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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">Mga nilalaman</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">itago</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">Simula</div> </a> </li> <li id="toc-Patibay_ng_pag-iibang-ayos" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Patibay_ng_pag-iibang-ayos"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Patibay ng pag-iibang-ayos</span> </div> </a> <ul id="toc-Patibay_ng_pag-iibang-ayos-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Iba_pang_anyo_ng_teorema" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Iba_pang_anyo_ng_teorema"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Iba pang anyo ng teorema</span> </div> </a> <ul id="toc-Iba_pang_anyo_ng_teorema-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mga_iba_pang_katibayan_ng_teorema" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mga_iba_pang_katibayan_ng_teorema"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Mga iba pang katibayan ng teorema</span> </div> </a> <button aria-controls="toc-Mga_iba_pang_katibayan_ng_teorema-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>Ipakita/Itago ang subseksyon na Mga iba pang katibayan ng teorema</span> </button> <ul id="toc-Mga_iba_pang_katibayan_ng_teorema-sublist" class="vector-toc-list"> <li id="toc-Katibayan_gamit_ang_magkahawig_na_tatsulok" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Katibayan_gamit_ang_magkahawig_na_tatsulok"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Katibayan gamit ang magkahawig na tatsulok</span> </div> </a> <ul id="toc-Katibayan_gamit_ang_magkahawig_na_tatsulok-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Katibayan_ni_Euclid" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Katibayan_ni_Euclid"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Katibayan ni Euclid</span> </div> </a> <ul id="toc-Katibayan_ni_Euclid-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mga_katibayan_sa_panisnisan_at_pagbabago_ng_ayos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mga_katibayan_sa_panisnisan_at_pagbabago_ng_ayos"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Mga katibayan sa panisnisan at pagbabago ng ayos</span> </div> </a> <ul id="toc-Mga_katibayan_sa_panisnisan_at_pagbabago_ng_ayos-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mga_sanggunian" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mga_sanggunian"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Mga sanggunian</span> </div> </a> <ul id="toc-Mga_sanggunian-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Mga nilalaman" 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="Itago/Ipakita ang talaan ng mga nilalaman" > <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">Itago/Ipakita ang talaan ng mga nilalaman</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">Teorema ni Pitagoras</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="Pumunta sa isang artikulo na nakasulat sa ibang wika. Mayroon ito sa 132 (na) wika" > <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-132" 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">132 wika</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/Pythagoras_se_stelling" title="Pythagoras se stelling – Afrikaans" lang="af" hreflang="af" data-title="Pythagoras se stelling" 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/Satz_des_Pythagoras" title="Satz des Pythagoras – Alemannic" lang="gsw" hreflang="gsw" data-title="Satz des Pythagoras" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" 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%8D%93%E1%8B%AD%E1%89%B3%E1%8C%8E%E1%88%A8%E1%88%B5_%E1%8A%A5%E1%88%AD%E1%8C%89%E1%8C%A5" title="ፓይታጎረስ እርጉጥ – Amharic" lang="am" hreflang="am" data-title="ፓይታጎረስ እርጉጥ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" 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/Teorema_de_Pitagoras" title="Teorema de Pitagoras – Aragonese" lang="an" hreflang="an" data-title="Teorema de Pitagoras" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%A8%D8%B1%D9%87%D9%86%D8%A9_%D9%81%D9%8A%D8%AB%D8%A7%D8%BA%D9%88%D8%B1%D8%B3" title="مبرهنة فيثاغورس – Arabic" lang="ar" hreflang="ar" data-title="مبرهنة فيثاغورس" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AA%E0%A6%BE%E0%A6%87%E0%A6%A5%E0%A6%BE%E0%A6%97%E0%A7%8B%E0%A7%B0%E0%A6%BE%E0%A6%9B%E0%A7%B0_%E0%A6%89%E0%A6%AA%E0%A6%AA%E0%A6%BE%E0%A6%A6%E0%A7%8D%E0%A6%AF" title="পাইথাগোৰাছৰ উপপাদ্য – Assamese" lang="as" hreflang="as" data-title="পাইথাগোৰাছৰ উপপাদ্য" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" 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/Teorema_de_Pit%C3%A1gores" title="Teorema de Pitágores – Asturian" lang="ast" hreflang="ast" data-title="Teorema de Pitágores" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-awa mw-list-item"><a href="https://awa.wikipedia.org/wiki/%E0%A4%AA%E0%A4%BE%E0%A4%87%E0%A4%A5%E0%A4%BE%E0%A4%97%E0%A5%8B%E0%A4%B0%E0%A4%B8_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%87%E0%A4%AF" title="पाइथागोरस प्रमेय – Awadhi" lang="awa" hreflang="awa" data-title="पाइथागोरस प्रमेय" data-language-autonym="अवधी" data-language-local-name="Awadhi" class="interlanguage-link-target"><span>अवधी</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Pifaqor_teoremi" title="Pifaqor teoremi – Azerbaijani" lang="az" hreflang="az" data-title="Pifaqor teoremi" 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/%D9%81%DB%8C%D8%AB%D8%A7%D8%BA%D9%88%D8%B1%D8%B3_%D8%AA%D8%A6%D9%88%D8%B1%DB%8C%D8%B3%DB%8C" title="فیثاغورس تئوریسی – South Azerbaijani" lang="azb" hreflang="azb" data-title="فیثاغورس تئوریسی" 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%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0%D2%BB%D1%8B" title="Пифагор теоремаһы – Bashkir" lang="ba" hreflang="ba" data-title="Пифагор теоремаһы" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-ban mw-list-item"><a href="https://ban.wikipedia.org/wiki/Rumus_Pythagoras" title="Rumus Pythagoras – Balinese" lang="ban" hreflang="ban" data-title="Rumus Pythagoras" data-language-autonym="Basa Bali" data-language-local-name="Balinese" class="interlanguage-link-target"><span>Basa Bali</span></a></li><li class="interlanguage-link interwiki-bar badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://bar.wikipedia.org/wiki/Sotz_vum_Pythagoras" title="Sotz vum Pythagoras – Bavarian" lang="bar" hreflang="bar" data-title="Sotz vum Pythagoras" data-language-autonym="Boarisch" data-language-local-name="Bavarian" 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/P%C4%97taguora_teuorema" title="Pėtaguora teuorema – Samogitian" lang="sgs" hreflang="sgs" data-title="Pėtaguora teuorema" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" 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/Teorema_ni_Pythagoras" title="Teorema ni Pythagoras – Central Bikol" lang="bcl" hreflang="bcl" data-title="Teorema ni Pythagoras" 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%A2%D1%8D%D0%B0%D1%80%D1%8D%D0%BC%D0%B0_%D0%9F%D1%96%D1%84%D0%B0%D0%B3%D0%BE%D1%80%D0%B0" title="Тэарэма Піфагора – Belarusian" lang="be" hreflang="be" data-title="Тэарэма Піфагора" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A2%D1%8D%D0%B0%D1%80%D1%8D%D0%BC%D0%B0_%D0%9F%D1%96%D1%82%D0%B0%D0%B3%D0%BE%D1%80%D0%B0" title="Тэарэма Пітагора – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Тэарэма Пітагора" 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%9F%D0%B8%D1%82%D0%B0%D0%B3%D0%BE%D1%80%D0%BE%D0%B2%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0" title="Питагорова теорема – Bulgarian" lang="bg" hreflang="bg" data-title="Питагорова теорема" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%BF%E0%A6%A5%E0%A6%BE%E0%A6%97%E0%A7%8B%E0%A6%B0%E0%A6%BE%E0%A6%B8%E0%A7%87%E0%A6%B0_%E0%A6%89%E0%A6%AA%E0%A6%AA%E0%A6%BE%E0%A6%A6%E0%A7%8D%E0%A6%AF" title="পিথাগোরাসের উপপাদ্য – Bangla" lang="bn" hreflang="bn" data-title="পিথাগোরাসের উপপাদ্য" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Teorem_Pythagoras" title="Teorem Pythagoras – Breton" lang="br" hreflang="br" data-title="Teorem Pythagoras" 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/Pitagorina_teorema" title="Pitagorina teorema – Bosnian" lang="bs" hreflang="bs" data-title="Pitagorina teorema" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Teorema_de_Pit%C3%A0gores" title="Teorema de Pitàgores – Catalan" lang="ca" hreflang="ca" data-title="Teorema de Pitàgores" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%8C%DB%86%D8%B1%D9%85%DB%8C_%D9%BE%DB%8C%D8%AA%D8%A7%DA%AF%DB%86%D8%B1%D8%B3" title="تیۆرمی پیتاگۆرس – Central Kurdish" lang="ckb" hreflang="ckb" data-title="تیۆرمی پیتاگۆرس" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" 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/Tiurema_di_Pitagora" title="Tiurema di Pitagora – Corsican" lang="co" hreflang="co" data-title="Tiurema di Pitagora" data-language-autonym="Corsu" data-language-local-name="Corsican" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Pythagorova_v%C4%9Bta" title="Pythagorova věta – Czech" lang="cs" hreflang="cs" data-title="Pythagorova věta" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B8" title="Пифагор теореми – Chuvash" lang="cv" hreflang="cv" data-title="Пифагор теореми" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" 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/Theorem_Pythagoras" title="Theorem Pythagoras – Welsh" lang="cy" hreflang="cy" data-title="Theorem Pythagoras" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Den_pythagor%C3%A6iske_l%C3%A6res%C3%A6tning" title="Den pythagoræiske læresætning – Danish" lang="da" hreflang="da" data-title="Den pythagoræiske læresætning" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://de.wikipedia.org/wiki/Satz_des_Pythagoras" title="Satz des Pythagoras – German" lang="de" hreflang="de" data-title="Satz des Pythagoras" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Teorem%C3%AA_Pisagori" title="Teoremê Pisagori – Zazaki" lang="diq" hreflang="diq" data-title="Teoremê Pisagori" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dtp mw-list-item"><a href="https://dtp.wikipedia.org/wiki/Teorem_Pythagoras" title="Teorem Pythagoras – Central Dusun" lang="dtp" hreflang="dtp" data-title="Teorem Pythagoras" data-language-autonym="Kadazandusun" data-language-local-name="Central Dusun" class="interlanguage-link-target"><span>Kadazandusun</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A0%CF%85%CE%B8%CE%B1%CE%B3%CF%8C%CF%81%CE%B5%CE%B9%CE%BF_%CE%B8%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1" title="Πυθαγόρειο θεώρημα – Greek" lang="el" hreflang="el" data-title="Πυθαγόρειο θεώρημα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" 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/Tior%C3%A9ma_%27d_Pit%C3%A0gora" title="Tioréma 'd Pitàgora – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Tioréma 'd Pitàgora" 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 badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://en.wikipedia.org/wiki/Pythagorean_theorem" title="Pythagorean theorem – English" lang="en" hreflang="en" data-title="Pythagorean theorem" data-language-autonym="English" data-language-local-name="English" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://eo.wikipedia.org/wiki/Teoremo_de_Pitagoro" title="Teoremo de Pitagoro – Esperanto" lang="eo" hreflang="eo" data-title="Teoremo de Pitagoro" 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/Teorema_de_Pit%C3%A1goras" title="Teorema de Pitágoras – Spanish" lang="es" hreflang="es" data-title="Teorema de Pitágoras" data-language-autonym="Español" data-language-local-name="Spanish" 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/Pythagorase_teoreem" title="Pythagorase teoreem – Estonian" lang="et" hreflang="et" data-title="Pythagorase teoreem" 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/Pitagorasen_teorema" title="Pitagorasen teorema – Basque" lang="eu" hreflang="eu" data-title="Pitagorasen teorema" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%82%D8%B6%DB%8C%D9%87_%D9%81%DB%8C%D8%AB%D8%A7%D8%BA%D9%88%D8%B1%D8%B3" title="قضیه فیثاغورس – Persian" lang="fa" hreflang="fa" data-title="قضیه فیثاغورس" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Pythagoraan_lause" title="Pythagoraan lause – Finnish" lang="fi" hreflang="fi" data-title="Pythagoraan lause" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Th%C3%A9or%C3%A8me_de_Pythagore" title="Théorème de Pythagore – French" lang="fr" hreflang="fr" data-title="Théorème de Pythagore" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Pythagoras_sin_reegel" title="Pythagoras sin reegel – Northern Frisian" lang="frr" hreflang="frr" data-title="Pythagoras sin reegel" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Teoirim_Ph%C3%ADotagar%C3%A1sach" title="Teoirim Phíotagarásach – Irish" lang="ga" hreflang="ga" data-title="Teoirim Phíotagarásach" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Teorema_de_Pit%C3%A1goras" title="Teorema de Pitágoras – Galician" lang="gl" hreflang="gl" data-title="Teorema de Pitágoras" 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/Pit%C3%A1gora_remimoa%C3%B1eter%C3%A3" title="Pitágora remimoañeterã – Guarani" lang="gn" hreflang="gn" data-title="Pitágora