language-autonym="Bislama" data-language-local-name="bislama" class="interlanguage-link-target"><span>Bislama</span></a></li><li class="interlanguage-link interwiki-bjn mw-list-item"><a href="https://bjn.wikipedia.org/wiki/Matamatika" title="Matamatika - banjar" lang="bjn" hreflang="bjn" data-title="Matamatika" data-language-autonym="Banjar" data-language-local-name="banjar" class="interlanguage-link-target"><span>Banjar</span></a></li><li class="interlanguage-link interwiki-blk mw-list-item"><a href="https://blk.wikipedia.org/wiki/%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="သင်္ချာ - Pa'O" lang="blk" hreflang="blk" data-title="သင်္ချာ" data-language-autonym="ပအိုဝ်ႏဘာႏသာႏ" data-language-local-name="Pa'O" class="interlanguage-link-target"><span>ပအိုဝ်ႏဘာႏသာႏ</span></a></li><li class="interlanguage-link interwiki-bm mw-list-item"><a href="https://bm.wikipedia.org/wiki/Matematiki" title="Matematiki - bambara" lang="bm" hreflang="bm" data-title="Matematiki" data-language-autonym="Bamanankan" data-language-local-name="bambara" class="interlanguage-link-target"><span>Bamanankan</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="গণিত - bengalin" lang="bn" hreflang="bn" data-title="গণিত" data-language-autonym="বাংলা" data-language-local-name="bengalin" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A2%E0%BE%A9%E0%BD%B2%E0%BD%A6%E0%BC%8B%E0%BD%A2%E0%BD%B2%E0%BD%82" title="རྩིས་རིག - tibetan" lang="bo" hreflang="bo" data-title="རྩིས་རིག" data-language-autonym="བོད་ཡིག" data-language-local-name="tibetan" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-bpy mw-list-item"><a href="https://bpy.wikipedia.org/wiki/%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="গণিত - bishnupriya" lang="bpy" hreflang="bpy" data-title="গণিত" data-language-autonym="বিষ্ণুপ্রিয়া মণিপুরী" data-language-local-name="bishnupriya" class="interlanguage-link-target"><span>বিষ্ণুপ্রিয়া মণিপুরী</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Matematik" title="Matematik - breton" lang="br" hreflang="br" data-title="Matematik" data-language-autonym="Brezhoneg" data-language-local-name="breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Matematika" title="Matematika - bosniac" lang="bs" hreflang="bs" data-title="Matematika" data-language-autonym="Bosanski" data-language-local-name="bosniac" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bug mw-list-item"><a href="https://bug.wikipedia.org/wiki/%E1%A8%86%E1%A8%88%E1%A8%9B%E1%A8%86%E1%A8%88%E1%A8%97%E1%A8%80" title="ᨆᨈᨛᨆᨈᨗᨀ - buginés" lang="bug" hreflang="bug" data-title="ᨆᨈᨛᨆᨈᨗᨀ" data-language-autonym="Basa Ugi" data-language-local-name="buginés" class="interlanguage-link-target"><span>Basa Ugi</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BE%D0%B3%D0%BE%D0%B9_%D1%83%D1%85%D0%B0%D0%B0%D0%BD" title="Тоогой ухаан - Russia Buriat" lang="bxr" hreflang="bxr" data-title="Тоогой ухаан" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Matem%C3%A0tiques" title="Matemàtiques - catalan" lang="ca" hreflang="ca" data-title="Matemàtiques" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cbk-zam mw-list-item"><a href="https://cbk-zam.wikipedia.org/wiki/Matematica" title="Matematica - Chavacano" lang="cbk" hreflang="cbk" data-title="Matematica" data-language-autonym="Chavacano de Zamboanga" data-language-local-name="Chavacano" class="interlanguage-link-target"><span>Chavacano de Zamboanga</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/S%C3%B3-h%C5%8Fk" title="Só-hŏk - Mindong" lang="cdo" hreflang="cdo" data-title="Só-hŏk" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - chechen" lang="ce" hreflang="ce" data-title="Математика" data-language-autonym="Нохчийн" data-language-local-name="chechen" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Isip" title="Isip - cebuan" lang="ceb" hreflang="ceb" data-title="Isip" data-language-autonym="Cebuano" data-language-local-name="cebuan" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-ch mw-list-item"><a href="https://ch.wikipedia.org/wiki/Matematika" title="Matematika - chamorro" lang="ch" hreflang="ch" data-title="Matematika" data-language-autonym="Chamoru" data-language-local-name="chamorro" class="interlanguage-link-target"><span>Chamoru</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%85%D8%A7%D8%AA%D9%85%D8%A7%D8%AA%DB%8C%DA%A9" title="ماتماتیک - kurd central" lang="ckb" hreflang="ckb" data-title="ماتماتیک" data-language-autonym="کوردی" data-language-local-name="kurd central" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Matematica" title="Matematica - còrs" lang="co" hreflang="co" data-title="Matematica" data-language-autonym="Corsu" data-language-local-name="còrs" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-crh mw-list-item"><a href="https://crh.wikipedia.org/wiki/Riyaziyat" title="Riyaziyat - tàtar de Crimea" lang="crh" hreflang="crh" data-title="Riyaziyat" data-language-autonym="Qırımtatarca" data-language-local-name="tàtar de Crimea" class="interlanguage-link-target"><span>Qırımtatarca</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Matematika" title="Matematika - chèc" lang="cs" hreflang="cs" data-title="Matematika" data-language-autonym="Čeština" data-language-local-name="chèc" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-csb mw-list-item"><a href="https://csb.wikipedia.org/wiki/Matematika" title="Matematika - caixubi" lang="csb" hreflang="csb" data-title="Matematika" data-language-autonym="Kaszëbsczi" data-language-local-name="caixubi" class="interlanguage-link-target"><span>Kaszëbsczi</span></a></li><li class="interlanguage-link interwiki-cu mw-list-item"><a href="https://cu.wikipedia.org/wiki/%D0%9C%D0%B0%D1%B3%D0%B8%D0%BC%D0%B0%D1%82%D1%97%D0%BA%D0%B0" title="Маѳиматїка - eslavon" lang="cu" hreflang="cu" data-title="Маѳиматїка" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="eslavon" class="interlanguage-link-target"><span>Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - chovash" lang="cv" hreflang="cv" data-title="Математика" data-language-autonym="Чӑвашла" data-language-local-name="chovash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Mathemateg" title="Mathemateg - gal·lès" lang="cy" hreflang="cy" data-title="Mathemateg" data-language-autonym="Cymraeg" data-language-local-name="gal·lès" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da badge-Q17559452 badge-recommendedarticle mw-list-item" title="article recomanat"><a href="https://da.wikipedia.org/wiki/Matematik" title="Matematik - danés" lang="da" hreflang="da" data-title="Matematik" data-language-autonym="Dansk" data-language-local-name="danés" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-dag mw-list-item"><a href="https://dag.wikipedia.org/wiki/Laasabu_malibu" title="Laasabu malibu - Dagbani" lang="dag" hreflang="dag" data-title="Laasabu malibu" data-language-autonym="Dagbanli" data-language-local-name="Dagbani" class="interlanguage-link-target"><span>Dagbanli</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="bons articles"><a href="https://de.wikipedia.org/wiki/Mathematik" title="Mathematik - alemand" lang="de" hreflang="de" data-title="Mathematik" data-language-autonym="Deutsch" data-language-local-name="alemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-din mw-list-item"><a href="https://din.wikipedia.org/wiki/Aku%C3%ABnk%C3%A4%C5%8B" title="Akuënkäŋ - dinka" lang="din" hreflang="din" data-title="Akuënkäŋ" data-language-autonym="Thuɔŋjäŋ" data-language-local-name="dinka" class="interlanguage-link-target"><span>Thuɔŋjäŋ</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Matematik" title="Matematik - Zazaki" lang="diq" hreflang="diq" data-title="Matematik" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dsb mw-list-item"><a href="https://dsb.wikipedia.org/wiki/Matematika" title="Matematika - baix sòrab" lang="dsb" hreflang="dsb" data-title="Matematika" data-language-autonym="Dolnoserbski" data-language-local-name="baix sòrab" class="interlanguage-link-target"><span>Dolnoserbski</span></a></li><li class="interlanguage-link interwiki-dtp mw-list-item"><a href="https://dtp.wikipedia.org/wiki/Matematik" title="Matematik - dusun central" lang="dtp" hreflang="dtp" data-title="Matematik" data-language-autonym="Kadazandusun" data-language-local-name="dusun central" class="interlanguage-link-target"><span>Kadazandusun</span></a></li><li class="interlanguage-link interwiki-dv mw-list-item"><a href="https://dv.wikipedia.org/wiki/%DE%83%DE%A8%DE%94%DE%A7%DE%9F%DE%A8%DE%87%DE%B0%DE%94%DE%A7%DE%8C%DE%AA" title="ރިޔާޟިއްޔާތު - divehi" lang="dv" hreflang="dv" data-title="ރިޔާޟިއްޔާތު" data-language-autonym="ދިވެހިބަސް" data-language-local-name="divehi" class="interlanguage-link-target"><span>ދިވެހިބަސް</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC" title="Μαθηματικά - grèc" lang="el" hreflang="el" data-title="Μαθηματικά" data-language-autonym="Ελληνικά" data-language-local-name="grèc" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Matem%C3%A2tica" title="Matemâtica - Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Matemâtica" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Mathematics" title="Mathematics - anglés" lang="en" hreflang="en" data-title="Mathematics" data-language-autonym="English" data-language-local-name="anglés" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Matematiko" title="Matematiko - esperanto" lang="eo" hreflang="eo" data-title="Matematiko" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Matem%C3%A1ticas" title="Matemáticas - espanhòl" lang="es" hreflang="es" data-title="Matemáticas" data-language-autonym="Español" data-language-local-name="espanhòl" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Matemaatika" title="Matemaatika - estonian" lang="et" hreflang="et" data-title="Matemaatika" data-language-autonym="Eesti" data-language-local-name="estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Matematika" title="Matematika - basc" lang="eu" hreflang="eu" data-title="Matematika" data-language-autonym="Euskara" data-language-local-name="basc" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Matem%C3%A1ticas" title="Matemáticas - extremeny" lang="ext" hreflang="ext" data-title="Matemáticas" data-language-autonym="Estremeñu" data-language-local-name="extremeny" class="interlanguage-link-target"><span>Estremeñu</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" title="ریاضیات - perse" lang="fa" hreflang="fa" data-title="ریاضیات" data-language-autonym="فارسی" data-language-local-name="perse" 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/Matematiikka" title="Matematiikka - finlandés" lang="fi" hreflang="fi" data-title="Matematiikka" data-language-autonym="Suomi" data-language-local-name="finlandés" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Mat%C3%B5maatiga" title="Matõmaatiga - võro" lang="vro" hreflang="vro" data-title="Matõmaatiga" data-language-autonym="Võro" data-language-local-name="võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Fika" title="Fika - fijian" lang="fj" hreflang="fj" data-title="Fika" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fijian" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/St%C3%B8ddfr%C3%B8%C3%B0i" title="Støddfrøði - feroés" lang="fo" hreflang="fo" data-title="Støddfrøði" data-language-autonym="Føroyskt" data-language-local-name="feroés" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Math%C3%A9matiques" title="Mathématiques - francés" lang="fr" hreflang="fr" data-title="Mathématiques" data-language-autonym="Français" data-language-local-name="francés" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frp mw-list-item"><a href="https://frp.wikipedia.org/wiki/Mat%C3%A8matiques" title="Matèmatiques - francoprovençal" lang="frp" hreflang="frp" data-title="Matèmatiques" data-language-autonym="Arpetan" data-language-local-name="francoprovençal" class="interlanguage-link-target"><span>Arpetan</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Matematiik" title="Matematiik - frisó septentrional" lang="frr" hreflang="frr" data-title="Matematiik" data-language-autonym="Nordfriisk" data-language-local-name="frisó septentrional" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Matematiche" title="Matematiche - friolan" lang="fur" hreflang="fur" data-title="Matematiche" data-language-autonym="Furlan" data-language-local-name="friolan" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Wiskunde" title="Wiskunde - frisó occidental" lang="fy" hreflang="fy" data-title="Wiskunde" data-language-autonym="Frysk" data-language-local-name="frisó occidental" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Matamaitic" title="Matamaitic - irlandés" lang="ga" hreflang="ga" data-title="Matamaitic" data-language-autonym="Gaeilge" data-language-local-name="irlandés" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E6%95%B8%E5%AD%B8" title="數學 - xinès gan" lang="gan" hreflang="gan" data-title="數學" data-language-autonym="贛語" data-language-local-name="xinès gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Mat%C3%A9matik" title="Matématik - créole guyanais" lang="gcr" hreflang="gcr" data-title="Matématik" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="créole guyanais" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Matamataig" title="Matamataig - gaelic escossés" lang="gd" hreflang="gd" data-title="Matamataig" data-language-autonym="Gàidhlig" data-language-local-name="gaelic escossés" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Matem%C3%A1ticas" title="Matemáticas - galician" lang="gl" hreflang="gl" data-title="Matemáticas" data-language-autonym="Galego" data-language-local-name="galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Papapykuaa" title="Papapykuaa - guaraní" lang="gn" hreflang="gn" data-title="Papapykuaa" data-language-autonym="Avañe'ẽ" data-language-local-name="guaraní" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gom mw-list-item"><a href="https://gom.wikipedia.org/wiki/%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%E0%B3%8D" title="ಗಣಿತ್ - concani de Goa" lang="gom" hreflang="gom" data-title="ಗಣಿತ್" data-language-autonym="गोंयची कोंकणी / Gõychi Konknni" data-language-local-name="concani de Goa" class="interlanguage-link-target"><span>गोंयची कोंकणी / Gõychi Konknni</span></a></li><li class="interlanguage-link interwiki-gor mw-list-item"><a href="https://gor.wikipedia.org/wiki/Matematika" title="Matematika - gorontalo" lang="gor" hreflang="gor" data-title="Matematika" data-language-autonym="Bahasa Hulontalo" data-language-local-name="gorontalo" class="interlanguage-link-target"><span>Bahasa Hulontalo</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%97%E0%AA%A3%E0%AA%BF%E0%AA%A4" title="ગણિત - gujarati" lang="gu" hreflang="gu" data-title="ગણિત" data-language-autonym="ગુજરાતી" data-language-local-name="gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Maddaght" title="Maddaght - manx" lang="gv" hreflang="gv" data-title="Maddaght" data-language-autonym="Gaelg" data-language-local-name="manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Lissafi" title="Lissafi - haussa" lang="ha" hreflang="ha" data-title="Lissafi" data-language-autonym="Hausa" data-language-local-name="haussa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Su-ho%CC%8Dk" title="Su-ho̍k - xinès hakka" lang="hak" hreflang="hak" data-title="Su-ho̍k" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="xinès hakka" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/Makemakika" title="Makemakika - hawaià" lang="haw" hreflang="haw" data-title="Makemakika" data-language-autonym="Hawaiʻi" data-language-local-name="hawaià" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94" title="מתמטיקה - ebrèu" lang="he" hreflang="he" data-title="מתמטיקה" data-language-autonym="עברית" data-language-local-name="ebrèu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित - Indi" lang="hi" hreflang="hi" data-title="गणित" data-language-autonym="हिन्दी" data-language-local-name="Indi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Mathematics" title="Mathematics - hindi de Fiji" lang="hif" hreflang="hif" data-title="Mathematics" data-language-autonym="Fiji Hindi" data-language-local-name="hindi de Fiji" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Matematika" title="Matematika - croat" lang="hr" hreflang="hr" data-title="Matematika" data-language-autonym="Hrvatski" data-language-local-name="croat" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Matematik" title="Matematik - crioll d’Haití" lang="ht" hreflang="ht" data-title="Matematik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="crioll d’Haití" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Matematika" title="Matematika - ongrés" lang="hu" hreflang="hu" data-title="Matematika" data-language-autonym="Magyar" data-language-local-name="ongrés" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1" title="Մաթեմատիկա - armèni" lang="hy" hreflang="hy" data-title="Մաթեմատիկա" data-language-autonym="Հայերեն" data-language-local-name="armèni" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><a href="https://ia.wikipedia.org/wiki/Mathematica" title="Mathematica - interlingua" lang="ia" hreflang="ia" data-title="Mathematica" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Matematik" title="Matematik - iban" lang="iba" hreflang="iba" data-title="Matematik" data-language-autonym="Jaku Iban" data-language-local-name="iban" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Matematika" title="Matematika - indonesian" lang="id" hreflang="id" data-title="Matematika" 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-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Matematica" title="Matematica - interlingue" lang="ie" hreflang="ie" data-title="Matematica" data-language-autonym="Interlingue" data-language-local-name="interlingue" class="interlanguage-link-target"><span>Interlingue</span></a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/%E1%BB%8Cm%C3%BAm%C3%BA-%C3%B3n%C3%BA%E1%BB%8Dg%E1%BB%A5g%E1%BB%A5" title="Ọmúmú-ónúọgụgụ - igbo" lang="ig" hreflang="ig" data-title="Ọmúmú-ónúọgụgụ" data-language-autonym="Igbo" data-language-local-name="igbo" class="interlanguage-link-target"><span>Igbo</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Matematika" title="Matematika - ilocano" lang="ilo" hreflang="ilo" data-title="Matematika" data-language-autonym="Ilokano" data-language-local-name="ilocano" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - ingúix" lang="inh" hreflang="inh" data-title="Математика" data-language-autonym="ГӀалгӀай" data-language-local-name="ingúix" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Matematiko" title="Matematiko - ido" lang="io" hreflang="io" data-title="Matematiko" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/St%C3%A6r%C3%B0fr%C3%A6%C3%B0i" title="Stærðfræði - islandés" lang="is" hreflang="is" data-title="Stærðfræði" data-language-autonym="Íslenska" data-language-local-name="islandés" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Matematica" title="Matematica - italian" lang="it" hreflang="it" data-title="Matematica" data-language-autonym="Italiano" data-language-local-name="italian" 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/%E6%95%B0%E5%AD%A6" title="数学 - japonés" lang="ja" hreflang="ja" data-title="数学" data-language-autonym="日本語" data-language-local-name="japonés" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Matimatix" title="Matimatix - crioll anglès de Jamaica" lang="jam" hreflang="jam" data-title="Matimatix" data-language-autonym="Patois" data-language-local-name="crioll anglès de Jamaica" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/cmaci" title="cmaci - lojban" lang="jbo" hreflang="jbo" data-title="cmaci" data-language-autonym="La .lojban." data-language-local-name="lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><a href="https://jv.wikipedia.org/wiki/Mat%C3%A9matika" title="Matématika - javanés" lang="jv" hreflang="jv" data-title="Matématika" data-language-autonym="Jawa" data-language-local-name="javanés" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="მათემატიკა - georgian" lang="ka" hreflang="ka" data-title="მათემატიკა" data-language-autonym="ქართული" data-language-local-name="georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Matematika" title="Matematika - karakalpak" lang="kaa" hreflang="kaa" data-title="Matematika" data-language-autonym="Qaraqalpaqsha" data-language-local-name="karakalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tusnakt" title="Tusnakt - cabil" lang="kab" hreflang="kab" data-title="Tusnakt" data-language-autonym="Taqbaylit" data-language-local-name="cabil" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kge mw-list-item"><a href="https://kge.wikipedia.org/wiki/Matematika" title="Matematika - Komering" lang="kge" hreflang="kge" data-title="Matematika" data-language-autonym="Kumoring" data-language-local-name="Komering" class="interlanguage-link-target"><span>Kumoring</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - cazac" lang="kk" hreflang="kk" data-title="Математика" data-language-autonym="Қазақша" data-language-local-name="cazac" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kl mw-list-item"><a href="https://kl.wikipedia.org/wiki/Matematikki" title="Matematikki - groenlandès" lang="kl" hreflang="kl" data-title="Matematikki" data-language-autonym="Kalaallisut" data-language-local-name="groenlandès" class="interlanguage-link-target"><span>Kalaallisut</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%82%E1%9E%8E%E1%9E%B7%E1%9E%8F%E1%9E%9C%E1%9E%B7%E1%9E%91%E1%9F%92%E1%9E%99%E1%9E%B6" title="គណិតវិទ្យា - cambojian" lang="km" hreflang="km" data-title="គណិតវិទ្យា" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="cambojian" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಗಣಿತ - kannada" lang="kn" hreflang="kn" data-title="ಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%88%98%ED%95%99" title="수학 - corean" lang="ko" hreflang="ko" data-title="수학" data-language-autonym="한국어" data-language-local-name="corean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-krc mw-list-item"><a href="https://krc.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - karatxai-balkar" lang="krc" hreflang="krc" data-title="Математика" data-language-autonym="Къарачай-малкъар" data-language-local-name="karatxai-balkar" class="interlanguage-link-target"><span>Къарачай-малкъар</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%DA%AF%D8%B1%D9%9B%D8%A0%D9%86%D8%AF%D9%8F%D8%AA" title="گرٛؠندُت - cashmiri" lang="ks" hreflang="ks" data-title="گرٛؠندُت" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="cashmiri" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Matemat%C3%AEk" title="Matematîk - curd" lang="ku" hreflang="ku" data-title="Matematîk" data-language-autonym="Kurdî" data-language-local-name="curd" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Awgrym" title="Awgrym - cornic" lang="kw" hreflang="kw" data-title="Awgrym" data-language-autonym="Kernowek" data-language-local-name="cornic" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%A1%D0%BE%D0%BC%D0%BE/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Википедия:Сомо/Математика - kirguís" lang="ky" hreflang="ky" data-title="Википедия:Сомо/Математика" data-language-autonym="Кыргызча" data-language-local-name="kirguís" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><a href="https://la.wikipedia.org/wiki/Mathematica" title="Mathematica - latin" lang="la" hreflang="la" data-title="Mathematica" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lad mw-list-item"><a href="https://lad.wikipedia.org/wiki/Matem%C3%A1tika" title="Matemátika - ladin" lang="lad" hreflang="lad" data-title="Matemátika" data-language-autonym="Ladino" data-language-local-name="ladin" class="interlanguage-link-target"><span>Ladino</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Mathematik" title="Mathematik - luxemborgés" lang="lb" hreflang="lb" data-title="Mathematik" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemborgés" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lez mw-list-item"><a href="https://lez.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - lesguià" lang="lez" hreflang="lez" data-title="Математика" data-language-autonym="Лезги" data-language-local-name="lesguià" class="interlanguage-link-target"><span>Лезги</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Matematica" title="Matematica - lingua franca nova" lang="lfn" hreflang="lfn" data-title="Matematica" data-language-autonym="Lingua Franca Nova" data-language-local-name="lingua franca nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Ekibalangulo" title="Ekibalangulo - ganda" lang="lg" hreflang="lg" data-title="Ekibalangulo" data-language-autonym="Luganda" data-language-local-name="ganda" class="interlanguage-link-target"><span>Luganda</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Mathematiek" title="Mathematiek - limburguès" lang="li" hreflang="li" data-title="Mathematiek" data-language-autonym="Limburgs" data-language-local-name="limburguès" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Matematica" title="Matematica - lígur" lang="lij" hreflang="lij" data-title="Matematica" data-language-autonym="Ligure" data-language-local-name="lígur" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lld mw-list-item"><a href="https://lld.wikipedia.org/wiki/Matematica" title="Matematica - Ladin" lang="lld" hreflang="lld" data-title="Matematica" data-language-autonym="Ladin" data-language-local-name="Ladin" class="interlanguage-link-target"><span>Ladin</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Matematega" title="Matematega - llombard" lang="lmo" hreflang="lmo" data-title="Matematega" data-language-autonym="Lombard" data-language-local-name="llombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94%E0%BA%AA%E0%BA%B2%E0%BA%94" title="ຄະນິດສາດ - laosian" lang="lo" hreflang="lo" data-title="ຄະນິດສາດ" data-language-autonym="ລາວ" data-language-local-name="laosian" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Matematika" title="Matematika - lituan" lang="lt" hreflang="lt" data-title="Matematika" data-language-autonym="Lietuvių" data-language-local-name="lituan" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Matem%C4%81tika" title="Matemātika - leton" lang="lv" hreflang="lv" data-title="Matemātika" data-language-autonym="Latviešu" data-language-local-name="leton" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mad mw-list-item"><a href="https://mad.wikipedia.org/wiki/Matematika" title="Matematika - madurès" lang="mad" hreflang="mad" data-title="Matematika" data-language-autonym="Madhurâ" data-language-local-name="madurès" class="interlanguage-link-target"><span>Madhurâ</span></a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित - maithili" lang="mai" hreflang="mai" data-title="गणित" data-language-autonym="मैथिली" data-language-local-name="maithili" class="interlanguage-link-target"><span>मैथिली</span></a></li><li class="interlanguage-link interwiki-map-bms mw-list-item"><a href="https://map-bms.wikipedia.org/wiki/Matematika" title="Matematika - Banyumasan" lang="jv-x-bms" hreflang="jv-x-bms" data-title="Matematika" data-language-autonym="Basa Banyumasan" data-language-local-name="Banyumasan" class="interlanguage-link-target"><span>Basa Banyumasan</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Matematika" title="Matematika - malgash" lang="mg" hreflang="mg" data-title="Matematika" data-language-autonym="Malagasy" data-language-local-name="malgash" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5" title="Математике - Eastern Mari" lang="mhr" hreflang="mhr" data-title="Математике" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Matematika" title="Matematika - minangkabau" lang="min" hreflang="min" data-title="Matematika" data-language-autonym="Minangkabau" data-language-local-name="minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - macedonian" lang="mk" hreflang="mk" data-title="Математика" data-language-autonym="Македонски" data-language-local-name="macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="ഗണിതം - malaiàlam" lang="ml" hreflang="ml" data-title="ഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="malaiàlam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><a href="https://mn.