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id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Pangunahing pagpipilian</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Pangunahing pagpipilian</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">ilipat sa gilid</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">itago</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Maglibot </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Unang_Pahina" title="Puntahan ang unang pahina [z]" accesskey="z"><span>Unang pahina</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Tingnan_ang_buod" title="Mga gabay sa pagbabasa ng laktaw-laktaw sa Wikipedia"><span>Mga nilalaman</span></a></li><li id="n-Napiling-nilalaman" class="mw-list-item"><a href="/wiki/Wikipedia:Mga_napiling_artikulo"><span>Napiling nilalaman</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Natatangi:Alin_man" title="Magpalabas ng kahit-anong artikulo [x]" accesskey="x"><span>Alinmang artikulo</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:Patungkol"><span>Patungkol sa Wikipedia</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Wikipedia:Kasalukuyang_pangyayari" title="Hanapin ang mga impormasyon tungkol sa mga kamakailang kaganapan"><span>Mga kaganapan</span></a></li> </ul> </div> </div> <div id="p-Pakikihalubilo" class="vector-menu mw-portlet mw-portlet-Pakikihalubilo" > <div class="vector-menu-heading"> Pakikihalubilo </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Puntahan_ng_pamayanan" title="Tungkol sa proyekto, ano ang maari mong gawin, at kung saan maari maghanap ng mga bagay"><span>Pamayanan</span></a></li><li id="n-Kapihan" class="mw-list-item"><a href="/wiki/Wikipedia:Kapihan"><span>Kapihan</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Natatangi:Mga_huling_binago" title="Tala ng mga huling pagbabago sa wiki. [r]" accesskey="r"><span>Mga huling binago</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="/wiki/Wikipedia:Makipag-ugnayan_sa_amin" title="Paano makokontak ang Wikipedia"><span>Makipag-ugnayan</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Wikipedia:Tulong" title="Ang lugar para maghanap ng tulong sa Wikipedia."><span>Tulong</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Unang_Pahina" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="Ang Malayang Ensiklopedya" src="/static/images/mobile/copyright/wikipedia-tagline-tl.svg" width="119" height="13" style="width: 7.4375em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Natatangi:Maghanap" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Maghanap sa Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Hanapin</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Maghanap sa Wikipedia" aria-label="Maghanap sa Wikipedia" autocapitalize="sentences" title="Maghanap sa Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Natatangi:Maghanap"> </div> <button class="cdx-button cdx-search-input__end-button">Hanapin</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Mga pansariling kagamitan"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Itsura"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Itsura" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Itsura</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_tl.wikipedia.org&uselang=tl" class=""><span>Donasyon</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Natatangi:Likhain_ang_kuwenta&returnto=Heometriya" title="Mas maganda kung gagawa ka ng account at magla-login; gayunpaman, hindi ka pinipilit gawin ito" class=""><span>Gumawa ng account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Natatangi:Paglagda_ng_tagagamit&returnto=Heometriya" title="Mas maganda kung magla-login ka; gayunpaman, hindi ka pinipilit gawin ito [o]" accesskey="o" class=""><span>Mag-login</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Marami pang pagpipilian" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Mga pansariling kagamitan" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Mga pansariling kagamitan</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_tl.wikipedia.org&uselang=tl"><span>Donasyon</span></a></li><li id="pt-contribute" class="mw-list-item"><a href="/wiki/Natatangi:Contribute"><span class="vector-icon mw-ui-icon-edit mw-ui-icon-wikimedia-edit"></span> <span>Mag-ambag</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Natatangi:Likhain_ang_kuwenta&returnto=Heometriya" title="Mas maganda kung gagawa ka ng account at magla-login; gayunpaman, hindi ka pinipilit gawin ito"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Gumawa ng account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Natatangi:Paglagda_ng_tagagamit&returnto=Heometriya" title="Mas maganda kung magla-login ka; gayunpaman, hindi ka pinipilit gawin ito [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Mag-login</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Mga pahina para sa naka-logout na mga patnugot o editor <a href="/wiki/Wikipedia:Maligayang_pagdating!" aria-label="Alamin pa ang tungkol sa pagpapatnugot"><span>alamin pa</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Natatangi:Usapan_ko" title="Usapang tungkol sa mga pagbabagong ginawa sa ip address na ito [n]" accesskey="n"><span>Usapan</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sayt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Mga