remimoañeterã" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AA%E0%AA%BE%E0%AA%AF%E0%AA%A5%E0%AA%BE%E0%AA%97%E0%AB%8B%E0%AA%B0%E0%AA%B8%E0%AA%A8%E0%AB%81%E0%AA%82_%E0%AA%AA%E0%AB%8D%E0%AA%B0%E0%AA%AE%E0%AB%87%E0%AA%AF" title="પાયથાગોરસનું પ્રમેય – Gujarati" lang="gu" hreflang="gu" data-title="પાયથાગોરસનું પ્રમેય" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%A4%D7%99%D7%AA%D7%92%D7%95%D7%A8%D7%A1" title="משפט פיתגורס – Hebrew" lang="he" hreflang="he" data-title="משפט פיתגורס" data-language-autonym="עברית" data-language-local-name="Hebrew" 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%AA%E0%A4%BE%E0%A4%87%E0%A4%A5%E0%A4%BE%E0%A4%97%E0%A5%8B%E0%A4%B0%E0%A4%B8_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%87%E0%A4%AF" title="पाइथागोरस प्रमेय – Hindi" lang="hi" hreflang="hi" data-title="पाइथागोरस प्रमेय" data-language-autonym="हिन्दी" data-language-local-name="Hindi" 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/Pythagorean_theorem" title="Pythagorean theorem – Fiji Hindi" lang="hif" hreflang="hif" data-title="Pythagorean theorem" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" 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/Pitagorin_pou%C4%8Dak" title="Pitagorin poučak – Croatian" lang="hr" hreflang="hr" data-title="Pitagorin poučak" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hsb mw-list-item"><a href="https://hsb.wikipedia.org/wiki/Sada_Pythagorasa" title="Sada Pythagorasa – Upper Sorbian" lang="hsb" hreflang="hsb" data-title="Sada Pythagorasa" data-language-autonym="Hornjoserbsce" data-language-local-name="Upper Sorbian" class="interlanguage-link-target"><span>Hornjoserbsce</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Pitagorasz-t%C3%A9tel" title="Pitagorasz-tétel – Hungarian" lang="hu" hreflang="hu" data-title="Pitagorasz-tétel" data-language-autonym="Magyar" data-language-local-name="Hungarian" 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%8A%D5%B5%D5%B8%D6%82%D5%A9%D5%A1%D5%A3%D5%B8%D6%80%D5%A1%D5%BD%D5%AB_%D5%A9%D5%A5%D5%B8%D6%80%D5%A5%D5%B4" title="Պյութագորասի թեորեմ – Armenian" lang="hy" hreflang="hy" data-title="Պյութագորասի թեորեմ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Theorema_de_Pythagoras" title="Theorema de Pythagoras – Interlingua" lang="ia" hreflang="ia" data-title="Theorema de Pythagoras" 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/Teorem_Pythagoras" title="Teorem Pythagoras – Iban" lang="iba" hreflang="iba" data-title="Teorem Pythagoras" 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/Teorema_Pythagoras" title="Teorema Pythagoras – Indonesian" lang="id" hreflang="id" data-title="Teorema Pythagoras" 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-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Teoremo_di_Pitagoro" title="Teoremo di Pitagoro – Ido" lang="io" hreflang="io" data-title="Teoremo di Pitagoro" 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/Regla_P%C3%BD%C3%BEag%C3%B3rasar" title="Regla Pýþagórasar – Icelandic" lang="is" hreflang="is" data-title="Regla Pýþagórasar" data-language-autonym="Íslenska" data-language-local-name="Icelandic" 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/Teorema_di_Pitagora" title="Teorema di Pitagora – Italian" lang="it" hreflang="it" data-title="Teorema di Pitagora" 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/%E3%83%94%E3%82%BF%E3%82%B4%E3%83%A9%E3%82%B9%E3%81%AE%E5%AE%9A%E7%90%86" title="ピタゴラスの定理 – Japanese" lang="ja" hreflang="ja" data-title="ピタゴラスの定理" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9E%E1%83%98%E1%83%97%E1%83%90%E1%83%92%E1%83%9D%E1%83%A0%E1%83%90%E1%83%A1_%E1%83%97%E1%83%94%E1%83%9D%E1%83%A0%E1%83%94%E1%83%9B%E1%83%90" title="პითაგორას თეორემა – Georgian" lang="ka" hreflang="ka" data-title="პითაგორას თეორემა" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Asekkud_n_Pythagore" title="Asekkud n Pythagore – Kabyle" lang="kab" hreflang="kab" data-title="Asekkud n Pythagore" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80_%D0%B8_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D1%8D" title="Пифагор и теоремэ – Kabardian" lang="kbd" hreflang="kbd" data-title="Пифагор и теоремэ" data-language-autonym="Адыгэбзэ" data-language-local-name="Kabardian" class="interlanguage-link-target"><span>Адыгэбзэ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0%D1%81%D1%8B" title="Пифагор теоремасы – Kazakh" lang="kk" hreflang="kk" data-title="Пифагор теоремасы" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%91%E1%9F%92%E1%9E%9A%E1%9E%B9%E1%9E%9F%E1%9F%92%E1%9E%8F%E1%9E%B8%E1%9E%94%E1%9E%91%E1%9E%96%E1%9E%B8%E1%9E%8F%E1%9E%B6%E1%9E%80%E1%9E%9A" title="ទ្រឹស្តីបទពីតាករ – Khmer" lang="km" hreflang="km" data-title="ទ្រឹស្តីបទពីតាករ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%BC%ED%83%80%EA%B3%A0%EB%9D%BC%EC%8A%A4_%EC%A0%95%EB%A6%AC" title="피타고라스 정리 – Korean" lang="ko" hreflang="ko" data-title="피타고라스 정리" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Teorema_P%C3%AEtagoras" title="Teorema Pîtagoras – Kurdish" lang="ku" hreflang="ku" data-title="Teorema Pîtagoras" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0%D1%81%D1%8B" title="Пифагор теоремасы – Kyrgyz" lang="ky" hreflang="ky" data-title="Пифагор теоремасы" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Theorema_Pythagorae" title="Theorema Pythagorae – Latin" lang="la" hreflang="la" data-title="Theorema Pythagorae" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Teorem_de_Pitagora" title="Teorem de Pitagora – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Teorem de Pitagora" 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-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Teorema_de_Pitagora" title="Teorema de Pitagora – Lombard" lang="lmo" hreflang="lmo" data-title="Teorema de Pitagora" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-ln mw-list-item"><a href="https://ln.wikipedia.org/wiki/Bondeko_ya_mpanzi-mis%C3%A1to" title="Bondeko ya mpanzi-misáto – Lingala" lang="ln" hreflang="ln" data-title="Bondeko ya mpanzi-misáto" data-language-autonym="Lingála" data-language-local-name="Lingala" class="interlanguage-link-target"><span>Lingála</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%97%E0%BA%B4%E0%BA%94%E0%BA%AA%E0%BA%B0%E0%BA%94%E0%BA%B5_%E0%BA%9B%E0%BA%B5%E0%BA%97%E0%BA%B2%E0%BB%82%E0%BA%81%E0%BA%A3%E0%BA%BD%E0%BA%99" title="ທິດສະດີ ປີທາໂກຣຽນ – Lao" lang="lo" hreflang="lo" data-title="ທິດສະດີ ປີທາໂກຣຽນ" data-language-autonym="ລາວ" data-language-local-name="Lao" 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/Pitagoro_teorema" title="Pitagoro teorema – Lithuanian" lang="lt" hreflang="lt" data-title="Pitagoro teorema" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" 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/Pitagora_teor%C4%93ma" title="Pitagora teorēma – Latvian" lang="lv" hreflang="lv" data-title="Pitagora teorēma" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Raikitr%27_Pytagore" title="Raikitr' Pytagore – Malagasy" lang="mg" hreflang="mg" data-title="Raikitr' Pytagore" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%B8%D1%82%D0%B0%D0%B3%D0%BE%D1%80%D0%BE%D0%B2%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0" title="Питагорова теорема – Macedonian" lang="mk" hreflang="mk" data-title="Питагорова теорема" 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%AA%E0%B5%88%E0%B4%A4%E0%B4%97%E0%B5%8B%E0%B4%B1%E0%B4%B8%E0%B5%8D_%E0%B4%B8%E0%B4%BF%E0%B4%A6%E0%B5%8D%E0%B4%A7%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%82" title="പൈതഗോറസ് സിദ്ധാന്തം – Malayalam" lang="ml" hreflang="ml" data-title="പൈതഗോറസ് സിദ്ധാന്തം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80%D1%8B%D0%BD_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC" title="Пифагорын теорем – Mongolian" lang="mn" hreflang="mn" data-title="Пифагорын теорем" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A4%BE%E0%A4%AF%E0%A4%A5%E0%A4%BE%E0%A4%97%E0%A5%8B%E0%A4%B0%E0%A4%B8%E0%A4%9A%E0%A4%BE_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4" title="पायथागोरसचा सिद्धान्त – Marathi" lang="mr" hreflang="mr" data-title="पायथागोरसचा सिद्धान्त" 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/Teorem_Pythagoras" title="Teorem Pythagoras – Malay" lang="ms" hreflang="ms" data-title="Teorem Pythagoras" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%95%E1%80%AD%E1%80%AF%E1%80%80%E1%80%BA%E1%80%9E%E1%80%AC%E1%80%82%E1%80%AD%E1%80%AF%E1%80%9B_%E1%80%9E%E1%80%AE%E1%80%A1%E1%80%AD%E1%80%AF%E1%80%9B%E1%80%99%E1%80%BA" title="ပိုက်သာဂိုရ သီအိုရမ် – Burmese" lang="my" hreflang="my" data-title="ပိုက်သာဂိုရ သီအိုရမ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Satz_van_Pythagoras" title="Satz van Pythagoras – Low German" lang="nds" hreflang="nds" data-title="Satz van Pythagoras" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AA%E0%A4%BE%E0%A4%87%E0%A4%A5%E0%A4%BE%E0%A4%97%E0%A5%8B%E0%A4%B0%E0%A4%B8_%E0%A4%B8%E0%A4%BE%E0%A4%A7%E0%A5%8D%E0%A4%AF" title="पाइथागोरस साध्य – Nepali" lang="ne" hreflang="ne" data-title="पाइथागोरस साध्य" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Stelling_van_Pythagoras" title="Stelling van Pythagoras – Dutch" lang="nl" hreflang="nl" data-title="Stelling van Pythagoras" data-language-autonym="Nederlands" data-language-local-name="Dutch" 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/Den_pytagoreiske_l%C3%A6resetninga" title="Den pytagoreiske læresetninga – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Den pytagoreiske læresetninga" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://no.wikipedia.org/wiki/Pytagoras%E2%80%99_l%C3%A6resetning" title="Pytagoras’ læresetning – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Pytagoras’ læresetning" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Teor%C3%A8ma_de_Pitag%C3%B2ras" title="Teorèma de Pitagòras – Occitan" lang="oc" hreflang="oc" data-title="Teorèma de Pitagòras" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80%D1%8B_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%C3%A6" title="Пифагоры теоремæ – Ossetic" lang="os" hreflang="os" data-title="Пифагоры теоремæ" data-language-autonym="Ирон" data-language-local-name="Ossetic" 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%AA%E0%A8%BE%E0%A8%88%E0%A8%A5%E0%A8%BE%E0%A8%97%E0%A9%8B%E0%A8%B0%E0%A8%B8_%E0%A8%A5%E0%A8%BF%E0%A8%8A%E0%A8%B0%E0%A8%AE" title="ਪਾਈਥਾਗੋਰਸ ਥਿਊਰਮ – Punjabi" lang="pa" hreflang="pa" data-title="ਪਾਈਥਾਗੋਰਸ ਥਿਊਰਮ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Twierdzenie_Pitagorasa" title="Twierdzenie Pitagorasa – Polish" lang="pl" hreflang="pl" data-title="Twierdzenie Pitagorasa" data-language-autonym="Polski" data-language-local-name="Polish" 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/Teorema_%C3%ABd_Pit%C3%A0gora" title="Teorema ëd Pitàgora – Piedmontese" lang="pms" hreflang="pms" data-title="Teorema ëd Pitàgora" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" 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/%D9%85%D8%B3%D9%84%DB%81_%D9%81%DB%8C%D8%B3%D8%A7%D8%BA%D9%88%D8%B1%D8%B3" title="مسلہ فیساغورس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="مسلہ فیساغورس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Teorema_de_Pit%C3%A1goras" title="Teorema de Pitágoras – Portuguese" lang="pt" hreflang="pt" data-title="Teorema de Pitágoras" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-pwn mw-list-item"><a href="https://pwn.wikipedia.org/wiki/sasusuan_ni_pitaguras" title="sasusuan ni pitaguras – Paiwan" lang="pwn" hreflang="pwn" data-title="sasusuan ni pitaguras" data-language-autonym="Pinayuanan" data-language-local-name="Paiwan" class="interlanguage-link-target"><span>Pinayuanan</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Teorema_lui_Pitagora" title="Teorema lui Pitagora – Romanian" lang="ro" hreflang="ro" data-title="Teorema lui Pitagora" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80%D0%B0" title="Теорема Пифагора – Russian" lang="ru" hreflang="ru" data-title="Теорема Пифагора" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0%D1%82%D0%B0" title="Пифагор теоремата – Yakut" lang="sah" hreflang="sah" data-title="Пифагор теоремата" data-language-autonym="Саха тыла" data-language-local-name="Yakut" 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%AF%E1%B1%9F%E1%B1%AD%E1%B1%9B%E1%B1%B7%E1%B1%B3%E1%B1%9C%E1%B1%B3%E1%B1%A8%E1%B1%9A%E1%B1%B1_%E1%B1%9B%E1%B1%B7%E1%B1%A4%E1%B1%AD%E1%B1%9A%E1%B1%A8%E1%B1%9A%E1%B1%A2" title="ᱯᱟᱭᱛᱷᱳᱜᱳᱨᱚᱱ ᱛᱷᱤᱭᱚᱨᱚᱢ – Santali" lang="sat" hreflang="sat" data-title="ᱯᱟᱭᱛᱷᱳᱜᱳᱨᱚᱱ ᱛᱷᱤᱭᱚᱨᱚᱢ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="Santali" class="interlanguage-link-target"><span>ᱥᱟᱱᱛᱟᱲᱤ</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Tiurema_di_Pitagora" title="Tiurema di Pitagora – Sicilian" lang="scn" hreflang="scn" data-title="Tiurema di Pitagora" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-se mw-list-item"><a href="https://se.wikipedia.org/wiki/Pythagorasa_cealkka" title="Pythagorasa cealkka – Northern Sami" lang="se" hreflang="se" data-title="Pythagorasa cealkka" data-language-autonym="Davvisámegiella" data-language-local-name="Northern Sami" class="interlanguage-link-target"><span>Davvisámegiella</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Pitagorina_teorema" title="Pitagorina teorema – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Pitagorina teorema" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%B4%E0%B6%BA%E0%B7%92%E0%B6%AD%E0%B6%9C%E0%B6%BB%E0%B7%83%E0%B7%8A_%E0%B6%B4%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B6%B8%E0%B7%9A%E0%B6%BA%E0%B6%BA" title="පයිතගරස් ප්‍රමේයය – Sinhala" lang="si" hreflang="si" data-title="පයිතගරස් ප්‍රමේයය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" 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/Pythagorean_theorem" title="Pythagorean theorem – Simple English" lang="en-simple" hreflang="en-simple" data-title="Pythagorean theorem" 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/Pytagorova_veta" title="Pytagorova veta – Slovak" lang="sk" hreflang="sk" data-title="Pytagorova veta" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Pitagorov_izrek" title="Pitagorov izrek – Slovenian" lang="sl" hreflang="sl" data-title="Pitagorov izrek" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Dudzirazivo_raPythagoras" title="Dudzirazivo raPythagoras – Shona" lang="sn" hreflang="sn" data-title="Dudzirazivo raPythagoras" 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/Aragtida_Baytagoras" title="Aragtida Baytagoras – Somali" lang="so" hreflang="so" data-title="Aragtida Baytagoras" 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/Teorema_e_Pitagor%C3%ABs" title="Teorema e Pitagorës – Albanian" lang="sq" hreflang="sq" data-title="Teorema e Pitagorës" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%B8%D1%82%D0%B0%D0%B3%D0%BE%D1%80%D0%B8%D0%BD%D0%B0_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0" title="Питагорина теорема – Serbian" lang="sr" hreflang="sr" data-title="Питагорина теорема" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Pythagoras_sats" title="Pythagoras sats – Swedish" lang="sv" hreflang="sv" data-title="Pythagoras sats" data-language-autonym="Svenska" data-language-local-name="Swedish" 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/Uhakiki_wa_Pythagoras" title="Uhakiki wa Pythagoras – Swahili" lang="sw" hreflang="sw" data-title="Uhakiki wa Pythagoras" 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/Twjerdzy%C5%84y_Pitagorasa" title="Twjerdzyńy Pitagorasa – Silesian" lang="szl" hreflang="szl" data-title="Twjerdzyńy Pitagorasa" data-language-autonym="Ślůnski" data-language-local-name="Silesian" 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%AA%E0%AE%BF%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AF%87%E0%AE%95%E0%AF%8B%E0%AE%B0%E0%AE%9A%E0%AF%81_%E0%AE%A4%E0%AF%87%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%AE%E0%AF%8D" title="பித்தேகோரசு தேற்றம் – Tamil" lang="ta" hreflang="ta" data-title="பித்தேகோரசு தேற்றம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AA%E0%B1%88%E0%B0%A5%E0%B0%BE%E0%B0%97%E0%B0%B0%E0%B0%B8%E0%B1%8D_%E0%B0%B8%E0%B0%BF%E0%B0%A6%E0%B1%8D%E0%B0%A7%E0%B0%BE%E0%B0%82%E0%B0%A4%E0%B0%82" title="పైథాగరస్ సిద్ధాంతం – Telugu" lang="te" hreflang="te" data-title="పైథాగరస్ సిద్ధాంతం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%9A%E0%B8%97%E0%B8%9E%E0%B8%B5%E0%B8%97%E0%B8%B2%E0%B9%82%E0%B8%81%E0%B8%A3%E0%B8%B1%E0%B8%AA" title="ทฤษฎีบทพีทาโกรัส – Thai" lang="th" hreflang="th" data-title="ทฤษฎีบทพีทาโกรัส" data-language-autonym="ไทย" data-language-local-name="Thai" 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/Pifagory%C5%88_teoremasy" title="Pifagoryň teoremasy – Turkmen" lang="tk" hreflang="tk" data-title="Pifagoryň teoremasy" data-language-autonym="Türkmençe" data-language-local-name="Turkmen" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Pisagor_teoremi" title="Pisagor teoremi – Turkish" lang="tr" hreflang="tr" data-title="Pisagor teoremi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/Pifagor_teoremas%C4%B1" title="Pifagor teoreması – Tatar" lang="tt" hreflang="tt" data-title="Pifagor teoreması" 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-uk badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%9F%D1%96%D1%84%D0%B0%D0%B3%D0%BE%D1%80%D0%B0" title="Теорема Піфагора – Ukrainian" lang="uk" hreflang="uk" data-title="Теорема Піфагора" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%B3%D8%A6%D9%84%DB%82_%D9%81%DB%8C%D8%AB%D8%A7_%D8%BA%D9%88%D8%B1%D8%AB" title="مسئلۂ فیثا غورث – Urdu" lang="ur" hreflang="ur" data-title="مسئلۂ فیثا غورث" data-language-autonym="اردو" data-language-local-name="Urdu" 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/Pifagor_teoremasi" title="Pifagor teoremasi – Uzbek" lang="uz" hreflang="uz" data-title="Pifagor teoremasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Pifagoran_teorem" title="Pifagoran teorem – Veps" lang="vep" hreflang="vep" data-title="Pifagoran teorem" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%8Bnh_l%C3%BD_Pythagoras" title="Định lý Pythagoras – Vietnamese" lang="vi" hreflang="vi" data-title="Định lý Pythagoras" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Pitagorasnon_nga_teyorema" title="Pitagorasnon nga teyorema – Waray" lang="war" hreflang="war" data-title="Pitagorasnon nga teyorema" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86" title="勾股定理 – Wu" lang="wuu" hreflang="wuu" data-title="勾股定理" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%99%D7%98%D7%90%D7%92%D7%90%D7%A8%D7%90%D7%A1_%D7%A4%D7%A8%D7%99%D7%A0%D7%A6%D7%99%D7%A4" title="פיטאגאראס פרינציפ – Yiddish" lang="yi" hreflang="yi" data-title="פיטאגאראס פרינציפ" 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/%C3%80gb%C3%A9r%C3%B2_Pythagoras" title="Àgbérò Pythagoras – Yoruba" lang="yo" hreflang="yo" data-title="Àgbérò Pythagoras" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86" title="勾股定理 – Chinese" lang="zh" hreflang="zh" data-title="勾股定理" data-language-autonym="中文" data-language-local-name="Chinese" 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/%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86" title="勾股定理 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="勾股定理" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Pythagoras_t%C4%93ng-l%C3%AD" title="Pythagoras tēng-lí – Minnan" 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vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Itsura</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">itago</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Mula sa Wikipedia, ang malayang ensiklopedya</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="tl" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Pythagorean.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/260px-Pythagorean.svg.png" decoding="async" width="260" height="237" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/390px-Pythagorean.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/520px-Pythagorean.svg.png 2x" data-file-width="512" data-file-height="466" /></a><figcaption><b>Teorema ni Pitagoras</b> Magkatumbas ang kabuuan ng sukat ng dalawang parisukat sa mga paa (<i>a</i> at <i>b</i>) sa sukat ng parisukat ng gilis (<i>c</i>).</figcaption></figure> <table class="vertical-navbox nowraplinks plainlist" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;background:white;"><tbody><tr><th style="padding:0.2em 0.4em 0.2em;font-size:145%;line-height:1.2em"><a href="/wiki/Heometriya" title="Heometriya">Heometriya</a></th></tr><tr><td style="padding:0.2em 0 0.4em"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/Talaksan:Stereographic_projection_in_3D.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Stereographic_projection_in_3D.svg/220px-Stereographic_projection_in_3D.svg.png" decoding="async" width="220" height="162" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Stereographic_projection_in_3D.svg/330px-Stereographic_projection_in_3D.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Stereographic_projection_in_3D.svg/440px-Stereographic_projection_in_3D.svg.png 2x" data-file-width="870" data-file-height="639" /></a></span><div style="padding-top:0.2em;line-height:1.2em"><a href="/w/index.php?title=Heometriyang_proyektibo&action=edit&redlink=1" class="new" title="Heometriyang proyektibo (hindi pa naisusulat)">Pagproyekt</a> ng isang <a href="/wiki/Espera" title="Espera">espera</a> sa isang <a href="/wiki/Plano_(heometriya)" title="Plano (heometriya)">plano</a></div></td></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;">Mga sanay</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/w/index.php?title=Euclidean_geometry&action=edit&redlink=1" class="new" title="Euclidean geometry (hindi pa naisusulat)">Euclidean</a></li> <li><a href="/w/index.php?title=Non-Euclidean_geometry&action=edit&redlink=1" class="new" title="Non-Euclidean geometry (hindi pa naisusulat)">Non-Euclidean</a> <ul><li><a href="/w/index.php?title=Elliptic_geometry&action=edit&redlink=1" class="new" title="Elliptic geometry (hindi pa naisusulat)">Elliptic</a> <ul><li><a href="/w/index.php?title=Spherical_geometry&action=edit&redlink=1" class="new" title="Spherical geometry (hindi pa naisusulat)">Spherical</a></li></ul></li> <li><a href="/w/index.php?title=Hyperbolic_geometry&action=edit&redlink=1" class="new" title="Hyperbolic geometry (hindi pa naisusulat)">Hyperbolic</a></li></ul></li> <li><a href="/w/index.php?title=Non-Archimedean_geometry&action=edit&redlink=1" class="new" title="Non-Archimedean geometry (hindi pa naisusulat)">Non-Archimedean geometry</a></li> <li><a href="/w/index.php?title=Projective_geometry&action=edit&redlink=1" class="new" title="Projective geometry (hindi pa naisusulat)">Projective</a></li> <li><a href="/w/index.php?title=Affine_geometry&action=edit&redlink=1" class="new" title="Affine geometry (hindi pa naisusulat)">Affine</a></li> <li><a href="/w/index.php?title=Synthetic_geometry&action=edit&redlink=1" class="new" title="Synthetic geometry (hindi pa naisusulat)">Synthetic</a></li> <li><a href="/wiki/Analitikong_heometriya" class="mw-redirect" title="Analitikong heometriya">Analitiko</a></li> <li><a href="/wiki/Alhebraikong_heometriya" class="mw-redirect" title="Alhebraikong heometriya">Alhebraiko</a> <ul><li><a href="/w/index.php?title=Arithmetic_geometry&action=edit&redlink=1" class="new" title="Arithmetic geometry (hindi pa naisusulat)">Arithmetic</a></li> <li><a href="/w/index.php?title=Diophantine_geometry&action=edit&redlink=1" class="new" title="Diophantine geometry (hindi pa naisusulat)">Diophantine</a></li></ul></li> <li><a href="/wiki/Heometriyang_deribatibo" title="Heometriyang deribatibo">Deribatibo</a> <ul><li><a href="/wiki/Heometriyang_Riemanniano" title="Heometriyang Riemanniano">Riemanniano</a></li> <li><a href="/w/index.php?title=Symplectic_geometry&action=edit&redlink=1" class="new" title="Symplectic geometry (hindi pa naisusulat)">Symplectic</a></li> <li><a href="/w/index.php?title=Discrete_differential_geometry&action=edit&redlink=1" class="new" title="Discrete differential geometry (hindi pa naisusulat)">Discrete differential</a></li></ul></li> <li><a href="/w/index.php?title=Complex_geometry&action=edit&redlink=1" class="new" title="Complex geometry (hindi pa naisusulat)">Complex</a></li> <li><a href="/w/index.php?title=Finite_geometry&action=edit&redlink=1" class="new" title="Finite geometry (hindi pa naisusulat)">Finite</a></li> <li><a href="/wiki/Heometriyang_natatangi" title="Heometriyang natatangi">Natatangi</a> <ul><li><a href="/w/index.php?title=Digital_geometry&action=edit&redlink=1" class="new" title="Digital geometry (hindi pa naisusulat)">Digital</a></li></ul></li> <li><a href="/w/index.php?title=Convex_geometry&action=edit&redlink=1" class="new" title="Convex geometry (hindi pa naisusulat)">Convex</a></li> <li><a href="/w/index.php?title=Computational_geometry&action=edit&redlink=1" class="new" title="Computational geometry (hindi pa naisusulat)">Computational</a></li> <li><a href="/w/index.php?title=Fractal&action=edit&redlink=1" class="new" title="Fractal (hindi pa naisusulat)">Fractal</a></li> <li><a href="/w/index.php?title=Incidence_geometry&action=edit&redlink=1" class="new" title="Incidence geometry (hindi pa naisusulat)">Incidence </a></li> <li><a href="/w/index.php?title=Noncommutative_geometry&action=edit&redlink=1" class="new" title="Noncommutative geometry (hindi pa naisusulat)">Noncommutative geometry</a> <ul><li><a href="/w/index.php?title=Noncommutative_algebraic_geometry&action=edit&redlink=1" class="new" title="Noncommutative algebraic geometry (hindi pa naisusulat)">Noncommutative algebraic geometry</a></li></ul></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><div class="hlist hlist-separated"><ul><li>Mga konsepto</li><li>Mga katangian</li></ul></div></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><a href="/wiki/Dimensiyon" title="Dimensiyon">Dimensiyon</a> <ul><li><a href="/w/index.php?title=Straightedge_and_compass_construction&action=edit&redlink=1" class="new" title="Straightedge and compass construction (hindi pa naisusulat)">Straightedge and compass constructions</a></li></ul> <ul><li><a href="/wiki/Anggulo" title="Anggulo">Anggulo</a></li> <li><a href="/wiki/Kurba" title="Kurba">Kurba</a></li> <li><a href="/w/index.php?title=Diagonal&action=edit&redlink=1" class="new" title="Diagonal (hindi pa naisusulat)">Diagonal</a></li> <li><a href="/wiki/Ortogonalidad" title="Ortogonalidad">Ortogonalidad</a> (<a href="/wiki/Perpendikular" title="Perpendikular">Perpendikular</a>)</li> <li><a href="/wiki/Paralelo" title="Paralelo">Paralelo</a></li> <li><a href="/w/index.php?title=Vertex_(geometry)&action=edit&redlink=1" class="new" title="Vertex (geometry) (hindi pa naisusulat)">Vertex</a></li></ul> <ul><li><a href="/w/index.php?title=Congruence_(geometry)&action=edit&redlink=1" class="new" title="Congruence (geometry) (hindi pa naisusulat)">Congruence</a></li> <li><a