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA" title="Математик - mongòl" lang="mn" hreflang="mn" data-title="Математик" data-language-autonym="Монгол" data-language-local-name="mongòl" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mni mw-list-item"><a href="https://mni.wikipedia.org/wiki/%EA%AF%86%EA%AF%A9%EA%AF%81%EA%AF%A4%EA%AF%A1%EA%AF%82%EA%AF%A3%EA%AF%9F" title="ꯆꯩꯁꯤꯡꯂꯣꯟ - manipurí" lang="mni" hreflang="mni" data-title="ꯆꯩꯁꯤꯡꯂꯣꯟ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="manipurí" class="interlanguage-link-target"><span>ꯃꯤꯇꯩ ꯂꯣꯟ</span></a></li><li class="interlanguage-link interwiki-mnw mw-list-item"><a href="https://mnw.wikipedia.org/wiki/%E1%80%9E%E1%81%9A%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="သၚ်္ချာ - Mon" lang="mnw" hreflang="mnw" data-title="သၚ်္ချာ" data-language-autonym="ဘာသာမန်" data-language-local-name="Mon" class="interlanguage-link-target"><span>ဘာသာမန်</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित - marathi" lang="mr" hreflang="mr" data-title="गणित" 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/Matematik" title="Matematik - malai" lang="ms" hreflang="ms" data-title="Matematik" data-language-autonym="Bahasa Melayu" data-language-local-name="malai" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Matematika" title="Matematika - maltés" lang="mt" hreflang="mt" data-title="Matematika" data-language-autonym="Malti" data-language-local-name="maltés" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Matem%C3%A1tica" title="Matemática - mirandés" lang="mwl" hreflang="mwl" data-title="Matemática" data-language-autonym="Mirandés" data-language-local-name="mirandés" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="သင်္ချာ - birman" lang="my" hreflang="my" data-title="သင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birman" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - mordovià erza" lang="myv" hreflang="myv" data-title="Математика" data-language-autonym="Эрзянь" data-language-local-name="mordovià erza" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%D8%B1%D9%82%D9%85" title="رقم - mazanderani" lang="mzn" hreflang="mzn" data-title="رقم" data-language-autonym="مازِرونی" data-language-local-name="mazanderani" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-nah mw-list-item"><a href="https://nah.wikipedia.org/wiki/Tlap%C5%8Dhualmatiliztli" title="Tlapōhualmatiliztli - Nahuatl" lang="nah" hreflang="nah" data-title="Tlapōhualmatiliztli" data-language-autonym="Nāhuatl" data-language-local-name="Nahuatl" class="interlanguage-link-target"><span>Nāhuatl</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Mathematik" title="Mathematik - baix alemany" lang="nds" hreflang="nds" data-title="Mathematik" data-language-autonym="Plattdüütsch" data-language-local-name="baix alemany" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nds-nl mw-list-item"><a href="https://nds-nl.wikipedia.org/wiki/Wiskunde" title="Wiskunde - baix saxó" lang="nds-NL" hreflang="nds-NL" data-title="Wiskunde" data-language-autonym="Nedersaksies" data-language-local-name="baix saxó" class="interlanguage-link-target"><span>Nedersaksies</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित - nepalés" lang="ne" hreflang="ne" data-title="गणित" data-language-autonym="नेपाली" data-language-local-name="nepalés" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B2%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%83%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="ल्याःज्या - newari" lang="new" hreflang="new" data-title="ल्याःज्या" data-language-autonym="नेपाल भाषा" data-language-local-name="newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nia mw-list-item"><a href="https://nia.wikipedia.org/wiki/Matematika" title="Matematika - nias" lang="nia" hreflang="nia" data-title="Matematika" data-language-autonym="Li Niha" data-language-local-name="nias" class="interlanguage-link-target"><span>Li Niha</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wiskunde" title="Wiskunde - neerlandés" lang="nl" hreflang="nl" data-title="Wiskunde" data-language-autonym="Nederlands" data-language-local-name="neerlandés" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Matematikk" title="Matematikk - norvegian nynorsk" lang="nn" hreflang="nn" data-title="Matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegian 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" title="Matematikk - norvegian bokmål" lang="nb" hreflang="nb" data-title="Matematikk" data-language-autonym="Norsk bokmål" data-language-local-name="norvegian bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Matematike" title="Matematike - novial" lang="nov" hreflang="nov" data-title="Matematike" data-language-autonym="Novial" data-language-local-name="novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-nrm mw-list-item"><a href="https://nrm.wikipedia.org/wiki/Caltchul" title="Caltchul - Norman" lang="nrf" hreflang="nrf" data-title="Caltchul" data-language-autonym="Nouormand" data-language-local-name="Norman" class="interlanguage-link-target"><span>Nouormand</span></a></li><li class="interlanguage-link interwiki-nv mw-list-item"><a href="https://nv.wikipedia.org/wiki/A%C5%82hii%CA%BCn%C3%ADn%C3%A1%CA%BCiidz%C3%B3%C3%B3h" title="Ałhiiʼnínáʼiidzóóh - navaho" lang="nv" hreflang="nv" data-title="Ałhiiʼnínáʼiidzóóh" data-language-autonym="Diné bizaad" data-language-local-name="navaho" class="interlanguage-link-target"><span>Diné bizaad</span></a></li><li class="interlanguage-link interwiki-olo mw-list-item"><a href="https://olo.wikipedia.org/wiki/Matematiekku" title="Matematiekku - Livvi-Karelian" lang="olo" hreflang="olo" data-title="Matematiekku" data-language-autonym="Livvinkarjala" data-language-local-name="Livvi-Karelian" class="interlanguage-link-target"><span>Livvinkarjala</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Herrega" title="Herrega - oromo" lang="om" hreflang="om" data-title="Herrega" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%97%E0%AC%A3%E0%AC%BF%E0%AC%A4" title="ଗଣିତ - oriya" lang="or" hreflang="or" data-title="ଗଣିତ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="oriya" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%C3%A6" title="Математикæ - osseta" lang="os" hreflang="os" data-title="Математикæ" data-language-autonym="Ирон" data-language-local-name="osseta" class="interlanguage-link-target"><span>Ирон</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%97%E0%A8%A3%E0%A8%BF%E0%A8%A4" title="ਗਣਿਤ - punjabi" lang="pa" hreflang="pa" data-title="ਗਣਿਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pag mw-list-item"><a href="https://pag.wikipedia.org/wiki/Matematiks" title="Matematiks - pangasinan" lang="pag" hreflang="pag" data-title="Matematiks" data-language-autonym="Pangasinan" data-language-local-name="pangasinan" class="interlanguage-link-target"><span>Pangasinan</span></a></li><li class="interlanguage-link interwiki-pam mw-list-item"><a href="https://pam.wikipedia.org/wiki/Matematica" title="Matematica - pampanga" lang="pam" hreflang="pam" data-title="Matematica" data-language-autonym="Kapampangan" data-language-local-name="pampanga" class="interlanguage-link-target"><span>Kapampangan</span></a></li><li class="interlanguage-link interwiki-pap mw-list-item"><a href="https://pap.wikipedia.org/wiki/Matem%C3%A1tika" title="Matemátika - papiament" lang="pap" hreflang="pap" data-title="Matemátika" data-language-autonym="Papiamentu" data-language-local-name="papiament" class="interlanguage-link-target"><span>Papiamentu</span></a></li><li class="interlanguage-link interwiki-pcd mw-list-item"><a href="https://pcd.wikipedia.org/wiki/Mat%C3%A9matikes" title="Matématikes - picard" lang="pcd" hreflang="pcd" data-title="Matématikes" data-language-autonym="Picard" data-language-local-name="picard" class="interlanguage-link-target"><span>Picard</span></a></li><li class="interlanguage-link interwiki-pi mw-list-item"><a href="https://pi.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A4%82" title="गणितं - pali" lang="pi" hreflang="pi" data-title="गणितं" data-language-autonym="पालि" data-language-local-name="pali" class="interlanguage-link-target"><span>पालि</span></a></li><li class="interlanguage-link interwiki-pih mw-list-item"><a href="https://pih.wikipedia.org/wiki/Maethamatiks" title="Maethamatiks - Norfuk / Pitkern" lang="pih" hreflang="pih" data-title="Maethamatiks" data-language-autonym="Norfuk / Pitkern" data-language-local-name="Norfuk / Pitkern" class="interlanguage-link-target"><span>Norfuk / Pitkern</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Matematyka" title="Matematyka - polonés" lang="pl" hreflang="pl" data-title="Matematyka" data-language-autonym="Polski" data-language-local-name="polonés" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Matem%C3%A0tica" title="Matemàtica - piemontès" lang="pms" hreflang="pms" data-title="Matemàtica" data-language-autonym="Piemontèis" data-language-local-name="piemontès" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="ریاضی - Western Punjabi" lang="pnb" hreflang="pnb" data-title="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-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%B4%D9%85%DB%90%D8%B1%D9%BE%D9%88%D9%87%D9%86%D9%87" title="شمېرپوهنه - pashto" lang="ps" hreflang="ps" data-title="شمېرپوهنه" data-language-autonym="پښتو" data-language-local-name="pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Matem%C3%A1tica" title="Matemática - portugués" lang="pt" hreflang="pt" data-title="Matemática" data-language-autonym="Português" data-language-local-name="portugués" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Yupay_yachay" title="Yupay yachay - quechua" lang="qu" hreflang="qu" data-title="Yupay yachay" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Matematic%C4%83" title="Matematică - romanés" lang="ro" hreflang="ro" data-title="Matematică" data-language-autonym="Română" data-language-local-name="romanés" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-roa-rup mw-list-item"><a href="https://roa-rup.wikipedia.org/wiki/Mathematic%C3%A2" title="Mathematicâ - aromanès" lang="rup" hreflang="rup" data-title="Mathematicâ" data-language-autonym="Armãneashti" data-language-local-name="aromanès" class="interlanguage-link-target"><span>Armãneashti</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" title="Математика - rus" lang="ru" hreflang="ru" data-title="Математика" data-language-autonym="Русский" data-language-local-name="rus" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D1%96%D0%BA%D0%B0" title="Математіка - ruthène" lang="rue" hreflang="rue" data-title="Математіка" data-language-autonym="Русиньскый" data-language-local-name="ruthène" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A4%AE%E0%A5%8D" title="गणितम् - sanscrit" lang="sa" hreflang="sa" data-title="गणितम्" data-language-autonym="संस्कृतम्" data-language-local-name="sanscrit" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - iacut" lang="sah" hreflang="sah" data-title="Математика" data-language-autonym="Саха тыла" data-language-local-name="iacut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%AE%E1%B1%9E%E1%B1%A0%E1%B1%B7%E1%B1%9F" title="ᱮᱞᱠᱷᱟ - santali" lang="sat" hreflang="sat" data-title="ᱮᱞᱠᱷᱟ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="santali" class="interlanguage-link-target"><span>ᱥᱟᱱᱛᱟᱲᱤ</span></a></li><li class="interlanguage-link interwiki-sc badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><a href="https://sc.wikipedia.org/wiki/Matem%C3%A0tica" title="Matemàtica - sard" lang="sc" hreflang="sc" data-title="Matemàtica" data-language-autonym="Sardu" data-language-local-name="sard" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Matim%C3%A0tica" title="Matimàtica - sicilian" lang="scn" hreflang="scn" data-title="Matimàtica" data-language-autonym="Sicilianu" data-language-local-name="sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Mathematics" title="Mathematics - escossés" lang="sco" hreflang="sco" data-title="Mathematics" data-language-autonym="Scots" data-language-local-name="escossés" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A" title="رياضي - sindi" lang="sd" hreflang="sd" data-title="رياضي" data-language-autonym="سنڌي" data-language-local-name="sindi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Matematika" title="Matematika - serbocroat" lang="sh" hreflang="sh" data-title="Matematika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroat" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Tusnakt" title="Tusnakt - taixelhit" lang="shi" hreflang="shi" data-title="Tusnakt" data-language-autonym="Taclḥit" data-language-local-name="taixelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%BA" title="ගණිතය - singalès" lang="si" hreflang="si" data-title="ගණිතය" data-language-autonym="සිංහල" data-language-local-name="singalès" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Mathematics" title="Mathematics - Simple English" lang="en-simple" hreflang="en-simple" data-title="Mathematics" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Matematika" title="Matematika - eslovac" lang="sk" hreflang="sk" data-title="Matematika" data-language-autonym="Slovenčina" data-language-local-name="eslovac" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-skr mw-list-item"><a href="https://skr.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="ریاضی - Saraiki" lang="skr" hreflang="skr" data-title="ریاضی" data-language-autonym="سرائیکی" data-language-local-name="Saraiki" class="interlanguage-link-target"><span>سرائیکی</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Matematika" title="Matematika - eslovèn" lang="sl" hreflang="sl" data-title="Matematika" data-language-autonym="Slovenščina" data-language-local-name="eslovèn" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sm mw-list-item"><a href="https://sm.wikipedia.org/wiki/Matematika" title="Matematika - samoan" lang="sm" hreflang="sm" data-title="Matematika" data-language-autonym="Gagana Samoa" data-language-local-name="samoan" class="interlanguage-link-target"><span>Gagana Samoa</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Masvomhu" title="Masvomhu - shona" lang="sn" hreflang="sn" data-title="Masvomhu" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Tiromaal" title="Tiromaal - somali" lang="so" hreflang="so" data-title="Tiromaal" data-language-autonym="Soomaaliga" data-language-local-name="somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Matematika" title="Matematika - albanés" lang="sq" hreflang="sq" data-title="Matematika" data-language-autonym="Shqip" data-language-local-name="albanés" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - serbi" lang="sr" hreflang="sr" data-title="Математика" data-language-autonym="Српски / srpski" data-language-local-name="serbi" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-srn mw-list-item"><a href="https://srn.wikipedia.org/wiki/Sabi_fu_Teri" title="Sabi fu Teri - sranan" lang="srn" hreflang="srn" data-title="Sabi fu Teri" data-language-autonym="Sranantongo" data-language-local-name="sranan" class="interlanguage-link-target"><span>Sranantongo</span></a></li><li class="interlanguage-link interwiki-ss mw-list-item"><a href="https://ss.wikipedia.org/wiki/Tekubala" title="Tekubala - swazi" lang="ss" hreflang="ss" data-title="Tekubala" data-language-autonym="SiSwati" data-language-local-name="swazi" class="interlanguage-link-target"><span>SiSwati</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Mathematik" title="Mathematik - saterlandais" lang="stq" hreflang="stq" data-title="Mathematik" data-language-autonym="Seeltersk" data-language-local-name="saterlandais" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Matematika" title="Matematika - sondanès" lang="su" hreflang="su" data-title="Matematika" data-language-autonym="Sunda" data-language-local-name="sondanès" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Matematik" title="Matematik - suedés" lang="sv" hreflang="sv" data-title="Matematik" data-language-autonym="Svenska" data-language-local-name="suedés" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Hisabati" title="Hisabati - swahili" lang="sw" hreflang="sw" data-title="Hisabati" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Matymatyka" title="Matymatyka - silesià" lang="szl" hreflang="szl" data-title="Matymatyka" data-language-autonym="Ślůnski" data-language-local-name="silesià" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="கணிதம் - tamol" lang="ta" hreflang="ta" data-title="கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="tamol" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tcy mw-list-item"><a href="https://tcy.wikipedia.org/wiki/%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಗಣಿತ - toulou" lang="tcy" hreflang="tcy" data-title="ಗಣಿತ" data-language-autonym="ತುಳು" data-language-local-name="toulou" class="interlanguage-link-target"><span>ತುಳು</span></a></li><li class="interlanguage-link interwiki-tdd mw-list-item"><a href="https://tdd.wikipedia.org/wiki/%E1%A5%99%E1%A5%A3%E1%A5%AD%E1%A5%B0_%E1%A5%98%E1%A5%99%E1%A5%B3" title="ᥙᥣᥭᥰ ᥘᥙᥳ - Tai Nuea" lang="tdd" hreflang="tdd" data-title="ᥙᥣᥭᥰ ᥘᥙᥳ" data-language-autonym="ᥖᥭᥰ ᥖᥬᥲ ᥑᥨᥒᥰ" data-language-local-name="Tai Nuea" class="interlanguage-link-target"><span>ᥖᥭᥰ ᥖᥬᥲ ᥑᥨᥒᥰ</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%97%E0%B0%A3%E0%B0%BF%E0%B0%A4%E0%B0%82" title="గణితం - telogó" lang="te" hreflang="te" data-title="గణితం" data-language-autonym="తెలుగు" data-language-local-name="telogó" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tet mw-list-item"><a href="https://tet.wikipedia.org/wiki/Matem%C3%A1tika" title="Matemátika - tètum" lang="tet" hreflang="tet" data-title="Matemátika" data-language-autonym="Tetun" data-language-local-name="tètum" class="interlanguage-link-target"><span>Tetun</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A0%D0%B8%D1%91%D0%B7%D0%B8%D1%91%D1%82" title="Риёзиёт - tajic" lang="tg" hreflang="tg" data-title="Риёзиёт" data-language-autonym="Тоҷикӣ" data-language-local-name="tajic" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="คณิตศาสตร์ - tai" lang="th" hreflang="th" data-title="คณิตศาสตร์" data-language-autonym="ไทย" data-language-local-name="tai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Matematika" title="Matematika - turcmèn" lang="tk" hreflang="tk" data-title="Matematika" data-language-autonym="Türkmençe" data-language-local-name="turcmèn" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Matematika" title="Matematika - tagal" lang="tl" hreflang="tl" data-title="Matematika" data-language-autonym="Tagalog" data-language-local-name="tagal" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tly mw-list-item"><a href="https://tly.wikipedia.org/wiki/Rijozijot" title="Rijozijot - talix" lang="tly" hreflang="tly" data-title="Rijozijot" data-language-autonym="Tolışi" data-language-local-name="talix" class="interlanguage-link-target"><span>Tolışi</span></a></li><li class="interlanguage-link interwiki-tn mw-list-item"><a href="https://tn.wikipedia.org/wiki/Dipalo" title="Dipalo - setswana" lang="tn" hreflang="tn" data-title="Dipalo" data-language-autonym="Setswana" data-language-local-name="setswana" class="interlanguage-link-target"><span>Setswana</span></a></li><li class="interlanguage-link interwiki-tpi mw-list-item"><a href="https://tpi.wikipedia.org/wiki/Ol_matematik" title="Ol matematik - tok pisin" lang="tpi" hreflang="tpi" data-title="Ol matematik" data-language-autonym="Tok Pisin" data-language-local-name="tok pisin" class="interlanguage-link-target"><span>Tok Pisin</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Matematik" title="Matematik - turc" lang="tr" hreflang="tr" data-title="Matematik" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Dyondzo-Tinhlayo" title="Dyondzo-Tinhlayo - tsonga" lang="ts" hreflang="ts" data-title="Dyondzo-Tinhlayo" data-language-autonym="Xitsonga" data-language-local-name="tsonga" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - tatar" lang="tt" hreflang="tt" data-title="Математика" data-language-autonym="Татарча / tatarça" data-language-local-name="tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-udm mw-list-item"><a href="https://udm.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - udmurt" lang="udm" hreflang="udm" data-title="Математика" data-language-autonym="Удмурт" data-language-local-name="udmurt" class="interlanguage-link-target"><span>Удмурт</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - ucrainés" lang="uk" hreflang="uk" data-title="Математика" data-language-autonym="Українська" data-language-local-name="ucrainés" 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%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="ریاضی - ordó" lang="ur" hreflang="ur" data-title="ریاضی" data-language-autonym="اردو" data-language-local-name="ordó" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Matematika" title="Matematika - ozbèc" lang="uz" hreflang="uz" data-title="Matematika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="ozbèc" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Matem%C3%A0tega" title="Matemàtega - vènet" lang="vec" hreflang="vec" data-title="Matemàtega" data-language-autonym="Vèneto" data-language-local-name="vènet" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Matematik" title="Matematik - vepse" lang="vep" hreflang="vep" data-title="Matematik" data-language-autonym="Vepsän kel’" data-language-local-name="vepse" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi badge-Q17437798 badge-goodarticle mw-list-item" title="bons articles"><a href="https://vi.wikipedia.org/wiki/To%C3%A1n_h%E1%BB%8Dc" title="Toán học - vietnamian" lang="vi" hreflang="vi" data-title="Toán học" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamian" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Wiskunde" title="Wiskunde - flamenc occidental" lang="vls" hreflang="vls" data-title="Wiskunde" data-language-autonym="West-Vlams" data-language-local-name="flamenc occidental" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-vo badge-Q17437796 badge-featuredarticle mw-list-item" title="articles de qualitat"><a href="https://vo.wikipedia.org/wiki/Matemat" title="Matemat - volapuc" lang="vo" hreflang="vo" data-title="Matemat" data-language-autonym="Volapük" data-language-local-name="volapuc" class="interlanguage-link-target"><span>Volapük</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Matematike" title="Matematike - való" lang="wa" hreflang="wa" data-title="Matematike" data-language-autonym="Walon" data-language-local-name="való" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Matematika" title="Matematika - waray" lang="war" hreflang="war" data-title="Matematika" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Xayma" title="Xayma - wòlof" lang="wo" hreflang="wo" data-title="Xayma" data-language-autonym="Wolof" data-language-local-name="wòlof" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%95%B0%E5%AD%A6" title="数学 - xinès wu" lang="wuu" hreflang="wuu" data-title="数学" data-language-autonym="吴语" data-language-local-name="xinès wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика - kalmoc" lang="xal" hreflang="xal" data-title="Математика" data-language-autonym="Хальмг" data-language-local-name="kalmoc" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-Mathematics" title="I-Mathematics - xhòsa" lang="xh" hreflang="xh" data-title="I-Mathematics" data-language-autonym="IsiXhosa" data-language-local-name="xhòsa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="მათემატიკა - mingrelià" lang="xmf" hreflang="xmf" data-title="მათემატიკა" data-language-autonym="მარგალური" data-language-local-name="mingrelià" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%9E%D7%90%D7%98%D7%A2%D7%9E%D7%90%D7%98%D7%99%D7%A7" title="מאטעמאטיק - yiddish" lang="yi" hreflang="yi" data-title="מאטעמאטיק" data-language-autonym="ייִדיש" data-language-local-name="yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Mathim%C3%A1t%C3%ADk%C3%AC" title="Mathimátíkì - yoruba" lang="yo" hreflang="yo" data-title="Mathimátíkì" data-language-autonym="Yorùbá" data-language-local-name="yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-za mw-list-item"><a href="https://za.wikipedia.org/wiki/Soqyoz" title="Soqyoz - zhuang" lang="za" hreflang="za" data-title="Soqyoz" data-language-autonym="Vahcuengh" data-language-local-name="zhuang" class="interlanguage-link-target"><span>Vahcuengh</span></a></li><li class="interlanguage-link interwiki-zea mw-list-item"><a href="https://zea.wikipedia.org/wiki/Wiskunde" title="Wiskunde - zelandès" lang="zea" hreflang="zea" data-title="Wiskunde" data-language-autonym="Zeêuws" data-language-local-name="zelandès" class="interlanguage-link-target"><span>Zeêuws</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%9C%E2%B5%93%E2%B5%99%E2%B5%8F%E2%B4%B0%E2%B4%BD%E2%B5%9C" title="ⵜⵓⵙⵏⴰⴽⵜ - amazic estàndard marroquí" lang="zgh" hreflang="zgh" data-title="ⵜⵓⵙⵏⴰⴽⵜ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="amazic estàndard marroquí" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%95%B0%E5%AD%A6" title="数学 - chinés" lang="zh" hreflang="zh" data-title="数学" data-language-autonym="中文" data-language-local-name="chinés" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%95%B8%E5%AD%B8" title="數學 - xinès clàssic" lang="lzh" hreflang="lzh" data-title="數學" data-language-autonym="文言" data-language-local-name="xinès clàssic" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/S%C3%B2%CD%98-ha%CC%8Dk" title="Sò͘-ha̍k - xinès min del sud" lang="nan" hreflang="nan" data-title="Sò͘-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="xinès min del sud" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%95%B8%E5%AD%B8" title="數學 - cantonés" lang="yue" hreflang="yue" data-title="數學" data-language-autonym="粵語" data-language-local-name="cantonés" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Umchazazibalo" title="Umchazazibalo - zólo" lang="zu" hreflang="zu" data-title="Umchazazibalo" data-language-autonym="IsiZulu" data-language-local-name="zólo" class="interlanguage-link-target"><span>IsiZulu</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/Q395#sitelinks-wikipedia" title="Modificar los ligams interlenga" class="wbc-editpage">Modificar los ligams</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Espacis de noms"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Matematicas" title="Veire l’article [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Discutir:Matematicas" rel="discussion" title="Discussion a prepaus d'aquesta pagina [t]" accesskey="t"><span>Discussion</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Canvia la variant de llengua" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">occitan</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Afichatges"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Matematicas"><span>Legir</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Matematicas&veaction=edit" title="Modificar aquela pagina [v]" accesskey="v"><span>Modificar</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Matematicas&action=edit" title="Modificar lo còdi font d'aquela pagina [e]" accesskey="e"><span>Modificar lo còdi</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Matematicas&action=history" title="Los autors e versions precedentas d'aquesta pagina. 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.mergedtoprow{border-top:solid 1px #ccd2d9;padding:0.4em 0.6em 0.2em 0.6em}.mw-parser-output .infobox.geografia .mergedrow,.mw-parser-output .infobox.geografia .mergedrow{border:0;padding:0 0.6em 0.2em 0.6em}.mw-parser-output .infobox.geografia .mergedbottomrow,.mw-parser-output .infobox.geografia .mergedbottomrow{border-top:0;border-bottom:solid 1px #ccd2d9;padding:0 0.6em 0.4em 0.6em}.mw-parser-output .infobox.geografia .maptable td,.mw-parser-output .infobox.geografia .maptable th{border:0;padding:0}.mw-parser-output .ib-geografia-text{font-weight:normal}.mw-parser-output .ib-geografia-fn-alpha{list-style-type:lower-alpha;margin-left:1em}.mw-parser-output .ib-geografia-fn-num{margin-left:1em}</style> </p> <table class="infobox" style="border-spacing:3.8px; max-width:18em;"><tbody><tr><td colspan="2" class="" style="text-align:center; font-size: 125%; font-weight: bold; background-color: #ACE1AF">Sciéncias</td></tr><tr><td colspan="2" class="" style="text-align:center;"> <span typeof="mw:File"><a href="/wiki/Fichi%C3%A8r:Nuvola_Phys_Chem.svg" class="mw-file-description" title="Scientia debet esse sapientia"><img alt="Scientia debet esse sapientia" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Nuvola_Phys_Chem.svg/120px-Nuvola_Phys_Chem.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Nuvola_Phys_Chem.svg/180px-Nuvola_Phys_Chem.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Nuvola_Phys_Chem.svg/240px-Nuvola_Phys_Chem.svg.png 2x" data-file-width="64" data-file-height="64" /></a></span> </td></tr><tr><td colspan="2" class="" style="text-align:center;"><div class="mw-collapsible mw-collapsed" style="border:none; padding: 0;"> <div style="font-weight:bold; background-color: #ACE1AF; padding: 3px; font-size: 12px;"><a href="/w/index.php?title=Sci%C3%A9ncias_fisicas&action=edit&redlink=1" class="new" title="Sciéncias fisicas (la pagina existís pas)">Sciéncias fisicas</a></div><div class="mw-collapsible-content" style="text-align:left;"><a href="/wiki/Astronomia" title="Astronomia">Astronomia</a>  <b>·</b> <a href="/wiki/Biologia" title="Biologia">Biologia</a>  <b>·</b> <a href="/wiki/Fisica" title="Fisica">Fisica</a>  <b>·</b> <a href="/wiki/Geologia" title="Geologia">Geologia</a>  <b>·</b> <a href="/wiki/Quimia" title="Quimia">Quimia</a>  <b>·</b> <a href="/wiki/Sci%C3%A9ncias_de_la_T%C3%A8rra" title="Sciéncias de la Tèrra">Sciéncias de la Tèrra</a></div> </div></td></tr><tr><td colspan="2" class="" style="text-align:center;"><div class="mw-collapsible mw-collapsed" style="border:none; padding: 0;"> <div style="font-weight:bold; background-color: #ACE1AF; padding: 3px; font-size: 12px;"><a href="/wiki/Sci%C3%A9ncias_umanas" title="Sciéncias umanas">Sciéncias umanas</a></div><div class="mw-collapsible-content" style="text-align:left;"><a href="/wiki/Antropologia" title="Antropologia">Antropologia</a>  <b>·</b> <a href="/wiki/Economia" title="Economia">Economia</a>  <b>·</b> <a href="/wiki/Ling%C3%BCistica" title="Lingüistica">Lingüistica</a>  <b>·</b> <a href="/wiki/Psicologia" title="Psicologia">Psicologia</a>  <b>·</b> <a href="/wiki/Sociologia" title="Sociologia">Sociologia</a></div> </div></td></tr><tr><td colspan="2" class="" style="text-align:center;"><div class="mw-collapsible mw-collapsed" style="border:none; padding: 0;"> <div style="font-weight:bold; background-color: #ACE1AF; padding: 3px; font-size: 12px;"><a href="/wiki/Sci%C3%A9ncias_aplicadas" title="Sciéncias aplicadas">Sciéncias aplicadas</a></div><div class="mw-collapsible-content" style="text-align:left;"><a href="/wiki/Agricultura" title="Agricultura">Agricultura</a>  <b>·</b> <a href="/wiki/Engenhari%C3%A1" title="Engenhariá">Engenhariá</a>  <b>·</b> <a href="/wiki/Sci%C3%A9ncias_de_la_santat" title="Sciéncias de la santat">Sciéncias medicalas</a></div> </div></td></tr><tr><td colspan="2" class="" style="text-align:center;"><div class="mw-collapsible mw-collapsed" style="border:none; padding: 0;"> <div style="font-weight:bold; background-color: #ACE1AF; padding: 3px; font-size: 12px;"><a href="/w/index.php?title=Sci%C3%A9ncias_formalas&action=edit&redlink=1" class="new" title="Sciéncias formalas (la pagina existís pas)">Sciéncias formalas</a></div><div class="mw-collapsible-content" style="text-align:left;"><a href="/wiki/Estatistica" title="Estatistica">Estatistica</a>  <b>·</b> <a href="/wiki/Informatica" title="Informatica">Informatica</a>  <b>·</b> <a href="/wiki/Intellig%C3%A9ncia_artificiala" title="Intelligéncia artificiala">Intelligéncia artificiala</a>  <b>·</b> <a href="/wiki/Logica" title="Logica">Logica</a>  <b>·</b> <a class="mw-selflink selflink">Matematicas</a></div> </div></td></tr><tr><td class="navigation-only" colspan="2" style="border-top: 2px #AAAAAA solid; font-size: 80%; background:inherit; text-align: right;"><span class="plainlinks" style="float:left;"><a class="external text" href="https://oc.wikipedia.org/w/index.php?title=Matematicas&action=edit&section=0"><span style="color:#555;">modificar</span></a></span> <span title="Consultatz la documentacion del modèl"><span typeof="mw:File"><a href="/wiki/Mod%C3%A8l:Infodoc" title="Consultatz la documentacion del modèl"><img alt="Consultatz la documentacion del modèl" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Info_Simple.svg/12px-Info_Simple.