href="/w/index.php?title=Similarity_(geometry)&action=edit&redlink=1" class="new" title="Similarity (geometry) (hindi pa naisusulat)">Similarity</a></li> <li><a href="/wiki/Symmetry" class="mw-redirect" title="Symmetry">Symmetry</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/w/index.php?title=Serong_dimensiyonal_na_espasyo&action=edit&redlink=1" class="new" title="Serong dimensiyonal na espasyo (hindi pa naisusulat)">Serong dimensiyonal</a></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/wiki/Punto_(heometriya)" title="Punto (heometriya)">Punto</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/w/index.php?title=Isang_dimensiyonal_na_espasyo&action=edit&redlink=1" class="new" title="Isang dimensiyonal na espasyo (hindi pa naisusulat)">Isang dimensiyonal</a></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/wiki/Guhit_(heometriya)" title="Guhit (heometriya)">Guhit</a> <ul><li><a href="/wiki/Linyang_segmento" title="Linyang segmento">Segmento</a></li> <li><a href="/wiki/Guhit_(heometriya)#Rayos" title="Guhit (heometriya)">Rayos</a></li></ul></li> <li><a href="/wiki/Haba" title="Haba">Haba</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/w/index.php?title=Dalawang_dimensiyonal_na_espasyo&action=edit&redlink=1" class="new" title="Dalawang dimensiyonal na espasyo (hindi pa naisusulat)">Dalawang dimensiyonal</a></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;padding-bottom:0;"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;background-color: transparent; border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Plano_(heometriya)" title="Plano (heometriya)">Plano</a></li> <li><a href="/wiki/Sukat" title="Sukat">Sukat</a></li> <li><a href="/wiki/Poligon" title="Poligon">Poligon</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/wiki/Tatsulok" title="Tatsulok">Tatsulok</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Altitude_(triangle)&action=edit&redlink=1" class="new" title="Altitude (triangle) (hindi pa naisusulat)">Altitude</a></li> <li><a href="/wiki/Gilis" class="mw-redirect" title="Gilis">Gilis</a></li> <li><a class="mw-selflink selflink">Teorema ni Pitagoras</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/wiki/Paralelogram" title="Paralelogram">Paralelogram</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Parisukat" title="Parisukat">Parisukat</a></li> <li><a href="/wiki/Parihaba" title="Parihaba">Parihaba</a></li> <li><a href="/wiki/Rombus" title="Rombus">Rombus</a></li> <li><a href="/w/index.php?title=Romboide&action=edit&redlink=1" class="new" title="Romboide (hindi pa naisusulat)">Romboide</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/wiki/Kuwadrilateral" title="Kuwadrilateral">Kuwadrilateral</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Trapesoid" title="Trapesoid">Trapesoid</a></li> <li><a href="/w/index.php?title=Kite_(geometry)&action=edit&redlink=1" class="new" title="Kite (geometry) (hindi pa naisusulat)">Kite</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/wiki/Bilog" title="Bilog">Bilog</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Diyametro" title="Diyametro">Diyametro</a></li> <li><a href="/wiki/Sirkumperensiya" title="Sirkumperensiya">Sirkumperensiya</a></li> <li><a href="/w/index.php?title=Area_of_a_circle&action=edit&redlink=1" class="new" title="Area of a circle (hindi pa naisusulat)">Area</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/wiki/Tatlong_dimensiyonal_na_espasyo" class="mw-redirect" title="Tatlong dimensiyonal na espasyo">Tatlong dimensiyonal</a></div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/wiki/Volyum" title="Volyum">Volyum</a></li></ul> <ul><li><a href="/w/index.php?title=Kubo_(hugis)&action=edit&redlink=1" class="new" title="Kubo (hugis) (hindi pa naisusulat)">Kubo</a> <ul><li><a href="/w/index.php?title=Kuboide&action=edit&redlink=1" class="new" title="Kuboide (hindi pa naisusulat)">Kuboide</a></li></ul></li> <li><a href="/w/index.php?title=Silindro_(hugis)&action=edit&redlink=1" class="new" title="Silindro (hugis) (hindi pa naisusulat)">Silindro</a></li> <li><a href="/w/index.php?title=Dodecahedron&action=edit&redlink=1" class="new" title="Dodecahedron (hindi pa naisusulat)">Dodecahedron</a></li> <li><a href="/w/index.php?title=Icosahedron&action=edit&redlink=1" class="new" title="Icosahedron (hindi pa naisusulat)">Icosahedron</a></li> <li><a href="/w/index.php?title=Octahedron&action=edit&redlink=1" class="new" title="Octahedron (hindi pa naisusulat)">Octahedron</a></li> <li><a href="/w/index.php?title=Piramide_(hugis)&action=edit&redlink=1" class="new" title="Piramide (hugis) (hindi pa naisusulat)">Piramide</a></li> <li><a href="/w/index.php?title=Platonic_Solid&action=edit&redlink=1" class="new" title="Platonic Solid (hindi pa naisusulat)">Platonic Solid</a></li> <li><a href="/w/index.php?title=Sphere&action=edit&redlink=1" class="new" title="Sphere (hindi pa naisusulat)">Sphere</a></li> <li><a href="/w/index.php?title=Tetrahedron&action=edit&redlink=1" class="new" title="Tetrahedron (hindi pa naisusulat)">Tetrahedron</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;"><a href="/w/index.php?title=Apat_na_dimensiyonal_na_espasyo&action=edit&redlink=1" class="new" title="Apat na dimensiyonal na espasyo (hindi pa naisusulat)">Apat</a>- / ibang-dimensiyonal</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/w/index.php?title=Tesseract&action=edit&redlink=1" class="new" title="Tesseract (hindi pa naisusulat)">Tesseract</a></li> <li><a href="/w/index.php?title=Hypersphere&action=edit&redlink=1" class="new" title="Hypersphere (hindi pa naisusulat)">Hypersphere</a></li></ul></div></div></td> </tr><tr><th style="padding:0.1em;padding-bottom:0.2em;"> Mga heometra</th></tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;">ayon sa pangalan</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"> <ul><li><a href="/w/index.php?title=Yasuaki_Aida&action=edit&redlink=1" class="new" title="Yasuaki Aida (hindi pa naisusulat)">Aida</a></li> <li><a href="/w/index.php?title=Aryabhata&action=edit&redlink=1" class="new" title="Aryabhata (hindi pa naisusulat)">Aryabhata</a></li> <li><a href="/w/index.php?title=Ahmes&action=edit&redlink=1" class="new" title="Ahmes (hindi pa naisusulat)">Ahmes</a></li> <li><a href="/w/index.php?title=Alhazen&action=edit&redlink=1" class="new" title="Alhazen (hindi pa naisusulat)">Alhazen</a></li> <li><a href="/w/index.php?title=Apollonius_of_Perga&action=edit&redlink=1" class="new" title="Apollonius of Perga (hindi pa naisusulat)">Apollonius</a></li> <li><a href="/wiki/Arkimedes" title="Arkimedes">Arkimedes</a></li> <li><a href="/w/index.php?title=Michael_Atiyah&action=edit&redlink=1" class="new" title="Michael Atiyah (hindi pa naisusulat)">Atiyah</a></li> <li><a href="/w/index.php?title=Baudhayana&action=edit&redlink=1" class="new" title="Baudhayana (hindi pa naisusulat)">Baudhayana</a></li> <li><a href="/w/index.php?title=J%C3%A1nos_Bolyai&action=edit&redlink=1" class="new" title="János Bolyai (hindi pa naisusulat)">Bolyai</a></li> <li><a href="/w/index.php?title=Brahmagupta&action=edit&redlink=1" class="new" title="Brahmagupta (hindi pa naisusulat)">Brahmagupta</a></li> <li><a href="/w/index.php?title=%C3%89lie_Cartan&action=edit&redlink=1" class="new" title="Élie Cartan (hindi pa naisusulat)">Cartan</a></li> <li><a href="/w/index.php?title=Harold_Scott_MacDonald_Coxeter&action=edit&redlink=1" class="new" title="Harold Scott MacDonald Coxeter (hindi pa naisusulat)">Coxeter</a></li> <li><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes</a></li> <li><a href="/wiki/Euclides" title="Euclides">Euclides</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/w/index.php?title=Mikhail_Leonidovich_Gromov&action=edit&redlink=1" class="new" title="Mikhail Leonidovich Gromov (hindi pa naisusulat)">Gromov</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/w/index.php?title=Jye%E1%B9%A3%E1%B9%ADhadeva&action=edit&redlink=1" class="new" title="Jyeṣṭhadeva (hindi pa naisusulat)">Jyeṣṭhadeva</a></li> <li><a href="/w/index.php?title=K%C4%81ty%C4%81yana&action=edit&redlink=1" class="new" title="Kātyāyana (hindi pa naisusulat)">Kātyāyana</a></li> <li><a href="/wiki/Omar_Khayy%C3%A1m" class="mw-redirect" title="Omar Khayyám">Khayyám</a></li> <li><a href="/wiki/Felix_Klein" title="Felix Klein">Klein</a></li> <li><a href="/w/index.php?title=Nikolai_Lobachevsky&action=edit&redlink=1" class="new" title="Nikolai Lobachevsky (hindi pa naisusulat)">Lobachevsky</a></li> <li><a href="/w/index.php?title=Manava&action=edit&redlink=1" class="new" title="Manava (hindi pa naisusulat)">Manava</a></li> <li><a href="/w/index.php?title=Hermann_Minkowski&action=edit&redlink=1" class="new" title="Hermann Minkowski (hindi pa naisusulat)">Minkowski</a></li> <li><a href="/w/index.php?title=Minggatu&action=edit&redlink=1" class="new" title="Minggatu (hindi pa naisusulat)">Minggatu</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li> <li><a href="/w/index.php?title=Parameshvara&action=edit&redlink=1" class="new" title="Parameshvara (hindi pa naisusulat)">Parameshvara</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Riemann</a></li> <li><a href="/w/index.php?title=Sakabe_K%C5%8Dhan&action=edit&redlink=1" class="new" title="Sakabe Kōhan (hindi pa naisusulat)">Sakabe</a></li> <li><a href="/w/index.php?title=Sijzi&action=edit&redlink=1" class="new" title="Sijzi (hindi pa naisusulat)">Sijzi</a></li> <li><a href="/w/index.php?title=Nasir_al-Din_al-Tusi&action=edit&redlink=1" class="new" title="Nasir al-Din al-Tusi (hindi pa naisusulat)">al-Tusi</a></li> <li><a href="/w/index.php?title=Oswald_Veblen&action=edit&redlink=1" class="new" title="Oswald Veblen (hindi pa naisusulat)">Veblen</a></li> <li><a href="/w/index.php?title=Virasena&action=edit&redlink=1" class="new" title="Virasena (hindi pa naisusulat)">Virasena</a></li> <li><a href="/w/index.php?title=Yang_Hui&action=edit&redlink=1" class="new" title="Yang Hui (hindi pa naisusulat)">Yang Hui</a></li> <li><a href="/w/index.php?title=Ibn_al-Yasamin&action=edit&redlink=1" class="new" title="Ibn al-Yasamin (hindi pa naisusulat)">al-Yasamin</a></li> <li><a href="/wiki/Zhang_Heng" title="Zhang Heng">Zhang</a></li></ul></div></div></td> </tr><tr><td style="padding:0 0.1em 0.4em"> <div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left;background:#ddf; text-align:center;">ayon sa panahon</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center;padding-bottom:0;"><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;background-color: transparent; border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> <a href="/w/index.php?title=Before_Common_Era&action=edit&redlink=1" class="new" title="Before Common Era (hindi pa naisusulat)">BCE</a></th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Ahmes&action=edit&redlink=1" class="new" title="Ahmes (hindi pa naisusulat)">Ahmes</a></li> <li><a href="/w/index.php?title=Baudhayana&action=edit&redlink=1" class="new" title="Baudhayana (hindi pa naisusulat)">Baudhayana</a></li> <li><a href="/w/index.php?title=Manava&action=edit&redlink=1" class="new" title="Manava (hindi pa naisusulat)">Manava</a></li> <li><a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a></li> <li><a href="/wiki/Euclid" class="mw-redirect" title="Euclid">Euclid</a></li> <li><a href="/wiki/Archimedes" class="mw-redirect" title="Archimedes">Archimedes</a></li> <li><a href="/w/index.php?title=Apollonius_of_Perga&action=edit&redlink=1" class="new" title="Apollonius of Perga (hindi pa naisusulat)">Apollonius</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> 1–1400s</th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Zhang_Heng" title="Zhang Heng">Zhang</a></li> <li><a href="/w/index.php?title=K%C4%81ty%C4%81yana&action=edit&redlink=1" class="new" title="Kātyāyana (hindi pa naisusulat)">Kātyāyana</a></li> <li><a href="/w/index.php?title=Aryabhata&action=edit&redlink=1" class="new" title="Aryabhata (hindi pa naisusulat)">Aryabhata</a></li> <li><a href="/w/index.php?title=Brahmagupta&action=edit&redlink=1" class="new" title="Brahmagupta (hindi pa naisusulat)">Brahmagupta</a></li> <li><a href="/w/index.php?title=Virasena&action=edit&redlink=1" class="new" title="Virasena (hindi pa naisusulat)">Virasena</a></li> <li><a href="/w/index.php?title=Alhazen&action=edit&redlink=1" class="new" title="Alhazen (hindi pa naisusulat)">Alhazen</a></li> <li><a href="/w/index.php?title=Sijzi&action=edit&redlink=1" class="new" title="Sijzi (hindi pa naisusulat)">Sijzi</a></li> <li><a href="/wiki/Omar_Khayy%C3%A1m" class="mw-redirect" title="Omar Khayyám">Khayyám</a></li> <li><a href="/w/index.php?title=Ibn_al-Yasamin&action=edit&redlink=1" class="new" title="Ibn al-Yasamin (hindi pa naisusulat)">al-Yasamin</a></li> <li><a href="/w/index.php?title=Nasir_al-Din_al-Tusi&action=edit&redlink=1" class="new" title="Nasir al-Din al-Tusi (hindi pa naisusulat)">al-Tusi</a></li> <li><a href="/w/index.php?title=Yang_Hui&action=edit&redlink=1" class="new" title="Yang Hui (hindi pa naisusulat)">Yang Hui</a></li> <li><a href="/w/index.php?title=Parameshvara&action=edit&redlink=1" class="new" title="Parameshvara (hindi pa naisusulat)">Parameshvara</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> 1400s–1700s</th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Jye%E1%B9%A3%E1%B9%ADhadeva&action=edit&redlink=1" class="new" title="Jyeṣṭhadeva (hindi pa