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Info_Simple.svg/18px-Info_Simple.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/38/Info_Simple.svg/24px-Info_Simple.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span></span></td> </tr></tbody></table> <p>Las <b>matematicas</b> (var. <b>matematiques</b>) son un ensemble de disciplinas basadas sus la <a href="/w/index.php?title=Reflexion&action=edit&redlink=1" class="new" title="Reflexion (la pagina existís pas)">reflexion</a> e la <a href="/wiki/Logica" title="Logica">logica</a> que s'aplican sus l'utilizacion de nombres, de formulas, d'estructura, de donadas. </p><p>Lo mot « matematicas » es eissit deu nom comun en <a href="/wiki/Gr%C3%A8c_ancian" title="Grèc ancian">grèc ancian</a> <span lang="grc" style="font-family:georgia;">μάθημα</span> (<i>mathéma</i>, « leiçon ») derivat deu vèrb <span lang="grc" style="font-family:georgia;">μανθάνω</span> (<i>manthánô</i>, significant « aprene »). Significa <a href="/wiki/Etimologia" title="Etimologia">etimologicament</a> « sciéncia, coneissença », mas lo sens corrent es « matematic » de <span lang="grc" style="font-family:georgia;">μαθήματα</span> (<i>mathḗmata</i>). L'adjectiu <span lang="grc" style="font-family:georgia;">μαθηματικός</span> (<i>mathematikos</i>), primièr « relatiu au saber », puèi, « que concernís lei sciéncias matematicas ». Aquel adjectiu foguèt adoptat en latin (<i>mathematicus</i>). Las matematicas son utilizadas egalament dins mantun domeni de la vida vidanta. </p><p>Se considèra qu'un resultat matematic, o <a href="/wiki/Teor%C3%A8ma" title="Teorèma">teorèma</a>, es verai quand es estat demostrat. Una <a href="/w/index.php?title=Demostracion&action=edit&redlink=1" class="new" title="Demostracion (la pagina existís pas)">demostracion</a> es un rasonament deductiu que parte deis <a href="/wiki/Ipot%C3%A8si" title="Ipotèsi">ipotèsis</a> per arribar a la conclusion vouguda en seguent lei règlas de la logica; dins la practica, s'utiliza totjorn una mescla de lengatge formalizat e de lengatge <span class="citation">«naturau»</span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Evolucion_e_finalitat_dei_matematicas">Evolucion e finalitat dei matematicas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=1" title="Modificar la seccion : Evolucion e finalitat dei matematicas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=1" title="Edita el codi de la secció: Evolucion e finalitat dei matematicas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-section bandeau-niveau-detail loupe">Article detalhat: <a href="/w/index.php?title=Ist%C3%B2ria_dei_matematicas&action=edit&redlink=1" class="new" title="Istòria dei matematicas (la pagina existís pas)">Istòria dei matematicas</a>.</div><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fichi%C3%A8r:Euclid.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Euclid.jpg/320px-Euclid.jpg" decoding="async" width="320" height="268" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Euclid.jpg/480px-Euclid.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Euclid.jpg/640px-Euclid.jpg 2x" data-file-width="806" data-file-height="675" /></a><figcaption><a href="/wiki/Euclides" title="Euclides">Euclides</a>, detalh de <i>L'Escòla d'Atenas</i> per <a href="/wiki/Raf%C3%A8l" class="mw-redirect" title="Rafèl">Rafèl</a>.</figcaption></figure> <p>Lei <b>matematicas</b> an una lònga tradicion dins totei lei pòbles; foguèron la premiera disciplina a se dotar de metòdes d'auta rigor e portada, e a obtenir ansin l'estatut de <a href="/wiki/Sci%C3%A9ncia" title="Sciéncia">sciéncia</a>; an progressivament alargat lei tèmas de sa recèrca e estendut lei domenis que pòdon ajudar en matèria de calcul e de modelizacion. </p><p>Dins lo corrent de sa lònga istòria, e dins lei divèrseis environas culturalas, i aguèt de pontannadas de gròs progrès, e de pontannadas d'estanhacion deis estudis. Vèn en partida de l'importància dei quauquei personas capablas de portar d'innovacions prefondas e illuminativas e d'estimular la recèrca matematica. I aguèt tanben de pontannadas de reculament dei conoissenças e dei metòdes: mai se rescontrèron solament après de destruccions o en d'epòcas de decadéncia totala de la vida intellectuala e sociala. Dempuei 500 ans, còmpte tengut dau melhorament dei mejans de comunicacion, lo capitau de resultats e de metòdes s'es progressivament desvolopat. </p><p>Tot aquò s'apren a la natura deis activitats matematicas. Aquestei d'aicí tendon de lònga an una presentacion precisa dei problèmas e dei solucions, çò qu'impausa de comunicar en avent per tòca finala la possibilitat d'esclarzir totei lei detalhs dei construccions logicas e dei resultats (cèrts esclarziments exigisson un investiment important, de desenas d'ans de còps que i a). Es per aquò que i a pas d'exemple d'error matematica majora que seriá pas estada lèu reconeguda e corregida, o aumens senhalada. </p> <div class="mw-heading mw-heading2"><h2 id="Lei_divèrsei_brancas_dei_matematicas"><span id="Lei_div.C3.A8rsei_brancas_dei_matematicas"></span>Lei divèrsei brancas dei matematicas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=2" title="Modificar la seccion : Lei divèrsei brancas dei matematicas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=2" title="Edita el codi de la secció: Lei divèrsei brancas dei matematicas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Se destria actualament en matematicas tres grandei brancas mutualament liadas: </p> <ul><li>l'<a href="/wiki/Alg%C3%A8bra" title="Algèbra">algèbra</a> (exemples: <a href="/wiki/Alg%C3%A8bra_lineara" title="Algèbra lineara">algèbra lineara</a>, <a href="/wiki/Matematicas_discr%C3%A8tas" title="Matematicas discrètas">matematicas discrètas</a>)</li> <li>l'<a href="/w/index.php?title=Analisi_(matematicas)&action=edit&redlink=1" class="new" title="Analisi (matematicas) (la pagina existís pas)">analisi</a> (exemples: <a href="/wiki/Eq%C3%BCacion_diferenciala" class="mw-redirect" title="Eqüacion diferenciala">eqüacions diferencialas</a>, <a href="/w/index.php?title=Teoria_de_la_mesura&action=edit&redlink=1" class="new" title="Teoria de la mesura (la pagina existís pas)">teoria de la mesura</a>, <a href="/w/index.php?title=Calcul_dei_probabilitat&action=edit&redlink=1" class="new" title="Calcul dei probabilitat (la pagina existís pas)">calcul dei probabilitats</a>)</li> <li>la <a href="/wiki/Geometria" title="Geometria">geometria</a>, au jonhent de l'algèbra e de l'analisi (exemples: <a href="/wiki/Geometria_euclidiana" title="Geometria euclidiana">geometria euclidiana</a>, <a href="/w/index.php?title=Geometria_diferenciala&action=edit&redlink=1" class="new" title="Geometria diferenciala (la pagina existís pas)">geometria diferenciala</a>)</li></ul> <p>Lei liames entre aquelei brancas e leis usatges que caduna fa de l'autra son mai que prefonds e fondamentaus. La <a href="/wiki/Teoria_dei_nombres" class="mw-redirect" title="Teoria dei nombres">teoria dei nombres</a>, en particular la reflexion sus lei <a href="/w/index.php?title=Nombre_premier&action=edit&redlink=1" class="new" title="Nombre premier (la pagina existís pas)">nombres premiers</a>, es exemplara a regard d'aquò: a l'origina confonduda amb l'aritmetica elementària, s'es transformada au <a href="/wiki/S%C3%A8gle_XIX" title="Sègle XIX">sègle XIX</a> en una teoria onte l'analisi es venguda indispensabla. Au <a href="/wiki/S%C3%A8gle_XX" title="Sègle XX">sègle XX</a>, la <a href="/w/index.php?title=Geometria_algebrica&action=edit&redlink=1" class="new" title="Geometria algebrica (la pagina existís pas)">geometria algebrica</a> es venguda la terranha naturala acampant au còp metòdes algebrics, topologics e geometrics per afrontar lei problèmas de la teoria dei nombres, per exemple la <a href="/w/index.php?title=Conjectura_de_Fermat&action=edit&redlink=1" class="new" title="Conjectura de Fermat (la pagina existís pas)">conjectura de Fermat</a>, venguda gràcias an aquel apròchi novèu lo teorèma d'<a href="/w/index.php?title=Andrew_Wiles&action=edit&redlink=1" class="new" title="Andrew Wiles (la pagina existís pas)">Andrew Wiles</a> en 1994. Aqueu teorèma se formula en tèrmes algebrics, mai sa demostracion fa un usatge massís de matematicas liadas tant a l'algèbra coma a l'analisi e a la geometria. </p><p><i>Teorèma de Wiles</i>: </p><p>per tot <a href="/wiki/Entier_naturau" class="mw-redirect" title="Entier naturau">entier naturau</a> <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> superior o egau a 3, l'eqüacion <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^{n}+y^{n}=z^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x^{n}+y^{n}=z^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c538f4c6e2a173e980472d27fa1872b5cae07fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.755ex; height:2.676ex;" alt="{\displaystyle \ x^{n}+y^{n}=z^{n}}"></span> a ges de solucion entiera <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,y,z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (x,y,z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb9d98e83d71ef958a1bfbff62b8b3698fc017a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.031ex; height:2.843ex;" alt="{\displaystyle \ (x,y,z)}"></span> tala que <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 xyz\neq 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mi>y</mi> <mi>z</mi> <mo>≠</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle xyz\neq 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a973d82f9cbf7af25f67889652e6c9a9fcc10d48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.834ex; height:2.676ex;" alt="{\displaystyle xyz\neq 0}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="L'algèbra"><span id="L.27alg.C3.A8bra"></span>L'algèbra</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=3" title="Modificar la seccion : L'algèbra" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=3" title="Edita el codi de la secció: L'algèbra"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'<a href="/wiki/Alg%C3%A8bra" title="Algèbra">algèbra</a> es la partida dei matematicas qu'estúdia leis <a href="/wiki/Estructura_algebrica" title="Estructura algebrica">estructuras algebricas</a>. Se pòt destriar de sotadisciplinas, per exemple: </p> <ul><li>La teoria dei <a href="/wiki/Grop_(matematicas)" title="Grop (matematicas)">grops</a></li> <li>L'<a href="/wiki/Alg%C3%A8bra_lineara" title="Algèbra lineara">algèbra lineara</a> e <a href="/w/index.php?title=Alg%C3%A8bra_multilineara&action=edit&redlink=1" class="new" title="Algèbra multilineara (la pagina existís pas)">multilineara</a></li> <li>La <a href="/w/index.php?title=Teoria_de_Galois&action=edit&redlink=1" class="new" title="Teoria de Galois (la pagina existís pas)">teoria de Galois</a> (qu'un de sei resultats remarcables es l'impossibilitat, en generau, de resòuvre per radicaus leis eqüacions algebricas)</li> <li>L'<a href="/w/index.php?title=Alg%C3%A8bra_omologica&action=edit&redlink=1" class="new" title="Algèbra omologica (la pagina existís pas)">algèbra omologica</a> (fòrça utila en geometria)</li></ul> <p>En mai de son desvolopament intrinsec, es necessària a l'analisi e la geometria per progressar. Son interès per aquestei darrieras vèn dau fach que d'estructuras algebricas se retròban dins de domenis nombrós. </p><p>Per exemple, lo lengatge e lei teorèmas de l'algèbra lineara permeton de comprendre en prefondor de domenis <i>a priori</i> fòrça alunhats, pron qu'agan una estructura lineara: </p> <ul><li>leis eqüacions diferencialas linearas d'òrdre <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> (aquelei que fan intervenir la derivada <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>-ena de la foncion inconeguda) an exactament <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 n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> solucions independentas, donc de comportament diferent.</li> <li>en analisi, <a href="/w/index.php?title=Diferenciala&action=edit&redlink=1" class="new" title="Diferenciala (la pagina existís pas)">diferenciar</a> una foncion consistís a l'aprochar localament per una foncion afina (soma d'una constanta e d'una foncion lineara). Ansin, leis instruments de l'algèbra lineara (o bilineara) vènon indispensables per saupre s'un ponch critic (que se pòt determinar analiticament) d'una foncion diferenciabla es un ponch d'extremum (minimum, maximum) o un ponch còl.</li></ul> <div class="mw-heading mw-heading3"><h3 id="L'analisi"><span id="L.27analisi"></span>L'analisi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=4" title="Modificar la seccion : L'analisi" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=4" title="Edita el codi de la secció: L'analisi"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'<a href="/w/index.php?title=Analisi&action=edit&redlink=1" class="new" title="Analisi (la pagina existís pas)">analisi</a> es la partida dei matematicas qu'a inicialament per objècte principau l'estudi dei <a href="/wiki/Foncion_(matematicas)" class="mw-redirect" title="Foncion (matematicas)">foncions</a> de variablas realas, en çò que pertòca lei nocions de <a href="/w/index.php?title=Limit&action=edit&redlink=1" class="new" title="Limit (la pagina existís pas)">limit</a>, de <a href="/wiki/Derivada" title="Derivada">derivada</a> e d'<a href="/w/index.php?title=Integrala&action=edit&redlink=1" class="new" title="Integrala (la pagina existís pas)">integrala</a>. Emai ague de precursors tre l'<a href="/wiki/Antiquitat" title="Antiquitat">Antiquitat</a> (<a href="/wiki/Arquim%C3%A8des" title="Arquimèdes">Arquimèdes</a>), l'analisi comença fondamentalament amb <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> e <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a>, inventors au <a href="/wiki/S%C3%A8gle_XVII" title="Sègle XVII">sègle XVII</a> dau <a href="/wiki/Calcul_infinitesimau" class="mw-redirect" title="Calcul infinitesimau">calcul infinitesimau</a>. </p><p>Se i pòt destriar mai d'un domeni, per exemple: </p> <ul><li>Leis <a href="/wiki/Eq%C3%BCacion_diferenciala" class="mw-redirect" title="Eqüacion diferenciala">eqüacions diferencialas</a>. Son d'eqüacions liant una foncion inconeguda e d'unei de sei derivadas successivas; entre lei questions importantas pertocant lei solucions, citem: l'existéncia, l'unicitat, lo comportament qualitatiu o quantitatiu au bòrd dau domeni de definicion (per exemple, se la variabla es lo temps, coma se compòrta a tèrme lòng una solucion).</li> <li>L'<a href="/w/index.php?title=Analisi_de_Fourier&action=edit&redlink=1" class="new" title="Analisi de Fourier (la pagina existís pas)">analisi de Fourier</a> que permete de descompausar una foncion en soma d'armonics (<a href="/w/index.php?title=Serias_de_Fourier&action=edit&redlink=1" class="new" title="Serias de Fourier (la pagina existís pas)">serias de Fourier</a>, <a href="/w/index.php?title=Transformacion_de_Fourier&action=edit&redlink=1" class="new" title="Transformacion de Fourier (la pagina existís pas)">transformacion de Fourier</a>). Es essenciala en teoria dau senhau.</li> <li>Lo <a href="/w/index.php?title=Calcul_dei_probabilitats&action=edit&redlink=1" class="new" title="Calcul dei probabilitats (la pagina existís pas)">calcul dei probabilitats</a>: modeliza leis fluctuacions de l'<a href="/w/index.php?title=Azard&action=edit&redlink=1" class="new" title="Azard (la pagina existís pas)">azard</a>. A l'origina associat ai matematicas discrètas (jòcs de rèsta: lançament de dats, tiratges de cartas...), es estat finalament provesit per <a href="/w/index.php?title=Andrei_Nikolaievich_Kolmogorov&action=edit&redlink=1" class="new" title="Andrei Nikolaievich Kolmogorov (la pagina existís pas)">Kolmogorov</a> d'una axiomatica fòrça mai generala, fondada sus la <a href="/w/index.php?title=Teoria_de_la_mesura&action=edit&redlink=1" class="new" title="Teoria de la mesura (la pagina existís pas)">teoria de la mesura</a>; la probabilitat d'un eveniment es l'integrala d'una cèrta foncion liada a la natura dau modèl (per exemple, una <a href="/w/index.php?title=Densitat_de_probabilitat&action=edit&redlink=1" class="new" title="Densitat de probabilitat (la pagina existís pas)">densitat</a> <a href="/w/index.php?title=Gaussiana&action=edit&redlink=1" class="new" title="Gaussiana (la pagina existís pas)">gaussiana</a> se se mesura la talha d'una persona presa a l'azard dins una populacion omogenèa), sus un cèrt domeni (una <span class="citation">«forqueta»</span> dins aquest exemple, quand se cèrca la probabilitat que la talha siá compressa entre doas valors donadas).</li></ul> <p>Pasmens, l'analisi se limita pas ai foncions de variablas realas. Un capítol important, creat au sègle XIX per <a href="/w/index.php?title=Augustin_Cauchy&action=edit&redlink=1" class="new" title="Augustin Cauchy (la pagina existís pas)">Cauchy</a>, <a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Riemann</a> e <a href="/w/index.php?title=Karl_Weierstrass&action=edit&redlink=1" class="new" title="Karl Weierstrass (la pagina existís pas)">Weierstrass</a>, estúdia lei <a href="/w/index.php?title=Foncion_analitica&action=edit&redlink=1" class="new" title="Foncion analitica (la pagina existís pas)">foncions analiticas</a> de <a href="/wiki/Nombre_compl%C3%A8xe" title="Nombre complèxe">variablas complèxas</a>: es la teoria dei <a href="/wiki/Foncion_olom%C3%B2rfa" title="Foncion olomòrfa">foncions olomòrfas</a>. Existís d'autrei generalizacions de la nocion de foncion, coma la nocion recenta de <a href="/w/index.php?title=Distribucion&action=edit&redlink=1" class="new" title="Distribucion (la pagina existís pas)">distribucion</a>, deguda a <a href="/w/index.php?title=Laurent_Schwartz&action=edit&redlink=1" class="new" title="Laurent Schwartz (la pagina existís pas)">Laurent Schwartz</a>. </p> <div class="mw-heading mw-heading3"><h3 id="La_geometria">La geometria</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=5" title="Modificar la seccion : La geometria" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=5" title="Edita el codi de la secció: La geometria"><span>Modificar lo còdi</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/Fichi%C3%A8r:120px-Dodecahedron-slowturn.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/7/70/120px-Dodecahedron-slowturn.gif" decoding="async" width="120" height="120" class="mw-file-element" data-file-width="120" data-file-height="120" /></a><figcaption>Lo dodecaèdre regular, un dei cinc solids platonicians de l'espaci euclidian de dimension 3</figcaption></figure> <p>Es una disciplina atestada tre l'Antiquitat, e lo tèrme de <i>geomètra</i> foguèt fins au sègle XIX sinonim de <span class="citation">«matematician»</span>. L'objècte de la <a href="/wiki/Geometria" title="Geometria">geometria</a> es de comprendre la natura dei figuras d'un espaci, e lei relacions que s'establisson entre elei. <i>Espaci</i> pòt designar per exemple: l'<a href="/w/index.php?title=Espaci_euclidian&action=edit&redlink=1" class="new" title="Espaci euclidian (la pagina existís pas)">espaci euclidian</a> classic, un <a href="/wiki/Espaci_vectoriau" title="Espaci vectoriau">espaci vectoriau</a> pus generau, un espaci corbe o <a href="/w/index.php?title=Varietat_diferenciabla&action=edit&redlink=1" class="new" title="Varietat diferenciabla (la pagina existís pas)">varietat diferenciabla</a>... </p><p>Segon la concepcion modèrna formulada en 1872 per <a href="/w/index.php?title=F%C3%A8lix_Klein&action=edit&redlink=1" class="new" title="Fèlix Klein (la pagina existís pas)">Fèlix Klein</a>, una geometria se definís per un ensemble de ponchs e un <a href="/wiki/Grop_(matematicas)" title="Grop (matematicas)">grop</a> de transformacions <a href="/wiki/Bijeccion" title="Bijeccion">bijectivas</a> d'aquel ensemble, e s'interèssa ai proprietats invariantas per leis elements dau grop. </p><p>Se pòt destriar mai d'un domeni de la geometria, per exemple: </p> <ul><li>la <a href="/wiki/Geometria_euclidiana" title="Geometria euclidiana">geometria euclidiana</a></li> <li>la <a href="/w/index.php?title=Geometria_diferenciala&action=edit&redlink=1" class="new" title="Geometria diferenciala (la pagina existís pas)">geometria diferenciala</a>, qu'estúdia (localament o globalament) lei corbas, lei <a href="/wiki/Superf%C3%ADcia_(matematicas)" title="Superfícia (matematicas)">superfícias</a>, e pus generalament lei varietats diferenciablas</li> <li>lei <a href="/w/index.php?title=Geometrias_non_euclidianas&action=edit&redlink=1" class="new" title="Geometrias non euclidianas (la pagina existís pas)">geometrias non euclidianas</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Matematicas_aplicadas_e_matematicas_puras">Matematicas aplicadas e matematicas puras</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=6" title="Modificar la seccion : Matematicas aplicadas e matematicas puras" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=6" title="Edita el codi de la secció: Matematicas aplicadas e matematicas puras"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'activitat matematica s'interèssa naturalament ai generalizacions e abstraccions possiblas, en relacion amb leis esparnhes de pensada e lei melhoraments deis instruments (en particular leis instruments de calcul) qu'es portada a realizar. Sovent, lei generalizacions e lei abstraccions menan puei en de visions pus aprefondidas dei problèmas e en de sinergias importantas entre de recèrcas pertocant de questions inicialament sensa rapòrt. </p><p>Dins lo corrent dau desvolopament dei matematicas, se pòt notar de pontannadas e d'environas onte prevalon alternativament d'actituds generalas e de valors que se pòdon reduire en dos tipes de motivacions e d'apròchis: lei <i>motivacions practicas</i> que butan a descurbir de procediments eficaç (per exemple dins la resolucion de problèmas industriaus e tecnologics), e leis exigéncias de <i>creacion d'un sistèma conceptuau</i> amb sa tendéncia a la generalizacion e a l'abstraccion. </p><p>Entre aquelei doas menas d'actituds, i a de còps una oposicion, e mai charpinosa, mai en generau s'enriquisson mutualament e desvolopan de sinergias. Dins lei 30 o 40 darriers ans, i a agut, entre aqueleis actituds, un cèrt equilibri, amb de tensions, e tanben d'episòdis d'assisténcia mutuala. An aquel estat de causas contribuís mai que mai lo desvolopament espectaclós de l'informatica, e amb ela, de la partida algoritmica dei matematicas. </p> <div class="mw-heading mw-heading2"><h2 id="Lei_matematicas_e_leis_autrei_sciéncias"><span id="Lei_matematicas_e_leis_autrei_sci.C3.A9ncias"></span>Lei matematicas e leis autrei sciéncias</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=7" title="Modificar la seccion : Lei matematicas e leis autrei sciéncias" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=7" title="Edita el codi de la secció: Lei matematicas e leis autrei sciéncias"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Instrument_e_lengatge">Instrument e lengatge</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=8" title="Modificar la seccion : Instrument e lengatge" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=8" title="Edita el codi de la secció: Instrument e lengatge"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lei matematicas sièrvon de <a href="/wiki/Lengatge" title="Lengatge">lengatge</a> o de supòrt en de <a href="/w/index.php?title=Sci%C3%A9ncias&action=edit&redlink=1" class="new" title="Sciéncias (la pagina existís pas)">sciéncias</a> fòrça nombrosas (naturalas o umanas) afin de quantificar cèrts fenomèns. S'utilizan tanben per predire de formas e efectuar de prediccions qualitativas. </p><p>Lo principi de la matematizacion es aquest: una sciéncia donada, o una sotatematica de la sciéncia (par exemple la <a href="/wiki/Biologia" title="Biologia">biologia</a> o la <a href="/wiki/Termodinamica" title="Termodinamica">termodinamica</a>) selecciona cèrts paramètres supausats quantificables (lo temps, lo nombre de <a href="/wiki/Bact%C3%A8ri" title="Bactèri">bactèris</a>, la temperatura, lo pòrtafuelha d'un accionari) qu'entre elei s'es constatat de relacions (la populacion bacteriana creisse amb lo temps, la temperatura e la pression son liadas). Una <a href="/wiki/Eq%C3%BCacion" class="mw-redirect" title="Eqüacion">eqüacion</a>, fòrça sovent diferenciala, lia d'unei d'aquelei paramètres entre elei, e establís ansin d'un biais quantitatiu son interdependéncia. L'estudi matematic d'aqueleis eqüacions va permetre, après retorn ais èssers reaus associats ai paramètres, de <a href="/w/index.php?title=Prediccion&action=edit&redlink=1" class="new" title="Prediccion (la pagina existís pas)">predire</a>, valent a dire de constatar de <a href="/w/index.php?title=Relacion&action=edit&redlink=1" class="new" title="Relacion (la pagina existís pas)">relacions</a> novèlas entre lei tèrmes. En <a href="/wiki/Ecologia" title="Ecologia">ecologia</a> per exemple, una foncion pòt modelizar lo rapòrt entre una espècia e una autra espècia predatritz; l'estudi matematic de la foncion quand lo temps tende vèrs l'infinit va anonciar se lo sistèma ecologic evoluirà vèrs un sistèma estable e equilibrat, o ben (per exemple) s'una deis espècias dispareisserà. </p> <div class="mw-heading mw-heading3"><h3 id="Lo_cas_particular_de_la_fisica">Lo cas particular de la fisica</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=9" title="Modificar la seccion : Lo cas particular de la fisica" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=9" title="Edita el codi de la secció: Lo cas particular de la fisica"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Istoricament, fisica e matematicas son prefondament liadas. Se coneis la frasa famosa de <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galilei</a>, fondator de la fisica modèrna: <i>Lo libre de la natura es escrich en lengatge matematic</i>. L'<a href="/wiki/Astronomia" title="Astronomia">astronomia</a>, per exemple, es estada un dei motors principaus de l'emergéncia de la disciplina matematica. </p><p>Puei, fins a la fin dau sègle XIX, lei matematicians seràn tanben fisicians (e sovent filosòfs). Se pòt destriar mai d'un rapòrt de naturas diferentas entre lei doas sciéncias: </p> <ul><li>una teoria fisica novèla reclama un instrument matematic. Dos cas: <ul><li>l'instrument existís ja (per la relativitat generala: la geometria riemanniana)</li> <li>l'instrument se deu inventar (per la mecanica classica: lo calcul diferenciau e integrau)</li></ul></li> <li>una teoria matematica novèla encoratja lei fisicians a explorar pus luenh sa teoria.</li> <li>una teoria fisica novèla duerbe de perspectivas matematicas quand l'instrument matematic utilizat per lei fisicians es encara an un estadi euristic, valent a dire que demanda d'èsser mes en forma d'un biais rigorós (leis integralas de <a href="/w/index.php?title=Feynman&action=edit&redlink=1" class="new" title="Feynman (la pagina existís pas)">Feynman</a> ne son un exemple tipic).</li></ul> <div class="mw-heading mw-heading3"><h3 id="Liames_amb_leis_autrei_sciéncias_de_la_natura"><span id="Liames_amb_leis_autrei_sci.C3.A9ncias_de_la_natura"></span>Liames amb leis autrei sciéncias de la natura</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=10" title="Modificar la seccion : Liames amb leis autrei sciéncias de la natura" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=10" title="Edita el codi de la secció: Liames amb leis autrei sciéncias de la natura"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Quimia" title="Quimia">quimia</a>: parcialament matematizada</li> <li><a href="/wiki/Biologia" title="Biologia">biologia</a> e <a href="/wiki/Sci%C3%A9ncias_de_la_T%C3%A8rra" title="Sciéncias de la Tèrra">sciéncias de la Tèrra</a>: usage parciau dei matematicas</li></ul> <div class="mw-heading mw-heading3"><h3 id="Liames_amb_lei_sciéncias_umanas"><span id="Liames_amb_lei_sci.C3.A9ncias_umanas"></span>Liames amb lei sciéncias umanas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=11" title="Modificar la seccion : Liames amb lei sciéncias umanas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=11" title="Edita el codi de la secció: Liames amb lei sciéncias umanas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Son rapòrt amb lei sciéncias umanas se fa essencialament per leis <a href="/wiki/Estatistica" title="Estatistica">estatisticas</a> e lo <a href="/w/index.php?title=Calcul_dei_probabilitats&action=edit&redlink=1" class="new" title="Calcul dei probabilitats (la pagina existís pas)">calcul dei probabilitats</a>, mai tanben per d'<a href="/wiki/Eq%C3%BCacion_diferenciala" class="mw-redirect" title="Eqüacion diferenciala">eqüacions diferencialas</a>, en economia e en finança: </p> <ul><li><a href="/wiki/Sociologia" title="Sociologia">sociologia</a></li> <li><a href="/wiki/Psicologia" title="Psicologia">psicologia</a></li> <li><a href="/wiki/Economia" title="Economia">economia</a>, <a href="/w/index.php?title=Finan%C3%A7a&action=edit&redlink=1" class="new" title="Finança (la pagina existís pas)">finança</a>, <a href="/w/index.php?title=Gestion&action=edit&redlink=1" class="new" title="Gestion (la pagina existís pas)">gestion</a></li></ul> <p>Aqueu rapòrt es controversiat, estent la natura umana d'aquelei sciéncias, e lo refús per d'unei, dins aqueu domeni, dau <a href="/w/index.php?title=Determinisme&action=edit&redlink=1" class="new" title="Determinisme (la pagina existís pas)">determinisme</a> que lei matematicas li son naturalament estacadas. </p> <div class="mw-heading mw-heading3"><h3 id="L'àbit_matematic_fa_pas_la_sciéncia"><span id="L.27.C3.A0bit_matematic_fa_pas_la_sci.C3.A9ncia"></span>L'àbit matematic fa pas la sciéncia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=12" title="Modificar la seccion : L'àbit matematic fa pas la sciéncia" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=12" title="Edita el codi de la secció: L'àbit matematic fa pas la