naisusulat)">Jyeṣṭhadeva</a></li> <li><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes</a></li> <li><a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Pascal</a></li> <li><a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Huygens</a></li> <li><a href="/w/index.php?title=Minggatu&action=edit&redlink=1" class="new" title="Minggatu (hindi pa naisusulat)">Minggatu</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Euler</a></li> <li><a href="/w/index.php?title=Sakabe_K%C5%8Dhan&action=edit&redlink=1" class="new" title="Sakabe Kōhan (hindi pa naisusulat)">Sakabe</a></li> <li><a href="/w/index.php?title=Yasuaki_Aida&action=edit&redlink=1" class="new" title="Yasuaki Aida (hindi pa naisusulat)">Aida</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> 1700s–1900s</th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/w/index.php?title=Nikolai_Lobachevsky&action=edit&redlink=1" class="new" title="Nikolai Lobachevsky (hindi pa naisusulat)">Lobachevsky</a></li> <li><a href="/w/index.php?title=J%C3%A1nos_Bolyai&action=edit&redlink=1" class="new" title="János Bolyai (hindi pa naisusulat)">Bolyai</a></li> <li><a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Riemann</a></li> <li><a href="/wiki/Felix_Klein" title="Felix Klein">Klein</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Poincaré</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/w/index.php?title=Hermann_Minkowski&action=edit&redlink=1" class="new" title="Hermann Minkowski (hindi pa naisusulat)">Minkowski</a></li> <li><a href="/w/index.php?title=%C3%89lie_Cartan&action=edit&redlink=1" class="new" title="Élie Cartan (hindi pa naisusulat)">Cartan</a></li> <li><a href="/w/index.php?title=Oswald_Veblen&action=edit&redlink=1" class="new" title="Oswald Veblen (hindi pa naisusulat)">Veblen</a></li> <li><a href="/w/index.php?title=Harold_Scott_MacDonald_Coxeter&action=edit&redlink=1" class="new" title="Harold Scott MacDonald Coxeter (hindi pa naisusulat)">Coxeter</a></li></ul></td> </tr><tr><th style="padding:0.1em;background:#e6e6ff; font-weight:normal;"> Present day</th></tr><tr><td style="padding:0 0.1em 0.4em;padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Michael_Atiyah&action=edit&redlink=1" class="new" title="Michael Atiyah (hindi pa naisusulat)">Atiyah</a></li> <li><a href="/w/index.php?title=Mikhail_Leonidovich_Gromov&action=edit&redlink=1" class="new" title="Mikhail Leonidovich Gromov (hindi pa naisusulat)">Gromov</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td style="text-align:right;font-size:115%;padding-top: 0.6em;"><style data-mw-deduplicate="TemplateStyles:r1843287">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}.mw-parser-output .infobox .navbar{font-size:100%}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-tingnan"><a href="/wiki/Padron:Pangkalahatang_heometriya" title="Padron:Pangkalahatang heometriya"><abbr title="Tingnan ang padron">t</abbr></a></li><li class="nv-usapan"><a href="/w/index.php?title=Usapang_padron:Pangkalahatang_heometriya&action=edit&redlink=1" class="new" title="Usapang padron:Pangkalahatang heometriya (hindi pa naisusulat)"><abbr title="Pag-usapan ang padron">u</abbr></a></li><li class="nv-baguhin"><a class="external text" href="https://tl.wikipedia.org/w/index.php?title=Padron:Pangkalahatang_heometriya&action=edit"><abbr title="Baguhin ang padron">b</abbr></a></li></ul></div></td></tr></tbody></table><p>Sa sipnayan, ang <b>teorema ni Pitagoras</b> (<a href="/wiki/Wikang_Kastila" title="Wikang Kastila">Kastila</a>: <i lang="es">teorema de Pitágoras</i>, <a href="/wiki/Wikang_Ingles" title="Wikang Ingles">Ingles</a>: <i lang="en">Pythagorean theorem</i>) ay isang pangunahing relasyon sa <a href="/w/index.php?title=Heometriyang_Euclidean&action=edit&redlink=1" class="new" title="Heometriyang Euclidean (hindi pa naisusulat)">heometriyang Euclidyana</a> ng tatlong gilid ng isang tatsulok na may <a href="/wiki/Tamang_anggulo" class="mw-redirect" title="Tamang anggulo">sihang tadlong</a>. Sinasabi nito na ang parirami ng <a href="/wiki/Hypotenuse" class="mw-redirect" title="Hypotenuse">gilis</a> (ang gilid katapat ng <a href="/wiki/Tamang_anggulo" class="mw-redirect" title="Tamang anggulo">sihang tadlong</a>) ay katumbas ng kabuuan ng parirami ng <a href="/w/index.php?title=Cathetus&action=edit&redlink=1" class="new" title="Cathetus (hindi pa naisusulat)">natitirang dalawang gilid</a>. Maaaring sulatin ang <a href="/w/index.php?title=Teorema&action=edit&redlink=1" class="new" title="Teorema (hindi pa naisusulat)">teorema</a> bilang isang <a href="/wiki/Equation" class="mw-redirect" title="Equation">ekwasyon</a> na nag-uugnay ng mga haba ng gilid na nag-uugnay ng mga haba ng panig na <i>a</i>, <i>b</i> and <i>c</i> na kadalasang tinatawag na "Ekwasyong Pitagoriko":<sup id="cite_ref-Sally0_1-0" class="reference"><a href="#cite_note-Sally0-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></p><blockquote><p><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 a^{2}+b^{2}=c^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}+b^{2}=c^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92333b53991e3ea02f5d6384bac4911ae3060a1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.983ex; height:3.009ex;" alt="{\displaystyle a^{2}+b^{2}=c^{2},}"></span></p></blockquote><p>kung saan kumakatwan ang "c" sa haba ng gilis at ang "a" at "b" sa mga haba ng natitirang dalawang gilid. </p><p>Kahit madalas na pinagtatalunan na may kaalaman na sa teorema bago si Pitagoras,<sup id="cite_ref-Pos2_2-0" class="reference"><a href="#cite_note-Pos2-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> ipinangalan ang teorema kay <a href="/wiki/Pythagoras" title="Pythagoras">Pitagoras</a> (s. 570–495 BK), isang dalubbilang sa <a href="/wiki/Sinaunang_Gresya" title="Sinaunang Gresya">sinaunang Gresya</a>, dahil siya, ayon sa tradisyon, ang ipinalagay na may pinakaunang <a href="/wiki/Mathematical_proof" class="mw-redirect" title="Mathematical proof">patibay</a>, ngunit wala itong ebidensya.<sup id="cite_ref-Allman2_4-0" class="reference"><a href="#cite_note-Allman2-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-heath144_5-0" class="reference"><a href="#cite_note-heath144-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> May kaunting ebidensya na naintindihan ng mga <a href="/w/index.php?title=Babylonian_mathematics&action=edit&redlink=1" class="new" title="Babylonian mathematics (hindi pa naisusulat)">Babilonyang dalubbilang</a> ang pormula, ngunit halos walang nagpapahiwatig ng paggamit sa isang balangkas-sipnayan.<sup id="cite_ref-Neugebauer_7-0" class="reference"><a href="#cite_note-Neugebauer-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Livio_8-0" class="reference"><a href="#cite_note-Livio-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Nadiskubre nang magkahiwalay ng mga <a href="/wiki/Mesopotamia" class="mw-redirect" title="Mesopotamia">Mesopotamyang</a>, <a href="/w/index.php?title=Indian_mathematics&action=edit&redlink=1" class="new" title="Indian mathematics (hindi pa naisusulat)">Indiyanong</a> and <a href="/w/index.php?title=Chinese_mathematics&action=edit&redlink=1" class="new" title="Chinese mathematics (hindi pa naisusulat)">Tsinong dalubbilang</a>, at, sa mga ibang pagkakataon, ay nagbigay ng patibay para sa mga kasong espesyal. </p><p>Nabigyan ang teorema ng mararaming patibay, marahil na ang pinakamarami para sa anumang teoremang matematiko. Iba't iba ang mga ito, kabilang ang heometrikong patibay at alhebraikong patibay, ilan na pinetsahang libu-libong taon na ang nakalilipas. Maaaring heneralisahin ang teorema sa iba't ibang paraan, kasama na ang mga espasyo na may mas mataas na sukod, mga espasyong di-Euclidyano, sa mga bagay na hindi tatsihang tadlong, at sa katunayan, sa mga bagay na hindi tatsulok talaga, pero mga solido na may <i>n</i> na sukod. Nakaakit ang teoremang Pitagoras ng interes sa labas ng sipnayan bilang simbolo ng sipnayaning kalabuan, kahiwagaan, o kapangyarihang intelektuwal; managana ang mga pagtukoy nito sa panitikan, mga dula, mga musikal, mga kanta, mga selyo, at guhit-larawan. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Patibay_ng_pag-iibang-ayos">Patibay ng pag-iibang-ayos</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorema_ni_Pitagoras&veaction=edit&section=1" title="Baguhin seksiyon: Patibay ng pag-iibang-ayos" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorema_ni_Pitagoras&action=edit&section=1" title="Edit section's source code: Patibay ng pag-iibang-ayos"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Pythagoras-proof-anim.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Pythagoras-proof-anim.svg/220px-Pythagoras-proof-anim.svg.png" decoding="async" width="220" height="126" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Pythagoras-proof-anim.svg/330px-Pythagoras-proof-anim.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Pythagoras-proof-anim.svg/440px-Pythagoras-proof-anim.svg.png 2x" data-file-width="700" data-file-height="400" /></a><figcaption>Ang patibay ng pag-iibang-ayos (i-click para makita ang animasyon)</figcaption></figure> <p>Naglalaman ang dalawang malaking parisukat na ipinapakita sa pigura ng tig-apat na magkakaparehong tatsulok, at ang pagkakaiba lamang ng dalawang malaking parisukat ay magkaiba ang pagsasaayos ng mga tatsulok. Samakatuwid, magkatumbas dapat ang sukat ng mga puting puwang sa loob ng dalawang parisukat. Nagbubunga ang pag-ekweyt ng sukat ng puting puwang ng teorema ni Pitagoras, <a href="/w/index.php?title=Q.E.D.&action=edit&redlink=1" class="new" title="Q.E.D. (hindi pa naisusulat)">Q.E.D.</a><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Ibinibigay ni Heath ang patibay na ito sa kanyang komentaryo sa Proposition I.47 sa Mga Elemento ni Euclid, at ibinabangit ang mga panukala ni Bretschneider at Hankel na posibleng naunawaan ni Pitagoras ang patibay na ito. Mas gusto ni Heath mismo ang ibang panukala para sa Pitagorikong katibayan, pero inaamin sa umpisa pa lamang ng pagtatalakay na "Hindi naglalaman ang Griyegong panitikan na inaarian natin na nagmumula sa unang limang siglo pagkatapos ni Pitagoras ng pahayag na nagbabanggit dito o anumang dakilang heometrikong pagkatuklas mula sa kanya."<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Lumalaki ang pagdududa ng kamakailang iskolarsip sa anumang papel ni Pitagoras bilang manlilikha ng sipnayan, ngunit tuloy pa rin ang pakikipagtalo tungkol dito.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Iba_pang_anyo_ng_teorema">Iba pang anyo ng teorema</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorema_ni_Pitagoras&veaction=edit&section=2" title="Baguhin seksiyon: Iba pang anyo ng teorema" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorema_ni_Pitagoras&action=edit&section=2" title="Edit section's source code: Iba pang anyo ng teorema"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kapag tumutukoy ang <i>c</i> sa <a href="/w/index.php?title=Length&action=edit&redlink=1" class="new" title="Length (hindi pa naisusulat)">haba</a> ng gilis at tumutukoy ang <i>a</i> at <i>b</i> sa haba ng dalawa pang panig, maaaring ipahayag ang teorema ni Pitagoras bilang ang ekwasyong Pitagoriko: </p> <dl><dd><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 a^{2}+b^{2}=c^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}+b^{2}=c^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90b56b985c78deb115014efe90ce634d73dd51fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.983ex; height:2.843ex;" alt="{\displaystyle a^{2}+b^{2}=c^{2}.}"></span></dd></dl> <p>Kapag alam ang haba ng <i>a</i> at <i>b</i>, maaaring ikalkula ang <i>c</i> bilang </p> <dl><dd><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 c={\sqrt {a^{2}+b^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c={\sqrt {a^{2}+b^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fd521cee81d583ce94bf6710984cc2a9eb7c3da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.252ex; height:3.509ex;" alt="{\displaystyle c={\sqrt {a^{2}+b^{2}}}.}"></span></dd></dl> <p>Kapag alam ang gilis ng <i>c</i> at ng isang panig (<i>a</i> o <i>b</i>), maaaring ikalkula ang haba ng isa pang panig bilang </p> <dl><dd><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 a={\sqrt {c^{2}-b^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\sqrt {c^{2}-b^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca09e8ee119ce95c893ceb2ac1f7ccd3a40fad9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.605ex; height:3.509ex;" alt="{\displaystyle a={\sqrt {c^{2}-b^{2}}}}"></span></dd></dl> <p>o </p> <dl><dd><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 b={\sqrt {c^{2}-a^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b={\sqrt {c^{2}-a^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77e9dfccdb8a659eeb36f79af461f207265d5911" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.252ex; height:3.509ex;" alt="{\displaystyle b={\sqrt {c^{2}-a^{2}}}.