sciéncia"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Matematizacion significa pas autenticitat scientifica. D'efècte, lei postulats d'una <span class="citation">«pensada»</span> pòdon èsser extremament problematics, e mai folastres, mai se son quantificables, pòdon donar luòc en de calculs complèxes. Un cas evident es aqueu de l'<a href="/wiki/Astrologia" title="Astrologia">astrologia</a>, que sei postulats, supausant una influéncia dei planetas sus lo comportament uman, son rebutats quasi unanimament per la comunautat scientifica. </p><p>Fòrça mai subtil es lo cas de l'<a href="/wiki/Economia" title="Economia">economia</a> matematica. Lo <a href="/w/index.php?title=Postulat&action=edit&redlink=1" class="new" title="Postulat (la pagina existís pas)">postulat</a> fondamentau d'aquela disciplina es que l'activitat economica se pòt comprendre a partir d'un axiòma de natura antropologica, aqueu de l'actor individuau racionau. Dins aquela vision, cada individú cèrca per seis accions d'acréisser un cèrt <a href="/w/index.php?title=Profiech&action=edit&redlink=1" class="new" title="Profiech (la pagina existís pas)">profiech</a> d'un biais racionau. Aquela mena de vision <a href="/wiki/Atomisme" title="Atomisme">atomista</a> de l'economia permete an aquesta d'aicí de matematizar pron aisadament sa reflexion, puei que lo <a href="/w/index.php?title=Calcul&action=edit&redlink=1" class="new" title="Calcul (la pagina existís pas)">calcul</a> individuau se transpausa en calcul matematic. Pasmens, cèrts sociològs, coma P. <a href="/w/index.php?title=Bourdieu&action=edit&redlink=1" class="new" title="Bourdieu (la pagina existís pas)">Bourdieu</a>, e mai cèrts economistas, refusan aqueu postulat de l'<a href="/w/index.php?title=Homo_%C5%93conomicus&action=edit&redlink=1" class="new" title="Homo œconomicus (la pagina existís pas)">homo œconomicus</a>, en remarcant que lei motivacions deis individús comprenon non solament lo <a href="/wiki/Don" class="mw-redirect" title="Don">don</a>, mai dependon tanben d'autres engatges que l'interès financier n'es qu'una partida, o simpletament son pas racionalas. La <a href="/w/index.php?title=Matematizacion&action=edit&redlink=1" class="new" title="Matematizacion (la pagina existís pas)">matematizacion</a> es donc segon elei ren qu'una semblança permetent una valorizacion scientifica de la disciplina. </p> <div class="mw-heading mw-heading2"><h2 id="Lei_matematicas_dins_l'Istòria"><span id="Lei_matematicas_dins_l.27Ist.C3.B2ria"></span>Lei matematicas dins l'Istòria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=13" title="Modificar la seccion : Lei matematicas dins l'Istòria" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=13" title="Edita el codi de la secció: Lei matematicas dins l'Istòria"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L’origina istorica dei matematicas es liada a sei premiereis aplicacions concrètas: lo <a href="/wiki/Com%C3%A8rci" title="Comèrci">comèrci</a>, la mesura dei <a href="/wiki/Aira" title="Aira">superfícias</a>, la prediccion deis eveniments <a href="/wiki/Astronomia" title="Astronomia">astronomics</a>. </p><p>Inicialament viradas vèrs la mesura (<a href="/wiki/Geometria" title="Geometria">geometria</a>) e lo comptatge (<a href="/wiki/Aritmetica" title="Aritmetica">aritmetica</a>), lei matematicas se viran lèu vèrs l'abstraccion. Lei matematicians grècs amb <a href="/wiki/Euclides" title="Euclides">Euclides</a> e seis <a href="/wiki/Elements_d%27Euclides" title="Elements d'Euclides">Elements</a> li aduson sei premiereis estructuras <a href="/wiki/Axi%C3%B2ma" title="Axiòma">axiomaticas</a>, puei son passatge en cò dei matematicians de <a href="/wiki/Arabi" title="Arabi">lenga aràbia</a> permete la fusion amb lei coneissenças orientalas e la creacion dau sistèma d'escritura numerica <i>aràbia</i>. </p><p>Dins lo corrent dei sègles XVI e XVII, es en Euròpa que se desvolopa un aspècte novèu dei matematicas. La creacion d'un lengatge simbolic (<a href="/wiki/Fran%C3%A7ois_Vi%C3%A8te" title="François Viète">Viète</a> e <a href="/wiki/Descartes" class="mw-redirect" title="Descartes">Descartes</a>) permete lo desvolopament dau calcul algebric, mentre que <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> e <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a>, metent en plaça lo <a href="/wiki/Calcul_infinitesimau" class="mw-redirect" title="Calcul infinitesimau">calcul infinitesimau</a>, fornisson leis instruments necessaris au desvolopament de l'<a href="/w/index.php?title=Analisi_(matematicas)&action=edit&redlink=1" class="new" title="Analisi (matematicas) (la pagina existís pas)">analisi</a>. </p><p>Au sègle XIX, lei matematicians son portats a explicitar d'<a href="/wiki/Estructura_algebrica" title="Estructura algebrica">estructuras algebricas</a>: <a href="/wiki/Grop_(matematicas)" title="Grop (matematicas)">grops</a> (<a href="/wiki/%C3%89variste_Galois" title="Évariste Galois">Évariste Galois</a>), <a href="/w/index.php?title=An%C3%A8u_(matematicas)&action=edit&redlink=1" class="new" title="Anèu (matematicas) (la pagina existís pas)">anèus</a> (<a href="/w/index.php?title=Richard_Dedekind&action=edit&redlink=1" class="new" title="Richard Dedekind (la pagina existís pas)">Richard Dedekind</a>), <a href="/w/index.php?title=C%C3%B2rs_(matematicas)&action=edit&redlink=1" class="new" title="Còrs (matematicas) (la pagina existís pas)">còrs</a>, <a href="/wiki/Espaci_vectoriau" title="Espaci vectoriau">espacis vectoriaus</a> (<a href="/w/index.php?title=Giuseppe_Peano&action=edit&redlink=1" class="new" title="Giuseppe Peano (la pagina existís pas)">Giuseppe Peano</a>), <a href="/w/index.php?title=Espaci_projectiu&action=edit&redlink=1" class="new" title="Espaci projectiu (la pagina existís pas)">espacis projectius</a>... Es lo desvolopament d'una branca novèla dei matematicas: l'<a href="/wiki/Alg%C3%A8bra_generala" class="mw-redirect" title="Algèbra generala">algèbra generala</a>. </p><p>Lo sègle XIX vei amb <a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a> e <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a> lo desvolopament d'una teoria axiomatica de totei leis objèctes estudiats, que mena au problèma dei <a href="/w/index.php?title=Fondaments_dei_matematicas&action=edit&redlink=1" class="new" title="Fondaments dei matematicas (la pagina existís pas)">fondaments dei matematicas</a>. Aqueu desvolopament de l'axiomatica menarà au sègle XX a cercar de definir totei lei matematicas per mejan d'un lengatge: la <a href="/w/index.php?title=Logica_matematica&action=edit&redlink=1" class="new" title="Logica matematica (la pagina existís pas)">logica</a>. </p><p>Dins lo corrent dau sègle XX, lo desvolopament de l'instrument informatic fa enregar una draia novèla ai matematicas: aquela de la <a href="/w/index.php?title=Mod%C3%A8l_matematic&action=edit&redlink=1" class="new" title="Modèl matematic (la pagina existís pas)">modelizacion</a> e de la numerizacion. </p><p>Dins lo corrent dei dos mila ans passats, lei matematicas an cercat, d'una part de fornir d'instruments utilizables per leis autrei sciéncias (fisica, geografia; astronomia...) e d'autra part de resòuvre de problèmas nascuts en son dintre coma la <a href="/w/index.php?title=Q%C3%BCadratura_dau_ceucle&action=edit&redlink=1" class="new" title="Qüadratura dau ceucle (la pagina existís pas)">qüadratura dau ceucle</a>, lei <a href="/w/index.php?title=Nombre_constructible&action=edit&redlink=1" class="new" title="Nombre constructible (la pagina existís pas)">nombres constructibles</a>, la <a href="/w/index.php?title=Conjectura_de_Fermat&action=edit&redlink=1" class="new" title="Conjectura de Fermat (la pagina existís pas)">conjectura de Fermat</a>, l'<a href="/w/index.php?title=Ipot%C3%A8si_de_Riemann&action=edit&redlink=1" class="new" title="Ipotèsi de Riemann (la pagina existís pas)">ipotèsi de Riemann</a>, la <a href="/wiki/Conjectura_de_Poincar%C3%A9" title="Conjectura de Poincaré">conjectura de Poincaré</a>, lei proposicions <a href="/w/index.php?title=Indecidibilitat&action=edit&redlink=1" class="new" title="Indecidibilitat (la pagina existís pas)">indecidiblas</a>, lei problèmas <a href="/w/index.php?title=Teoria_de_la_complexitat&action=edit&redlink=1" class="new" title="Teoria de la complexitat (la pagina existís pas)">NP-complèts</a>... </p> <div class="mw-heading mw-heading2"><h2 id="Fondaments,_rigor_e_logica"><span id="Fondaments.2C_rigor_e_logica"></span>Fondaments, rigor e logica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=14" title="Modificar la seccion : Fondaments, rigor e logica" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=14" title="Edita el codi de la secció: Fondaments, rigor e logica"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Lei_fondaments_dei_matematicas">Lei fondaments dei matematicas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=15" title="Modificar la seccion : Lei fondaments dei matematicas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=15" title="Edita el codi de la secció: Lei fondaments dei matematicas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lei <a href="/wiki/Teoria_deis_ensembles" title="Teoria deis ensembles">teorias deis ensembles</a>, desvolopadas inicialament a la fin dau sègle XIX, son de teorias fòrça generalas que donan un quadre onte de matematicians esperèron de poder formular e provar totei lei coneissenças matematicas. Espèr condemnat fin finala a pas capitar: vejatz <a href="/w/index.php?title=Logica_matematica&action=edit&redlink=1" class="new" title="Logica matematica (la pagina existís pas)">logica matematica</a>. Citem un exemple de matematicas usualas, e que se reduson pas en la teoria deis ensembles: la <a href="/w/index.php?title=Teoria_dei_categorias&action=edit&redlink=1" class="new" title="Teoria dei categorias (la pagina existís pas)">teoria dei categorias</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Logica_e_matematicas">Logica e matematicas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=16" title="Modificar la seccion : Logica e matematicas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=16" title="Edita el codi de la secció: Logica e matematicas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La logica enóncia lei règlas, o principis, que fau respectar per faire de deduccions corrèctas. Coma tota sciéncia exacta, la matematica se fonda sus lo <i>principi dau tèrç exclús</i>: <i>tota proposicion (senada) es siá veraia siá faussa</i>. Una deduccion consistís a partir de premissas per arribar an una conclusion en procedissent per etapas logicas. </p><p>En matematicas, l’estudi de la forma dau rasonament, independentament de seis objèctes, a una importància cruciala. Mostrem-o sus un exemple. Lei meteis <a href="/wiki/Axi%C3%B2ma" title="Axiòma">axiòmas</a>, aquelei deis espacis vectoriaus, se pòdon utilizar au còp per estudiar d'espacis geometrics, coma l’espaci euclidian, e per estudiar l’ensemble dei solucions d’una eqüacion diferenciala lineara. Lei teorèmas sus leis espacis vectoriaus son donc valables au còp per la geometria euclidiana e per leis eqüacions diferencialas linearas. La teoria abstracha deis espacis vectoriaus consistís a estudiar lei formas de deduccions que parton dei meteis axiòmas, independentament dau contèxte, valent a dire deis objèctes particulars que li son aplicadas aquelei deduccions. </p><p>Aquela definicion convèn ben ai matematicas aplicadas. Fòrça teorias abstrachas (lei nombres entiers, lei nombres reaus, lei foncions realas de variablas realas e leis eqüacions diferencialas, leis espacis vectoriaus, lei grops, lo calcul dei probabilitats,...) an una utilitat generala per totei lei sciéncias, perque se pòdon aplicar en d'objèctes nombrós. L'òbra dei matematicas aplicadas consistís a desvolopar de teorias, que sa valor es universala, en vista d’ajudar ais autrei sciéncias. </p> <div class="mw-heading mw-heading3"><h3 id="Rigor_e_practica_dei_matematicas">Rigor e practica dei matematicas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=17" title="Modificar la seccion : Rigor e practica dei matematicas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=17" title="Edita el codi de la secció: Rigor e practica dei matematicas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Coma activitat umana, practicada per d'umans, lei matematicas s'aluenhan pasmens dau modèl d'una construccion, segon lei lèis de la logica, e independenta dau reau. Citem un fach e un fenomèn per illustrar aiçò. D'en premier, ges de demostracion matematica siègue formalament lei lèis de la logica, simplament perque la traduccion d'enonciats matematics complèxes en lengatge totalament formalizat es umanament impossibla (e, probable, sens interès). </p><p>L'acceptacion de la veracitat d'una demostracion se fonda donc <i>in fine</i> sus un <a href="/w/index.php?title=Consensus&action=edit&redlink=1" class="new" title="Consensus (la pagina existís pas)">consensus</a> d'especialistas. Ansin, la fisança de la comunautat matematica dins un de sei membres prepausant un resultat novèu es capitala dins la recepcion d'aqueu resultat, d'aitant mai s'es imprevist o que modifica lo biais de veire lei causas. Se pòt prendre per exemple istoric lei controvèrsias sus lei <a href="/w/index.php?title=Geometria_non_euclidiana&action=edit&redlink=1" class="new" title="Geometria non euclidiana (la pagina existís pas)">geometrias non euclidianas</a> au sègle XIX, onte leis òbras de <a href="/w/index.php?title=Nicola%C3%AF_Ivanovitch_Lobatchevsky&action=edit&redlink=1" class="new" title="Nicolaï Ivanovitch Lobatchevsky (la pagina existís pas)">Lobatchevsky</a> foguèron largament ignoradas; o ben, dins un autre domeni, la non recepcion per <a href="/w/index.php?title=Cauchy&action=edit&redlink=1" class="new" title="Cauchy (la pagina existís pas)">Cauchy</a>, captau monarquista, deis òbras dau jove republican <a href="/w/index.php?title=Galois&action=edit&redlink=1" class="new" title="Galois (la pagina existís pas)">Galois</a> au començament dau meteis sègle. Se poiriá multiplicar de taus exemples amb totei lei variacions desiradas (plaça dei fremas, nacionalisme, nepotisme...) </p> <div class="mw-heading mw-heading2"><h2 id="Filosofias_dei_matematicas">Filosofias dei matematicas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=18" title="Modificar la seccion : Filosofias dei matematicas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=18" title="Edita el codi de la secció: Filosofias dei matematicas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L'universalitat manifèsta dei matematicas e son eficacitat son, aumens dempuei l'Antiquitat grèca, la fònt de questions filosoficas e metafisicas. L'Istòria deis Idèas es intimament liada a la reflexion sus la natura dei matematicas. Se pòt destriar tres grandei questions: </p> <ul><li>Quin es lo mòde d'existéncia deis objèctes matematics? Son reaus? tombant lo cas, de quina <a href="/wiki/Realitat" title="Realitat">realitat</a> se tracta? Es ren qu'una produccion de la <a href="/wiki/Pensada" title="Pensada">pensada</a>?</li> <li>Perqué lei matematicas semblan universalas?