}"></span></dd></dl> <p>Iniuugnay ng ekwasyong Pitagoriko ang mga panig ng sihang tadlong sa simpleng paraan, kaya kung alam ang haba ng anumang dalawang panig, maaaring hanapin ang haba ng ikatlong panig. Isa pang koralariya ng teorema ay sa anumang sihang tadlong, mas malaki ang gilis kaysa sa isa sa mga iba pang panig, pero mas maliit kaysa sa kanilang kabuuan. </p><p>Isang heneralisasyon ng teoremang ito ang <a href="/w/index.php?title=Law_of_cosines&action=edit&redlink=1" class="new" title="Law of cosines (hindi pa naisusulat)">batas ng kasinway</a> na nagpapahintulot ng komputasyon ng haba ng anumang panig ng anumang tatsulok, basta nandoon ang haba ng dalawa pang panig at ang anggulo sa gitna nila. Kapag sihang tadlong ang anggulo sa gitna ng iba pang panig, pumapayak ang batas ng kasinway para maging ekwasyong Pitagoriko. </p> <div class="mw-heading mw-heading2"><h2 id="Mga_iba_pang_katibayan_ng_teorema">Mga iba pang katibayan ng teorema</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorema_ni_Pitagoras&veaction=edit&section=3" title="Baguhin seksiyon: Mga iba pang katibayan ng teorema" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorema_ni_Pitagoras&action=edit&section=3" title="Edit section's source code: Mga iba pang katibayan ng teorema"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Posible na ang teoremang ito ay mas maraming kilalang katibayan kaysa sa iba (ang batas ng <a href="/w/index.php?title=Quadratic_reciprocity&action=edit&redlink=1" class="new" title="Quadratic reciprocity (hindi pa naisusulat)">dawaking resiprosidad</a> ay isa pang kalaban para sa karangalan); naglalaman ang aklat na <i>The Pythagorean Proposition</i> ng 370 katibayan.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Katibayan_gamit_ang_magkahawig_na_tatsulok">Katibayan gamit ang magkahawig na tatsulok</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorema_ni_Pitagoras&veaction=edit&section=4" title="Baguhin seksiyon: Katibayan gamit ang magkahawig na tatsulok" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorema_ni_Pitagoras&action=edit&section=4" title="Edit section's source code: Katibayan gamit ang magkahawig na tatsulok"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Pythagoras_similar_triangles_simplified.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Pythagoras_similar_triangles_simplified.svg/220px-Pythagoras_similar_triangles_simplified.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Pythagoras_similar_triangles_simplified.svg/330px-Pythagoras_similar_triangles_simplified.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fb/Pythagoras_similar_triangles_simplified.svg/440px-Pythagoras_similar_triangles_simplified.svg.png 2x" data-file-width="512" data-file-height="385" /></a><figcaption>Proof using similar triangles</figcaption></figure> <p>Nakabatay ang pruwebang ito sa <a href="/w/index.php?title=Proportionality_(mathematics)&action=edit&redlink=1" class="new" title="Proportionality (mathematics) (hindi pa naisusulat)">pagkaproporsyonado</a> ng mga panig ng dalawang <a href="/w/index.php?title=Similarity_(geometry)&action=edit&redlink=1" class="new" title="Similarity (geometry) (hindi pa naisusulat)">magkahawig</a> na tatsulok, iyon ay, magkatumbas ang <a href="/wiki/Ratio" class="mw-redirect" title="Ratio">ratio</a> ng anumang dalawang naaayong panig ng magkahawig na tatsulok anuman ang laki ng mga tatsulok. </p><p>Ipalagay na kumakatawan ang <i>ABC</i> sa tatsihang tadlong kung saan matatagpuan ang sihang tadlong sa <i>C</i>, tulad ng ipinapakita sa larawan. Ilarawan ang <a href="/w/index.php?title=Altitude_(triangle)&action=edit&redlink=1" class="new" title="Altitude (triangle) (hindi pa naisusulat)">tayog</a> mula sa punto <i>C</i>, at tawagin ang <i>H</i> bilang kanyang sagandaan kasama ang panig <i>AB</i>. Hinahati ng punto <i>H</i> ang haba ng gilis <i>c</i> sa mga bahaging <i>d</i> at <i>e</i>. <a href="/w/index.php?title=Similarity_(geometry)&action=edit&redlink=1" class="new" title="Similarity (geometry) (hindi pa naisusulat)">Magkahawig</a> ang bagong tatsulok <i>ACH</i> sa tatsulok <i>ABC</i>, dahil may mga sihang tadlong sila (ayon sa kahulugan ng tayog), and nakikibahagi sila ng anggulo sa <i>A</i>, ibig sabihin na parehas din ang ikatlong anggulo sa dalawang tatsulok na iminamarka ng <i>θ</i> sa pigura. Sa katulad na pangangatuwiran, magkahawig din ang tatsulok <i>CBH</i> sa <i>ABC</i>. Kinakailangan ng katibayan ng pagkakahawig ng tatsulok ang <a href="/w/index.php?title=Triangle_postulate&action=edit&redlink=1" class="new" title="Triangle postulate (hindi pa naisusulat)">saligang tatsulok</a>: ang kabuuan ng mga anggulo sa isang tatsulok ay dalawang sihang tadlong, at magkatumbas ito sa <a href="/w/index.php?title=Parallel_postulate&action=edit&redlink=1" class="new" title="Parallel postulate (hindi pa naisusulat)">saligang agapay</a>. Humahantong ang pagkakahawig ng mga tatsulok sa katumbasan ng mga ratio ng mga naaayon na panig: </p> <dl><dd><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 {\frac {BC}{AB}}={\frac {BH}{BC}}{\text{ at }}{\frac {AC}{AB}}={\frac {AH}{AC}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>B</mi> <mi>C</mi> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>B</mi> <mi>H</mi> </mrow> <mrow> <mi>B</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext> at </mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <mi>C</mi> </mrow> <mrow> <mi>A</mi> <mi>B</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <mi>H</mi> </mrow> <mrow> <mi>A</mi> <mi>C</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {BC}{AB}}={\frac {BH}{BC}}{\text{ at }}{\frac {AC}{AB}}={\frac {AH}{AC}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a470fd3a190ac481a70a3845630274c2c336330f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:28.091ex; height:5.509ex;" alt="{\displaystyle {\frac {BC}{AB}}={\frac {BH}{BC}}{\text{ at }}{\frac {AC}{AB}}={\frac {AH}{AC}}.}"></span></dd></dl> <p>Pinapatumbas ng unang resulta ang <a href="/wiki/Cosine" class="mw-redirect" title="Cosine">kasinway</a> ng mga anggulong <i>θ</i>, samantalang pinapatumbas ng ikalawang resulta ang kanilang <a href="/wiki/Sine" class="mw-disambig" title="Sine">sinway</a>. </p><p> Maaaring isulat ang mga ratio bilang</p><blockquote><p><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 BC^{2}=AB\times BH{\text{ at }}AC^{2}=AB\times AH.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>A</mi> <mi>B</mi> <mo>×</mo> <mi>B</mi> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext> at </mtext> </mrow> <mi>A</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>A</mi> <mi>B</mi> <mo>×</mo> <mi>A</mi> <mi>H</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BC^{2}=AB\times BH{\text{ at }}AC^{2}=AB\times AH.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e854d4d3f11bdc516a22a160f9dfee7820e41f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:39.613ex; height:2.676ex;" alt="{\displaystyle BC^{2}=AB\times BH{\text{ at }}AC^{2}=AB\times AH.}"></span></p></blockquote><p>Nagreresulta ang pagdaragdag ng dalawang katumbasang ito sa</p><blockquote><p><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 BC^{2}+AC^{2}=AB\times BH+AB\times AH=AB\times (AH+BH)=AB^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>A</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>A</mi> <mi>B</mi> <mo>×</mo> <mi>B</mi> <mi>H</mi> <mo>+</mo> <mi>A</mi> <mi>B</mi> <mo>×</mo> <mi>A</mi> <mi>H</mi> <mo>=</mo> <mi>A</mi> <mi>B</mi> <mo>×</mo> <mo stretchy="false">(</mo> <mi>A</mi> <mi>H</mi> <mo>+</mo> <mi>B</mi> <mi>H</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BC^{2}+AC^{2}=AB\times BH+AB\times AH=AB\times (AH+BH)=AB^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a54facb8aee0cbb86bbab4d66389e911d66046bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:68.356ex; height:3.176ex;" alt="{\displaystyle BC^{2}+AC^{2}=AB\times BH+AB\times AH=AB\times (AH+BH)=AB^{2},}"></span></p></blockquote><p>na, pagkatapos ng pagpapayak, ay ipinapahayag ang teorema ni Pitagoras:</p><blockquote><p><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 BC^{2}+AC^{2}=AB^{2}\ .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>A</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>A</mi> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mtext> </mtext> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle BC^{2}+AC^{2}=AB^{2}\ .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4701212d48f8703c63d48e811d5b1f9797f562fe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:20.939ex; height:2.843ex;" alt="{\displaystyle BC^{2}+AC^{2}=AB^{2}\ .}"></span></p></blockquote> <div class="mw-heading mw-heading3"><h3 id="Katibayan_ni_Euclid">Katibayan ni Euclid</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorema_ni_Pitagoras&veaction=edit&section=5" title="Baguhin seksiyon: Katibayan ni Euclid" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorema_ni_Pitagoras&action=edit&section=5" title="Edit section's source code: Katibayan ni Euclid"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem.svg/220px-Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem.svg.png" decoding="async" width="220" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem.svg/330px-Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem.svg/440px-Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem.svg.png 2x" data-file-width="500" data-file-height="540" /></a><figcaption>Katibayan sa <i>Mga Elemento</i> ni Euclid</figcaption></figure> <p>Sa isang balangkas, narito kung paano ang pruweba sa <i><a href="/wiki/Euclid%27s_Elements" class="mw-redirect" title="Euclid's Elements">Mga Elemento</a></i> ni Euclid. Hinahati ang malaking parisukat sa isang kaliwa at isang kanang parisukat. Nabubuo ang isang tatsulok na may kalahating dawak ng kaliwang parihaba. Pagkatapos, may nabubuong tatsulok na may kalahating dawak ng parisukat sa kaliwang banda. Ipinapakita na <a href="/w/index.php?title=Congruence_(geometry)&action=edit&redlink=1" class="new" title="Congruence (geometry) (hindi pa naisusulat)">magkalapat</a> ang dalawang tatsulok na nagpapatunay na parehas ang dawak ng parisukat sa dawak ng kaliwang parihaba.Sumusunod sa argumentong ito ang isang magkatulad na bersyon para sa kanang parihaba at sa natitirang parisukat. Kapag isinama ang dalawang parihaba para ibuo muli ang parisukat sa gilis, parehas ang kanyang dawak sa kabuuan ng dawak ng dalawa pang parisukat. Sumusunod ang mga detalye. </p><p>Ipalagay na <i>A</i>, <i>B</i>, <i>C</i> ang mga <a href="/w/index.php?title=Vertex_(geometry)&action=edit&redlink=1" class="new" title="Vertex (geometry) (hindi pa naisusulat)">bagtasan</a> ng sihang tadlong na may sihang tadlong sa <i>A</i>. Maglagay ng perpendikular mula <i>A</i> hanggang sa panig katapat ng gilis sa parisukat sa gilis. Ang linyang iyon ay naghahati sa parisukat sa gilis para maging dalawang parihaba, bawat isa na may parehong dawak sa isa sa mga dalawang parisukat sa paa. </p><p>Para sa pormal na katibayan, kailangan ng apat na elementaryang <a href="/w/index.php?title=Lemma_(mathematics)&action=edit&redlink=1" class="new" title="Lemma (mathematics) (hindi pa naisusulat)">lemmata</a>: </p> <ol><li>Kapag ang dalawang tatsulok ay may dalawang panig ng isang tatsulok na magkatumbas sa dalawang panig ng isa pang tatsulok, bawat isa, at magkatumbas ang mga anggulo na isinama ng mga panig na iyon, magkalapat ang mga tatsulok (<a href="/w/index.php?title=Side_angle_side&action=edit&redlink=1" class="new" title="Side angle side (hindi pa naisusulat)">panig-anggulo-panig</a>).</li> <li>Ang dawak ng isang tatsulok ay kalahati ng dawak ng anumang paralelogram na nasa parehas na base at magkapareho ang tayog.</li> <li>Ang dawak ng parihaba ay magkatumbas sa produkto ng dalawang magkatabing panig.</li> <li>Ang dawak ng isang parisukat ay magkatumbas sa produkto ng kanyang dalawang panig (sumusunod mula sa 3).</li></ol><p> Pagkatapos, kaugnay ang bawat tuktok na parisukat sa isang tatsulok na magkalapat sa isa pang tatsulok na kaugnay naman sa isa sa dalawang parihaba na nagbubuo ng parisukat sa ibaba.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></p><div style="clear:both;"></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem2.svg/220px-Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem2.svg.png" decoding="async" width="220" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/59/Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem2.svg/330px-Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/59/Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem2.svg/440px-Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem2.svg.png 2x" data-file-width="500" data-file-height="540" /></a><figcaption>Larawan kasama ang mga bagong linya</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem3.svg/220px-Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem3.svg.png" decoding="async" width="220" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem3.svg/330px-Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem3.svg/440px-Illustration_to_Euclid%27s_proof_of_the_Pythagorean_theorem3.svg.png 2x" data-file-width="500" data-file-height="540" /></a><figcaption>Ipinapakita ang dalawang kalapat na tatsulok na kalahati ng dawak ng parihabang BDLK at parisukat na BAGF.</figcaption></figure> <p>Sumusunod ang katibayan: </p> <ol><li>Ipalagay na ACB ay isang tatsulok na may sihang tadlong na CAB.</li> <li>Sa bawat panig na BC, AB, at CA, gumuhit ng mga parisukat, CBDE, BAGF, at ACIH, sa ganoong pagkaayos. Kinakailangan ng pagbuo ng mga parisukat ang mga nakaraang teorema sa Euclid, at nakadepende sa batayang palagay ng pagkaagapay.<sup id="cite_ref-Gullberg_14-0" class="reference"><a href="#cite_note-Gullberg-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li>Mula sa A, gumuhit ng linyang agapay sa BD at CE. Tadlong ang pagbatas nito sa BC at DE sa K at L, ayon sa pagkabanggit.</li> <li>Pagsamahin ang CF at AD upang ibuo ang mga tatsulok na BCF at BDA.