</li> <li>Perqué lei matematicas, creacion de l'<a href="/wiki/Esperit" title="Esperit">esperit</a>, permeton de comprendre un aspècte de l'<a href="/wiki/Univ%C3%A8rs" title="Univèrs">univèrs</a>?</li></ul> <div class="mw-heading mw-heading3"><h3 id="Lo_platonisme">Lo platonisme</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=19" title="Modificar la seccion : Lo platonisme" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=19" title="Edita el codi de la secció: Lo platonisme"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>« <i>Degun intre aicí se non es geomètra</i> », èra gravat sus lo portau de l'Escòla de <a href="/wiki/Platon" title="Platon">Platon</a>. Per aqueu filosòf, lei matematicas son un intermediari per accedir au reiaume deis <a href="/w/index.php?title=Id%C3%A8as&action=edit&redlink=1" class="new" title="Idèas (la pagina existís pas)">Idèas</a>. </p> <div class="mw-heading mw-heading3"><h3 id="L'aristotelisme"><span id="L.27aristotelisme"></span>L'aristotelisme</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=20" title="Modificar la seccion : L'aristotelisme" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=20" title="Edita el codi de la secció: L'aristotelisme"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En çò que pertòca lei matematicas, <a href="/wiki/Arist%C3%B2tel" title="Aristòtel">Aristòtel</a> es encara fòrça emprench de <a href="/wiki/Platonisme" title="Platonisme">platonisme</a>. L'univèrs en delà de la Luna, leis estèlas e lei planetas, pòdon èsser comprés per lei matematicas, car s'ordenan segon de <a href="/wiki/L%C3%A8is" title="Lèis">lèis</a> etèrnas e perfiechas. En revenge, per Aristòtel, lo monde <a href="/w/index.php?title=Sublunar&action=edit&redlink=1" class="new" title="Sublunar (la pagina existís pas)">sublunar</a> es cambiadís e movedís, e la fisica pòt de ges de biais pretendre aquerir la rigor e l'universalitat dei matematicas. </p> <div class="mw-heading mw-heading3"><h3 id="Lo_logicisme">Lo logicisme</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=21" title="Modificar la seccion : Lo logicisme" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=21" title="Edita el codi de la secció: Lo logicisme"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lo <a href="/w/index.php?title=Logicisme&action=edit&redlink=1" class="new" title="Logicisme (la pagina existís pas)">logicisme</a> considèra que lei matematicas son entierament inclusas dins l'ensemble dei connexions logicas elementàrias, teoricament explicitablas, que compausan una demostracion. </p> <div class="mw-heading mw-heading3"><h3 id="L'intuicionisme"><span id="L.27intuicionisme"></span>L'intuicionisme</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=22" title="Modificar la seccion : L'intuicionisme" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=22" title="Edita el codi de la secció: L'intuicionisme"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>« <i>La simpla possibilitat de la sciéncia matematica sembla una contradiccion insolubla. S'aquela sciéncia es deductiva ren qu'en aparéncia, d'onte li vèn aquela rigor perfiecha que degun pensa de metre en dobte? Se, au contrari, totei lei proposicions qu'enóncia se pòdon tirar leis unei deis autrei per lei règlas de la logica formala, coma va que la matematica se redugue pas an una tautologia immensa? Lo sillogisme nos pòt ren aprendre d'essencialament novèu e, se tot deviá sortir dau principi d'identitat, tot deuriá tanben se i poder reduire.</i> », <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a>, <i>La Sciéncia e l'ipotèsi</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Lo_constructivisme">Lo constructivisme</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=23" title="Modificar la seccion : Lo constructivisme" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=23" title="Edita el codi de la secció: Lo constructivisme"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lei <a href="/w/index.php?title=Constructivisme&action=edit&redlink=1" class="new" title="Constructivisme (la pagina existís pas)">constructivistas</a> admeton que lei matematicas <b>construchas</b>. Pus tecnicament, accèptan dins lei demostracions que leis inferéncias finidas. Per exemple, se refusa lo <a href="/w/index.php?title=Rasonament_per_recurr%C3%A9ncia&action=edit&redlink=1" class="new" title="Rasonament per recurréncia (la pagina existís pas)">rasonament per recurréncia</a> e mai l'<a href="/w/index.php?title=Axi%C3%B2ma_de_la_chausida&action=edit&redlink=1" class="new" title="Axiòma de la chausida (la pagina existís pas)">axiòma de la chausida</a>. Lei demostracions per <a href="/w/index.php?title=Reduccion_a_l%27absurd&action=edit&redlink=1" class="new" title="Reduccion a l'absurd (la pagina existís pas)">reduccion a l'absurd</a> son tanben refusadas, puei que menan a l'existéncia de l'èsser matematic solament per l'impossibilitat de son non-èsser, e non pas per l'explicitacion dirècta de son existéncia. </p> <div class="mw-heading mw-heading2"><h2 id="Leis_arts_e_lei_matematicas">Leis arts e lei matematicas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=24" title="Modificar la seccion : Leis arts e lei matematicas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=24" title="Edita el codi de la secció: Leis arts e lei matematicas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De naturas fòrça diferentas, l'art e lei matematicas an pasmens totjorn agut de relacions fruchosas. </p> <div class="mw-heading mw-heading3"><h3 id="Armonia_e_musica">Armonia e musica</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=25" title="Modificar la seccion : Armonia e musica" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=25" title="Edita el codi de la secció: Armonia e musica"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Lei_simetrias">Lei simetrias</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=26" title="Modificar la seccion : Lei simetrias" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=26" title="Edita el codi de la secció: Lei simetrias"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichi%C3%A8r:Julia_set_(highres_01).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Julia_set_%28highres_01%29.jpg/220px-Julia_set_%28highres_01%29.jpg" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Julia_set_%28highres_01%29.jpg/330px-Julia_set_%28highres_01%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Julia_set_%28highres_01%29.jpg/440px-Julia_set_%28highres_01%29.jpg 2x" data-file-width="2048" data-file-height="2048" /></a><figcaption>Fractala possedent una simetria d'escala e una simetria centrala</figcaption></figure> <p>Es una constatacion comuna que s'atribuís una cèrta <a href="/wiki/Beutat" title="Beutat">beutat</a> ai figuras simetricas. Una <a href="/wiki/Simetria" title="Simetria">simetria</a> d'una figura geometrica es, informalament, l'existéncia d'un motiu de la figura que se reprodutz segon una <a href="/w/index.php?title=R%C3%A8gla&action=edit&redlink=1" class="new" title="Règla (la pagina existís pas)">règla</a> precisa. Matematicament, se ditz qu'una figura es simetrica s'es globalament invarianta per una accion non triviala d'un <a href="/wiki/Grop_(matematicas)" title="Grop (matematicas)">grop</a>. Autrament dich, l'intuicion de la règla se realiza matematicament per lo fach qu'es un grop qu'agís sus la figura, e lo sentiment qu'una règla riège la simetria es precisament degut a l'estructura d'aqueu grop. </p><p>Per exemple, la simetria dau mirau es liada au grop multiplicatiu <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 \{-1,+1\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mo>+</mo> <mn>1</mn> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{-1,+1\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc4c1ae11fc1c76dccf0e9353c6a9186d24b44b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.3ex; height:2.843ex;" alt="{\displaystyle \{-1,+1\}}"></span>. Un <a href="/wiki/Parpalhon" class="mw-redirect mw-disambig" title="Parpalhon">parpalhon</a> es una figura invarianta per aquela simetria, e pus generalament lo <a href="/wiki/C%C3%B2s" title="Còs">còrs</a> deis animaus (aumens tau coma se vei exteriorament). Quand se dessenha la superfícia de la mar, l'ensemble deis ondas possedís una simetria per translacion: de desplaçar nòstre regard de la longor separant doas crestas d'ondas càmbia pas la vista qu'avèm de la mar. Un autre cas de simetria, aquest còp non isometrica, es aqueu que se tròba dins lei <a href="/w/index.php?title=Fractalas&action=edit&redlink=1" class="new" title="Fractalas (la pagina existís pas)">fractalas</a>: un motiu donat se reprodutz a totei leis escalas de vision. </p> <div class="mw-heading mw-heading2"><h2 id="Annèxas"><span id="Ann.C3.A8xas"></span>Annèxas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=27" title="Modificar la seccion : Annèxas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=27" title="Edita el codi de la secció: Annèxas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Bibliografia">Bibliografia</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=28" title="Modificar la seccion : Bibliografia" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=28" title="Edita el codi de la secció: Bibliografia"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span style="font-size:0.95em; font-weight:bold; color:var(--color-subtle, #54595d);" title="En anglés">(<abbr title="">en</abbr>)</span> <span class="citation book" style="font-style:normal" id="CITEREFBoyerMerzbach"><span style="font-variant: small-caps;">Boyer</span>, Carl B.; <span style="font-variant: small-caps;">Merzbach</span>, Uta C. A History of Mathematics (2<sup>a</sup> edicion).  Wiley. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Obratge_de_refer%C3%A9ncia/0-471-54397-7" title="Especial:Obratge de referéncia/0-471-54397-7">ISBN 0-471-54397-7</a></span>.</span><span style="display: none;"> </span></li> <li><span style="font-size:0.95em; font-weight:bold; color:var(--color-subtle, #54595d);" title="En francés">(<abbr title="">fr</abbr>)</span><span class="citation book" style="font-style:normal" id="CITEREF"> L’enseignement des sciences mathématiques : Commission de réflexion sur l’enseignement des mathématiques.  Odile Jacob. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Obratge_de_refer%C3%A9ncia/2-7381-1138-6" title="Especial:Obratge de referéncia/2-7381-1138-6">ISBN 2-7381-1138-6</a></span>.</span><span style="display: none;"> </span></li> <li><span style="font-size:0.95em; font-weight:bold; color:var(--color-subtle, #54595d);" title="En anglés">(<abbr title="">en</abbr>)</span> <span class="citation book" style="font-style:normal" id="CITEREFMaier"><span style="font-variant: small-caps;">Maier</span>, Annelise. At the Threshold of Exact Science: Selected Writings of Annaliese Maier on Late Medieval Natural Philosophy.  University of Pennsylvania Press.</span><span style="display: none;"> </span></li></ul> <div class="mw-heading mw-heading3"><h3 id="Articles_connèxes"><span id="Articles_conn.C3.A8xes"></span>Articles connèxes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=29" title="Modificar la seccion : Articles connèxes" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=29" title="Edita el codi de la secció: Articles connèxes"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Per accedir ais articles de matematicas, vejatz </p> <ul><li><a href="/wiki/Categoria:Matematicas" title="Categoria:Matematicas">Categoria:Matematicas</a> e totei sei soscategorias</li> <li><a href="/w/index.php?title=Portau:matematicas&action=edit&redlink=1" class="new" title="Portau:matematicas (la pagina existís pas)">Portau:matematicas</a></li> <li><a href="/wiki/Lista_deis_articles_de_matematicas" title="Lista deis articles de matematicas">Lista deis articles de matematicas</a></li> <li><a href="/w/index.php?title=Lista_dei_teor%C3%A8mas&action=edit&redlink=1" class="new" title="Lista dei teorèmas (la pagina existís pas)">Lista dei teorèmas</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Liames_extèrnes"><span id="Liames_ext.C3.A8rnes"></span>Liames extèrnes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=30" title="Modificar la seccion : Liames extèrnes" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=30" title="Edita el codi de la secció: Liames extèrnes"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Listas_de_liames">Listas de liames</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=31" title="Modificar la seccion : Listas de liames" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=31" title="Edita el codi de la secció: Listas de liames"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://mathslinker.chez-alice.fr/">Maths linker</a> Un indèx de ressorsas matematicas sus lo web</li> <li><a rel="nofollow" class="external text" href="http://spoirier.lautre.net/liensmaths.html">Liames de matematicas dau superior</a> Autra lista de liames</li> <li><a rel="nofollow" class="external text" href="http://www.yakeo.com/fr/cours_exercices_mathematiques/">Yakeo</a> Bòn portau de liames per lei matematicas</li></ul> <div class="mw-heading mw-heading4"><h4 id="Ressorsas">Ressorsas</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=32" title="Modificar la seccion : Ressorsas" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=32" title="Edita el codi de la secció: Ressorsas"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span style="font-size:0.95em; font-weight:bold; color:var(--color-subtle, #54595d);" title="En anglés">(<abbr title="">en</abbr>)</span> <a rel="nofollow" class="external text" href="https://planetmath.org/">Planetmath</a>: enciclopèdia collaborativa, libra (GFDL) sus lei matematicas.</li> <li><span style="font-size:0.95em; font-weight:bold; color:var(--color-subtle, #54595d);" title="En francés">(<abbr title="">fr</abbr>)</span> <a rel="nofollow" class="external text" href="http://www.chronomath.com/">Chronomath</a>: una cronologia dei matematicas fòrça rica.</li> <li><span style="font-size:0.95em; font-weight:bold; color:var(--color-subtle, #54595d);" title="En anglés">(<abbr title="">en</abbr>)</span> <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/">Mathworld-Wolfram</a>: la pus complèta dei ressorsas en matematicas</li></ul> <div class="mw-heading mw-heading4"><h4 id="Logiciaus_libres">Logiciaus libres</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematicas&veaction=edit&section=33" title="Modificar la seccion : Logiciaus libres" class="mw-editsection-visualeditor"><span>modificar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematicas&action=edit&section=33" title="Edita el codi de la secció: Logiciaus libres"><span>Modificar lo còdi</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://maxima.sourceforge.net/">Maxima</a>, lo logiciau libre (GPL) pus sofisticat per leis operacions algebricas.</li> <li><a rel="nofollow" class="external text" href="http://pari.math.u-bordeaux.fr/">PARI/GP</a>, un logiciau libre fòrça utilizat en teoria dei nombres.</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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