</li> <li>Kapwa sihang tadlong ang sihang CAB at BAG; samakatuwid <a href="/w/index.php?title=Line_(geometry)&action=edit&redlink=1" class="new" title="Line (geometry) (hindi pa naisusulat)">kaguhit</a> ang C, A, at G. Ganito rin para sa B, A, at H.</li> <li>Kapwa sihang tadlong ang sihang CBD at FBA; samakatuwid magkatumbas ang sihang ABD at sihang FBC, dahil kapwa kabuuan ang dalawa ng tadlong sihang at sihang ABC.</li> <li>Dahil magkatumbas ang AB sa FB, at magkatumbas ang BD sa BC, sa gayon dapat magkalapat ang tatsulok na ABD sa tatsulok na FBC.</li> <li>Dahil tuwid na linya ang A-K-L na agapay sa BD, doble ang dawak ng parihabang BDLK ng tatsulok na ABD dahil parehong BD ang kani-kanilang base, at magkapareho ang kanilang tayog na BK, ibig sabihin na isang linyang pareho sa kanilang magkaparehong base na kumokonekta sa mga agapayang linyang BD at AL. (ika-2 lemmata)</li> <li>Dahil kaguhit ang C sa A at G, dapat doble ang dawak ng parisukat na BAGF sa tatsulok na FBC.</li> <li>Samakatuwid, magkatumbas dapat ang dawak ng tatsulok BAGF = AB<sup>2</sup>.</li> <li>Katulad nito, maaaring ipakita na dapat magkatumbas ang dawak ng parihabang CKLE at ang parisukat ACIH = AC<sup>2</sup>.</li> <li>Kapag ipinagsama ang dalawang resulta, AB<sup>2</sup> + AC<sup>2</sup> = BD × BK + KL × KC</li> <li>Dahil BD = KL, BD × BK + KL × KC = BD(BK + KC) = BD × BC</li> <li>Samakatuwid, AB<sup>2</sup> + AC<sup>2</sup> = BC<sup>2</sup>, dahil parisukat ang CBDE.</li></ol> <p>Pinapatunayan ng katibayang ito na mahahanap sa <i>Mga Elemento</i> ni Euclid sa Panukalang 47 sa Ika-1 Aklat,<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> na ang dawak ng parisukat sa gilis ay ang kabuuan ng dawak ng dalawa pang parisukat.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>Kakaiba ito sa katibayan gamit ang magkahawig na tatsulok na ipinapalagay ay ang katibayan na ginamit ni Pitagoras.<sup id="cite_ref-Hawking_17-0" class="reference"><a href="#cite_note-Hawking-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Pythagoras_18-0" class="reference"><a href="#cite_note-Pythagoras-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Mga_katibayan_sa_panisnisan_at_pagbabago_ng_ayos">Mga katibayan sa panisnisan at pagbabago ng ayos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorema_ni_Pitagoras&veaction=edit&section=6" title="Baguhin seksiyon: Mga katibayan sa panisnisan at pagbabago ng ayos" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorema_ni_Pitagoras&action=edit&section=6" title="Edit section's source code: Mga katibayan sa panisnisan at pagbabago ng ayos"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Napag-usapan na natin ang katibayang Pitagoriko na isang katibayan sa pagbabago ng ayos. Ipinapayahag ang parehong ideya sa pinakakaliwang animasyon sa ibaba na binubuo ng isang malaking parisukat, panig <span class="nowrap"><i>a</i> + <i>b</i></span>, na naglalaman ng apat na magkaparehong sihang tadlong. Ipinapakita ang mga tatsulok sa dalawang pagsasaayos, ang una kung saan hindi natatakip ang dalawang parisukat na <i>a</i><sup>2</sup> at <i>b<sup>2</sup>,</i> at ang ikalawa kung saan hindi nakatakip ang parisukat na <i>c</i><sup>2</sup> . Hindi nagbabago ang dawak ng panlabas na parisukat, at magkapareho ang dawak ng apat na tatsulok sa simula at sa huli, kaya dapat magkatumbas ang mga dawak ng mga itim na parisukat, samakatuwid <span class="nowrap"><i>a</i><sup>2</sup> + <i>b</i><sup>2</sup> = <i>c</i><sup>2</sup>.</span> </p><p>Ibinibigay ng gitnang animasyon ang ikalawang katibayan sa pagbabago ng ayos. Nabubuo ang isang malaking parisukat na may dawak na <i>c<sup>2</sup></i> mula apat na magkaparehong tadlong sihang na may panig na <i>a</i>, <i>b</i> at <i>c</i>, na kinasya sa isang maliit na parisukat sa gitna. Pagkatapos, nabubuo ang dalawang parihaba na may panig na <i>a</i> at <i>b</i> sa pamamagitan ng paggalaw ng mga tatsulok. Kapag pinagsama ang mas maliit na parisukat sa mga parihaba, nabubuo ang dalawang parisukat na may dawak na <i>a</i><sup>2</sup> at <i>b<sup>2</sup></i>, na may parehong dawak dapat sa unang malaking parisukat.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>Mayroon ding katibayan ang ikaltong pinakakanang larawan. Nakahati ang mga dalawang parisukat sa itaas tulad ng ipinakita ng mga kulay bughaw at luntian na maaaring ikasya sa parisukat sa ibaba sa gilis – o pasalungat nito maaaring hatiin ang malaking parisuat tulad ng ipinapakita sa mga piraso na nagpupuno ng dalawa pang parisukat. Tinatawag na <a href="/w/index.php?title=Dissection_problem&action=edit&redlink=1" class="new" title="Dissection problem (hindi pa naisusulat)">panisnisan</a> ang ganitong paraan ng paghati sa isang pigura sa mga piraso at ayusin muli para matamo ang isa pang pigura. Ipinapakita nito na magkatumbas ang dawak ng malaking parisukat sa dawak ng dalawang mas maliit na parisukat.<sup id="cite_ref-specifics_20-0" class="reference"><a href="#cite_note-specifics-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <table> <tbody><tr> <td><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Pythag_anim.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/6/65/Pythag_anim.gif" decoding="async" width="200" height="200" class="mw-file-element" data-file-width="200" data-file-height="200" /></a><figcaption>Isang animasyon na nagpapakita ng katibayan sa pamamagitan ng apat na magkakaparehong tatsulok na may tadlong sihang</figcaption></figure> </td> <td><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Pythagoras-2a.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pythagoras-2a.gif/220px-Pythagoras-2a.gif" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pythagoras-2a.gif/330px-Pythagoras-2a.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Pythagoras-2a.gif/440px-Pythagoras-2a.gif 2x" data-file-width="590" data-file-height="590" /></a><figcaption>Isang animasyon na nagpapakita ng isa pang katibayan sa pamamagitan ng pagbabago ng ayos</figcaption></figure> </td> <td><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Pythagorean_theorem_rearrangement.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Pythagorean_theorem_rearrangement.svg/220px-Pythagorean_theorem_rearrangement.svg.png" decoding="async" width="220" height="230" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Pythagorean_theorem_rearrangement.svg/330px-Pythagorean_theorem_rearrangement.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Pythagorean_theorem_rearrangement.svg/440px-Pythagorean_theorem_rearrangement.svg.png 2x" data-file-width="512" data-file-height="536" /></a><figcaption>Isang katibayan gamit ang isang masalimuot na pag-iibang-ayos</figcaption></figure> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Mga_sanggunian">Mga sanggunian</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Teorema_ni_Pitagoras&veaction=edit&section=7" title="Baguhin seksiyon: Mga sanggunian" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Teorema_ni_Pitagoras&action=edit&section=7" title="Edit section's source code: Mga sanggunian"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r2121818">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Sally0-1"><span class="mw-cite-backlink"><a href="#cite_ref-Sally0_1-0">↑</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r2132731">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFJudith_D._SallyPaul_Sally2007" class="citation book cs1">Judith D. Sally; Paul Sally (2007). "Chapter 3: Pythagorean triples". <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nHxBw-WlECUC&pg=PA63"><i>Roots to research: a vertical development of mathematical problems</i></a>. American Mathematical Society Bookstore. p. 63. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/0-8218-4403-2" title="Natatangi:Mga pinagmulang aklat/0-8218-4403-2"><bdi>0-8218-4403-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+3%3A+Pythagorean+triples&rft.btitle=Roots+to+research%3A+a+vertical+development+of+mathematical+problems&rft.pages=63&rft.pub=American+Mathematical+Society+Bookstore&rft.date=2007&rft.isbn=0-8218-4403-2&rft.au=Judith+D.+Sally&rft.au=Paul+Sally&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DnHxBw-WlECUC%26pg%3DPA63&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-Pos2-2"><span class="mw-cite-backlink"><a href="#cite_ref-Pos2_2-0">↑</a></span> <span class="reference-text">Posamentier, Alfred. <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=fHFuCkSrfysC&pg=PA23">The Pythagorean Theorem: The Story of Its Power and Beauty</a></i>, p. 23 (Prometheus Books 2010).</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFO'ConnorRobertson2000" class="citation web cs1">O'Connor, J J; Robertson, E F (Disyembre 2000). <a rel="nofollow" class="external text" href="http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_Pythagoras.html">"Pythagoras's theorem in Babylonian mathematics"</a>. <i>School of Mathematics and Statistics</i>. University of St. Andrews, Scotland<span class="reference-accessdate">. Nakuha noong <span class="nowrap">25 Enero</span> 2017</span>. <q>In this article we examine four Babylonian tablets which all have some connection with Pythagoras's theorem. Certainly the Babylonians were familiar with Pythagoras's theorem.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=School+of+Mathematics+and+Statistics&rft.atitle=Pythagoras%27s+theorem+in+Babylonian+mathematics&rft.date=2000-12&rft.aulast=O%27Connor&rft.aufirst=J+J&rft.au=Robertson%2C+E+F&rft_id=http%3A%2F%2Fwww-history.mcs.st-and.ac.uk%2FHistTopics%2FBabylonian_Pythagoras.html&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_web" title="Padron:Cite web">cite web</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-Allman2-4"><span class="mw-cite-backlink"><a href="#cite_ref-Allman2_4-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFGeorge_Johnston_Allman1889" class="citation book cs1">George Johnston Allman (1889). <a rel="nofollow" class="external text" href="https://books.google.com/?id=-gYCAAAAYAAJ&pg=PA26"><i>Greek Geometry from Thales to Euclid</i></a> (ika-Reprinted by Kessinger Publishing LLC 2005 (na) edisyon). Hodges, Figgis, & Co. p. 26. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/1-4326-0662-X" title="Natatangi:Mga pinagmulang aklat/1-4326-0662-X"><bdi>1-4326-0662-X</bdi></a>. <q>The discovery of the law of three squares, commonly called the "theorem of Pythagoras" is attributed to him by – amongst others – Vitruvius, Diogenes Laertius, Proclus, and Plutarch ...</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Greek+Geometry+from+Thales+to+Euclid&rft.pages=26&rft.edition=Reprinted+by+Kessinger+Publishing+LLC+2005&rft.pub=Hodges%2C+Figgis%2C+%26+Co&rft.date=1889&rft.isbn=1-4326-0662-X&rft.au=George+Johnston+Allman&rft_id=https%3A%2F%2Fbooks.google.com%2F%3Fid%3D-gYCAAAAYAAJ%26pg%3DPA26&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-heath144-5"><span class="mw-cite-backlink"><a href="#cite_ref-heath144_5-0">↑</a></span> <span class="reference-text">(<a href="#CITEREFHeath1921">Heath 1921</a>, Vol I, p. 144)<span class="error harv-error" style="display: none; font-size:100%"> harv error: no target: CITEREFHeath1921 (<a href="/wiki/Kategorya:Harv_and_Sfn_template_errors" title="Kategorya:Harv and Sfn template errors">help</a>)</span>: "Though this is the proposition universally associated by tradition with the name of Pythagoras, no really trustworthy evidence exists that it was actually discovered by him. The comparatively late writers who attribute it to him add the story that he sacrificed an ox to celebrate his discovery."</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">According to <a href="#CITEREFHeath1921">Heath 1921</a>, Vol I, p. 147<span class="error harv-error" style="display: none; font-size:100%"> harv error: no target: CITEREFHeath1921 (<a href="/wiki/Kategorya:Harv_and_Sfn_template_errors" title="Kategorya:Harv and Sfn template errors">help</a>)</span>, Vitruvius says that Pythagoras first discovered the triangle (3,4,5); the fact that the latter is right-angled led to the theorem.</span> </li> <li id="cite_note-Neugebauer-7"><span class="mw-cite-backlink"><a href="#cite_ref-Neugebauer_7-0">↑</a></span> <span class="reference-text"><a href="#CITEREFNeugebauer1969">Neugebauer 1969</a>, p. 36<span class="error harv-error" style="display: none; font-size:100%"> harv error: no target: CITEREFNeugebauer1969 (<a href="/wiki/Kategorya:Harv_and_Sfn_template_errors" title="Kategorya:Harv and Sfn template errors">help</a>)</span>. For a different view, see <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFDick_Teresi2003" class="citation book cs1">Dick Teresi (2003). <a rel="nofollow" class="external text" href="https://books.google.com/?id=pheL_ubbXD0C&pg=PA52"><i>Lost Discoveries: The Ancient Roots of Modern Science</i></a>. Simon and Schuster. p. 52. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/0-7432-4379-X" title="Natatangi:Mga pinagmulang aklat/0-7432-4379-X"><bdi>0-7432-4379-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Lost+Discoveries%3A+The+Ancient+Roots+of+Modern+Science&rft.pages=52&rft.pub=Simon+and+Schuster&rft.date=2003&rft.isbn=0-7432-4379-X&rft.au=Dick+Teresi&rft_id=https%3A%2F%2Fbooks.google.com%2F%3Fid%3DpheL_ubbXD0C%26pg%3DPA52&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span>, where the speculation is made that the first column of <a href="/w/index.php?title=Plimpton_322&action=edit&redlink=1" class="new" title="Plimpton 322 (hindi pa naisusulat)">tablet 322 in the Plimpton collection</a> supports a Babylonian knowledge of some elements of trigonometry. That notion is pretty much laid to rest, however, by <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFEleanor_Robson2002" class="citation journal cs1">Eleanor Robson (2002). <a rel="nofollow" class="external text" href="https://archive.org/details/sim_american-mathematical-monthly_2002-02_109_2/page/105">"Words and Pictures: New Light on Plimpton 322"</a>. <i>The American Mathematical Monthly</i>. Mathematical Association of America. <b>109</b> (2): 105–120. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2695324">10.2307/2695324</a>. <a href="/w/index.php?title=JSTOR_(identifier)&action=edit&redlink=1" class="new" title="JSTOR (identifier) (hindi pa naisusulat)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2695324">2695324</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=Words+and+Pictures%3A+New+Light+on+Plimpton+322&rft.volume=109&rft.issue=2&rft.pages=105-120&rft.date=2002&rft_id=info%3Adoi%2F10.2307%2F2695324&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2695324%23id-name%3DJSTOR&rft.au=Eleanor+Robson&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_american-mathematical-monthly_2002-02_109_2%2Fpage%2F105&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_journal" title="Padron:Cite journal">cite journal</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Invalid <code class="cs1-code">|ref=harv</code> (<a href="https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_param_val" class="extiw" title="en:Help:CS1 errors">tulong</a>)</span><span class="cs1-maint citation-comment">CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span> (<a rel="nofollow" class="external text" href="http://www.dma.ulpgc.es/profesores/pacheco/Robson.pdf">pdf file</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130921054112/http://www.dma.ulpgc.es/profesores/pacheco/Robson.pdf">Naka-arkibo</a> 2013-09-21 sa <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.). The generally accepted view today is that the Babylonians had no awareness of trigonometric functions. See also <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFAbdulrahman_A._Abdulaziz2010" class="citation arxiv cs1">Abdulrahman A. Abdulaziz (2010). "The Plimpton 322 Tablet and the Babylonian Method of Generating Pythagorean Triples". <a href="/w/index.php?title=ArXiv_(identifier)&action=edit&redlink=1" class="new" title="ArXiv (identifier) (hindi pa naisusulat)">arXiv</a>:<span class="cs1-lock-free" title="Libreng maa-access"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1004.0025">1004.0025</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/math.HO">math.HO</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=The+Plimpton+322+Tablet+and+the+Babylonian+Method+of+Generating+Pythagorean+Triples&rft.date=2010&rft_id=info%3Aarxiv%2F1004.0025&rft.au=Abdulrahman+A.+Abdulaziz&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_arXiv" title="Padron:Cite arXiv">cite arXiv</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Invalid <code class="cs1-code">|ref=harv</code> (<a href="https://en.wikipedia.org/wiki/Help:CS1_errors#invalid_param_val" class="extiw" title="en:Help:CS1 errors">tulong</a>)</span><span class="cs1-maint citation-comment">CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span> §2, p. 7.</span> </li> <li id="cite_note-Livio-8"><span class="mw-cite-backlink"><a href="#cite_ref-Livio_8-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFMario_Livio2003" class="citation book cs1">Mario Livio (2003). <a rel="nofollow" class="external text" href="https://books.google.com/?id=bUARfgWRH14C&pg=PA25"><i>The golden ratio: the story of phi, the world's most astonishing number</i></a>. Random House, Inc. p. 25. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/0-7679-0816-3" title="Natatangi:Mga pinagmulang aklat/0-7679-0816-3"><bdi>0-7679-0816-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+golden+ratio%3A+the+story+of+phi%2C+the+world%27s+most+astonishing+number&rft.pages=25&rft.pub=Random+House%2C+Inc&rft.date=2003&rft.isbn=0-7679-0816-3&rft.au=Mario+Livio&rft_id=https%3A%2F%2Fbooks.google.com%2F%3Fid%3DbUARfgWRH14C%26pg%3DPA25&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text">Benson, Donald. <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=8_vbuzxrpfIC&pg=PA172">The Moment of Proof : Mathematical Epiphanies</a></i>, pp. 172–173 (Oxford University Press, 1999).</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text"><a href="#CITEREFEuclid1956">Euclid (1956)</a>, pp. 351–352</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><a href="#cite_ref-11">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFHuffman" class="citation encyclopaedia cs1">Huffman, Carl. <a rel="nofollow" class="external text" href="https://plato.stanford.edu/archives/win2018/entries/pythagoras/">"Pythagoras"</a>. Sa <a href="/w/index.php?title=Edward_N._Zalta&action=edit&redlink=1" class="new" title="Edward N. Zalta (hindi pa naisusulat)">Zalta, Edward N.</a> (pat.). <i>The Stanford Encyclopedia of Philosophy (Winter 2018 Edition)</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Pythagoras&rft.btitle=The+Stanford+Encyclopedia+of+Philosophy+%28Winter+2018+Edition%29&rft.aulast=Huffman&rft.aufirst=Carl&rft_id=https%3A%2F%2Fplato.stanford.edu%2Farchives%2Fwin2018%2Fentries%2Fpythagoras%2F&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span>, "It should now be clear that decisions about sources are crucial in addressing the question of whether Pythagoras was a mathematician and scientist. The view of Pythagoras’ cosmos sketched in the first five paragraphs of this section, according to which he was neither a mathematician nor a scientist, remains the consensus."</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text">(<a href="#CITEREFLoomis1968">Loomis 1968</a>)<span class="error harv-error" style="display: none; font-size:100%"> harv error: no target: CITEREFLoomis1968 (<a href="/wiki/Kategorya:Harv_and_Sfn_template_errors" title="Kategorya:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text">See for example <a rel="nofollow" class="external text" href="http://www.slu.edu/classes/maymk/GeoGebra/Pythagoras.html">Pythagorean theorem by shear mapping</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161014165156/http://www.slu.edu/classes/maymk/GeoGebra/Pythagoras.html">Naka-arkibo</a> 2016-10-14 sa <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>., Saint Louis University website Java applet</span> </li> <li id="cite_note-Gullberg-14"><span class="mw-cite-backlink"><a href="#cite_ref-Gullberg_14-0">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFJan_Gullberg1997" class="citation book cs1">Jan Gullberg (1997). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=E09fBi9StpQC&pg=PA435"><i>Mathematics: from the birth of numbers</i></a>. W. W. Norton & Company. p. 435. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/0-393-04002-X" title="Natatangi:Mga pinagmulang aklat/0-393-04002-X"><bdi>0-393-04002-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics%3A+from+the+birth+of+numbers&rft.pages=435&rft.pub=W.+W.+Norton+%26+Company&rft.date=1997&rft.isbn=0-393-04002-X&rft.au=Jan+Gullberg&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DE09fBi9StpQC%26pg%3DPA435&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus:text:1999.01.0085:book=1:proposition=47">Elements 1.47</a> by Euclid. Retrieved 19 December 2006.</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><a href="#cite_ref-16">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI47.html">Euclid's Elements, Book I, Proposition 47</a>: web page version using Java applets from <a rel="nofollow" class="external text" href="http://aleph0.clarku.edu/~djoyce/java/elements/elements.html">Euclid's Elements</a> by Prof. David E. Joyce, Clark University</span> </li> <li id="cite_note-Hawking-17"><span class="mw-cite-backlink"><a href="#cite_ref-Hawking_17-0">↑</a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFStephen_W._Hawking2005" class="citation book cs1">Stephen W. Hawking (2005). <a rel="nofollow" class="external text" href="https://books.google.com/?id=3zdFSOS3f4AC&pg=PA12"><i>God created the integers: the mathematical breakthroughs that changed history</i></a>. Philadelphia: Running Press Book Publishers. p. 12. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/0-7624-1922-9" title="Natatangi:Mga pinagmulang aklat/0-7624-1922-9"><bdi>0-7624-1922-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=God+created+the+integers%3A+the+mathematical+breakthroughs+that+changed+history&rft.place=Philadelphia&rft.pages=12&rft.pub=Running+Press+Book+Publishers&rft.date=2005&rft.isbn=0-7624-1922-9&rft.au=Stephen+W.+Hawking&rft_id=https%3A%2F%2Fbooks.google.com%2F%3Fid%3D3zdFSOS3f4AC%26pg%3DPA12&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_book" title="Padron:Cite book">cite book</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span> This proof first appeared after a computer program was set to check Euclidean proofs.</span> </li> <li id="cite_note-Pythagoras-18"><span class="mw-cite-backlink"><a href="#cite_ref-Pythagoras_18-0">↑</a></span> <span class="reference-text">The proof by Pythagoras probably was not a general one, as the theory of proportions was developed only two centuries after Pythagoras; see (<a href="#CITEREFMaor2007">Maor 2007</a>, p. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Z5VoBGy3AoAC&pg=PA25&hl=en#v=onepage&q&f=false">25</a>)<span class="error harv-error" style="display: none; font-size:100%"> harv error: no target: CITEREFMaor2007 (<a href="/wiki/Kategorya:Harv_and_Sfn_template_errors" title="Kategorya:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><a href="#cite_ref-19">↑</a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r2132731"><cite id="CITEREFAlexander_Bogomolny" class="citation web cs1"><a href="/w/index.php?title=Alexander_Bogomolny&action=edit&redlink=1" class="new" title="Alexander Bogomolny (hindi pa naisusulat)">Alexander Bogomolny</a>. <a rel="nofollow" class="external text" href="http://www.cut-the-knot.org/pythagoras/index.shtml#10">"Pythagorean theorem, proof number 10"</a>. <i>Cut the Knot</i><span class="reference-accessdate">. Nakuha noong <span class="nowrap">27 Pebrero</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Cut+the+Knot&rft.atitle=Pythagorean+theorem%2C+proof+number+10&rft.au=Alexander+Bogomolny&rft_id=http%3A%2F%2Fwww.cut-the-knot.org%2Fpythagoras%2Findex.shtml%2310&rfr_id=info%3Asid%2Ftl.wikipedia.org%3ATeorema+ni+Pitagoras" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Padron:Cite_web" title="Padron:Cite web">cite web</a>}}</code>: CS1 maint: date auto-translated (<a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">link</a>)</span></span> </li> <li id="cite_note-specifics-20"><span class="mw-cite-backlink"><a href="#cite_ref-specifics_20-0">↑</a></span> <span class="reference-text">(<a href="#CITEREFLoomis1968">Loomis 1968</a>, p. 113, Geometric proof 22 and Figure 123)<span class="error harv-error" style="display: none; font-size:100%"> harv error: no target: CITEREFLoomis1968 (<a href="/wiki/Kategorya:Harv_and_Sfn_template_errors" title="Kategorya:Harv and Sfn template errors">help</a>)</span></span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Kinuha sa "<a dir="ltr" href="https://tl.wikipedia.org/w/index.php?title=Teorema_ni_Pitagoras&oldid=2045276">https://tl.wikipedia.org/w/index.php?title=Teorema_ni_Pitagoras&oldid=2045276</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Natatangi:Mga_kategorya" title="Natatangi:Mga kategorya">Kategorya</a>: <ul><li><a href="/wiki/Kategorya:Heometriyang_Euclidean" title="Kategorya:Heometriyang Euclidean">Heometriyang Euclidean</a></li><li><a href="/wiki/Kategorya:Mga_ekwasyon" title="Kategorya:Mga ekwasyon">Mga ekwasyon</a></li><li><a href="/wiki/Kategorya:Pythagoras" title="Kategorya:Pythagoras">Pythagoras</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Mga nakatagong kategorya: <ul><li><a href="/wiki/Kategorya:CS1_maint:_date_auto-translated" title="Kategorya:CS1 maint: date auto-translated">CS1 maint: date auto-translated</a></li><li><a href="/wiki/Kategorya:Harv_and_Sfn_no-target_errors" title="Kategorya:Harv and Sfn no-target errors">Harv and Sfn no-target errors</a></li><li><a href="/wiki/Kategorya:CS1_errors:_invalid_parameter_value" title="Kategorya:CS1 errors: invalid parameter value">CS1 errors: invalid parameter value</a></li><li><a href="/wiki/Kategorya:Webarchive_template_wayback_links" title="Kategorya:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Kategorya:Mga_artikulong_naglalaman_ng_Kastila" title="Kategorya:Mga artikulong naglalaman ng Kastila">Mga artikulong naglalaman ng Kastila</a></li><li><a href="/wiki/Kategorya:Mga_artikulong_naglalaman_ng_Ingles" title="Kategorya:Mga artikulong naglalaman ng Ingles">Mga artikulong naglalaman ng Ingles</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Huling pagbabago: 18:31, 22 Setyembre 2023.</li> <li id="footer-info-copyright">Magagamit ang teksto sa ilalim ng <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Lisensyang Creative Commons Attribution/Share-Alike</a>; maaaring mailapat ang karagdagang termino. 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