nilalaman" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">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-Buod" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Buod"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Buod</span> </div> </a> <button aria-controls="toc-Buod-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 Buod</span> </button> <ul id="toc-Buod-sublist" class="vector-toc-list"> <li id="toc-Heometriyang_praktikal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_praktikal"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Heometriyang praktikal</span> </div> </a> <ul id="toc-Heometriyang_praktikal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heometriyang_aksiyomatiko" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_aksiyomatiko"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Heometriyang aksiyomatiko</span> </div> </a> <ul id="toc-Heometriyang_aksiyomatiko-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mga_konstruksiyong_heometriko" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mga_konstruksiyong_heometriko"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Mga konstruksiyong heometriko</span> </div> </a> <ul id="toc-Mga_konstruksiyong_heometriko-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mga_bilang_sa_heometriya" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mga_bilang_sa_heometriya"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Mga bilang sa heometriya</span> </div> </a> <ul id="toc-Mga_bilang_sa_heometriya-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heometriya_ng_posisyon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriya_ng_posisyon"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Heometriya ng posisyon</span> </div> </a> <ul id="toc-Heometriya_ng_posisyon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heometriyang_lagpas_kay_Euclid" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_lagpas_kay_Euclid"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Heometriyang lagpas kay Euclid</span> </div> </a> <ul id="toc-Heometriyang_lagpas_kay_Euclid-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dimensiyon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dimensiyon"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.7</span> <span>Dimensiyon</span> </div> </a> <ul id="toc-Dimensiyon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Simetriya" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Simetriya"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.8</span> <span>Simetriya</span> </div> </a> <ul id="toc-Simetriya-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Kontemporaryong_heometriya" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kontemporaryong_heometriya"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Kontemporaryong heometriya</span> </div> </a> <button aria-controls="toc-Kontemporaryong_heometriya-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 Kontemporaryong heometriya</span> </button> <ul id="toc-Kontemporaryong_heometriya-sublist" class="vector-toc-list"> <li id="toc-Heometriyang_Euclidyano" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_Euclidyano"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Heometriyang Euclidyano</span> </div> </a> <ul id="toc-Heometriyang_Euclidyano-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heometriyang_diperensiyal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometriyang_diperensiyal"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Heometriyang diperensiyal</span> </div> </a> <ul id="toc-Heometriyang_diperensiyal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Topolohiya_at_heometriya" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Topolohiya_at_heometriya"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Topolohiya at heometriya</span> </div> </a> <ul id="toc-Topolohiya_at_heometriya-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heometrikang_alhebraiko" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heometrikang_alhebraiko"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Heometrikang alhebraiko</span> </div> </a> <ul id="toc-Heometrikang_alhebraiko-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">3</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">Heometriya</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 179 (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-179" 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">179 (na) 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/Meetkunde" title="Meetkunde – Afrikaans" lang="af" hreflang="af" data-title="Meetkunde" 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/Geometrie" title="Geometrie – Alemannic" lang="gsw" hreflang="gsw" data-title="Geometrie" 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%8C%82%E1%8B%8E%E1%88%9C%E1%89%B5%E1%88%AA" title="ጂዎሜትሪ – Amharic" lang="am" hreflang="am" data-title="ጂዎሜትሪ" 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/Cheometr%C3%ADa" title="Cheometría – Aragonese" lang="an" hreflang="an" data-title="Cheometría" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="ज्यामिति – Angika" lang="anp" hreflang="anp" data-title="ज्यामिति" data-language-autonym="अंगिका" data-language-local-name="Angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%87%D9%86%D8%AF%D8%B3%D8%A9_%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A9" title="هندسة رياضية – Arabic" lang="ar" hreflang="ar" data-title="هندسة رياضية" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%AA%D8%B3%D8%B7%D8%A7%D8%B1" title="تسطار – Moroccan Arabic" lang="ary" hreflang="ary" data-title="تسطار" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%9C%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A6%BF" title="জ্যামিতি – Assamese" lang="as" hreflang="as" data-title="জ্যামিতি" 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/Xeometr%C3%ADa" title="Xeometría – Asturian" lang="ast" hreflang="ast" data-title="Xeometría" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/H%C9%99nd%C9%99s%C9%99" title="Həndəsə – Azerbaijani" lang="az" hreflang="az" data-title="Həndəsə" 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%87%D9%86%D8%AF%D8%B3%D9%87" title="هندسه – South Azerbaijani" lang="azb" hreflang="azb" data-title="هندسه" 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%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия – Bashkir" lang="ba" hreflang="ba" data-title="Геометрия" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Geuometr%C4%97j%C4%97" title="Geuometrėjė – Samogitian" lang="sgs" hreflang="sgs" data-title="Geuometrėjė" 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/Heometriya" title="Heometriya – Central Bikol" lang="bcl" hreflang="bcl" data-title="Heometriya" 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%93%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Геаметрыя – Belarusian" lang="be" hreflang="be" data-title="Геаметрыя" 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%93%D0%B5%D0%B0%D0%BC%D1%8D%D1%82%D1%80%D1%8B%D1%8F" title="Геамэтрыя – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Геамэтрыя" 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%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия – Bulgarian" lang="bg" hreflang="bg" data-title="Геометрия" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A5%89%E0%A4%AE%E0%A5%87%E0%A4%9F%E0%A5%8D%E0%A4%B0%E0%A5%80" title="ज्यॉमेट्री – Bhojpuri" lang="bh" hreflang="bh" data-title="ज्यॉमेट्री" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Jiometri" title="Jiometri – Bislama" lang="bi" hreflang="bi" data-title="Jiometri" data-language-autonym="Bislama" data-language-local-name="Bislama" class="interlanguage-link-target"><span>Bislama</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9C%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AE%E0%A6%BF%E0%A6%A4%E0%A6%BF" title="জ্যামিতি – Bangla" lang="bn" hreflang="bn" data-title="জ্যামিতি" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%91%E0%BD%96%E0%BE%B1%E0%BD%B2%E0%BD%96%E0%BD%A6%E0%BC%8B%E0%BD%A2%E0%BE%A9%E0%BD%B2%E0%BD%A6%E0%BC%8B%E0%BD%A2%E0%BD%B2%E0%BD%82%E0%BC%8B%E0%BD%94%E0%BC%8D" title="དབྱིབས་རྩིས་རིག་པ། – Tibetan" lang="bo" hreflang="bo" data-title="དབྱིབས་རྩིས་རིག་པ།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetan" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Mentoniezh" title="Mentoniezh – Breton" lang="br" hreflang="br" data-title="Mentoniezh" 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/Geometrija" title="Geometrija – Bosnian" lang="bs" hreflang="bs" data-title="Geometrija" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8" title="Геометри – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Геометри" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Geometria" title="Geometria – Catalan" lang="ca" hreflang="ca" data-title="Geometria" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-chr mw-list-item"><a href="https://chr.wikipedia.org/wiki/%E1%8F%97%E1%8F%8E%E1%8F%8D%E1%8F%97_%E1%8F%93%E1%8F%8D%E1%8F%93%E1%8F%85%E1%8F%85" title="ᏗᏎᏍᏗ ᏓᏍᏓᏅᏅ – Cherokee" lang="chr" hreflang="chr" data-title="ᏗᏎᏍᏗ ᏓᏍᏓᏅᏅ" data-language-autonym="ᏣᎳᎩ" data-language-local-name="Cherokee" class="interlanguage-link-target"><span>ᏣᎳᎩ</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A6%DB%95%D9%86%D8%AF%D8%A7%D8%B2%DB%95" title="ئەندازە – Central Kurdish" lang="ckb" hreflang="ckb" data-title="ئەندازە" 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/Geumitria" title="Geumitria – Corsican" lang="co" hreflang="co" data-title="Geumitria" data-language-autonym="Corsu" data-language-local-name="Corsican" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://cs.wikipedia.org/wiki/Geometrie" title="Geometrie – Czech" lang="cs" hreflang="cs" data-title="Geometrie" 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%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8" title="Геометри – Chuvash" lang="cv" hreflang="cv" data-title="Геометри" 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/Geometreg" title="Geometreg – Welsh" lang="cy" hreflang="cy" data-title="Geometreg" 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/Geometri" title="Geometri – Danish" lang="da" hreflang="da" data-title="Geometri" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Geometrie" title="Geometrie – German" lang="de" hreflang="de" data-title="Geometrie" 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/Geometri" title="Geometri – Zazaki" lang="diq" hreflang="diq" data-title="Geometri" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%93%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1" title="Γεωμετρία – Greek" lang="el" hreflang="el" data-title="Γεωμετρία" 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/Geometr%C3%AE" title="Geometrî – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Geometrî" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Geometry" title="Geometry – English" lang="en" hreflang="en" data-title="Geometry" data-language-autonym="English" data-language-local-name="English" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Geometrio" title="Geometrio – Esperanto" lang="eo" hreflang="eo" data-title="Geometrio" 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/Geometr%C3%ADa" title="Geometría – Spanish" lang="es" hreflang="es" data-title="Geometría" 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/Geomeetria" title="Geomeetria – Estonian" lang="et" hreflang="et" data-title="Geomeetria" 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/Geometria" title="Geometria – Basque" lang="eu" hreflang="eu" data-title="Geometria" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Geometria" title="Geometria – Extremaduran" lang="ext" hreflang="ext" data-title="Geometria" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D9%86%D8%AF%D8%B3%D9%87" title="هندسه – Persian" lang="fa" hreflang="fa" data-title="هندسه" 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/Geometria" title="Geometria – Finnish" lang="fi" hreflang="fi" data-title="Geometria" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Geomeetri%C3%A4" title="Geomeetriä – Võro" lang="vro" hreflang="vro" data-title="Geomeetriä" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Geometry" title="Geometry – Fijian" lang="fj" hreflang="fj" data-title="Geometry" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijian" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Geometri" title="Geometri – Faroese" lang="fo" hreflang="fo" data-title="Geometri" data-language-autonym="Føroyskt" data-language-local-name="Faroese" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/G%C3%A9om%C3%A9trie" title="Géométrie – French" lang="fr" hreflang="fr" data-title="Géométrie" 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/Geometrii" title="Geometrii – Northern Frisian" lang="frr" hreflang="frr" data-title="Geometrii" 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/Geoim%C3%A9adracht" title="Geoiméadracht – Irish" lang="ga" hreflang="ga" data-title="Geoiméadracht" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%B9%BE%E4%BD%95%E5%AD%B8" title="幾何學 – Gan" lang="gan" hreflang="gan" data-title="幾何學" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/J%C3%A9om%C3%A9tri" title="Jéométri – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Jéométri" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Geoimeatras" title="Geoimeatras – Scottish Gaelic" lang="gd" hreflang="gd" data-title="Geoimeatras" data-language-autonym="Gàidhlig" data-language-local-name="Scottish Gaelic" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Xeometr%C3%ADa" title="Xeometría – Galician" lang="gl" hreflang="gl" data-title="Xeometría" 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/Ysajarekokuaa" title="Ysajarekokuaa – Guarani" lang="gn" hreflang="gn" data-title="Ysajarekokuaa" 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%AD%E0%AB%82%E0%AA%AE%E0%AA%BF%E0%AA%A4%E0%AA%BF" title="ભૂમિતિ – Gujarati" lang="gu" hreflang="gu" data-title="ભૂમિતિ" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Towse-oaylleeaght" title="Towse-oaylleeaght – Manx" lang="gv" hreflang="gv" data-title="Towse-oaylleeaght" data-language-autonym="Gaelg" data-language-local-name="Manx" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/K%C3%AD-h%C3%B2-ho%CC%8Dk" title="Kí-hò-ho̍k – Hakka Chinese" lang="hak" hreflang="hak" data-title="Kí-hò-ho̍k" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94" title="גאומטריה – Hebrew" lang="he" hreflang="he" data-title="גאומטריה" 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%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="ज्यामिति – Hindi" lang="hi" hreflang="hi" data-title="ज्यामिति" 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/Geometry" title="Geometry – Fiji Hindi" lang="hif" hreflang="hif" data-title="Geometry" 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/Geometrija" title="Geometrija – Croatian" lang="hr" hreflang="hr" data-title="Geometrija" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Jewometri" title="Jewometri – Haitian Creole" lang="ht" hreflang="ht" data-title="Jewometri" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Geometria" title="Geometria – Hungarian" lang="hu" hreflang="hu" data-title="Geometria" 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/%D4%B5%D6%80%D5%AF%D6%80%D5%A1%D5%B9%D5%A1%D6%83%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Երկրաչափություն – Armenian" lang="hy" hreflang="hy" data-title="Երկրաչափություն" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia badge-Q17437796 badge-featuredarticle mw-list-item" title="mga napiling artikulo"><a href="https://ia.wikipedia.org/wiki/Geometria" title="Geometria – Interlingua" lang="ia" hreflang="ia" data-title="Geometria" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Geometri" title="Geometri – Indonesian" lang="id" hreflang="id" data-title="Geometri" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Geometrie" title="Geometrie – Interlingue" lang="ie" hreflang="ie" data-title="Geometrie" data-language-autonym="Interlingue" data-language-local-name="Interlingue" class="interlanguage-link-target"><span>Interlingue</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Heometria" title="Heometria – Iloko" lang="ilo" hreflang="ilo" data-title="Heometria" data-language-autonym="Ilokano" data-language-local-name="Iloko" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Geometrio" title="Geometrio – Ido" lang="io" hreflang="io" data-title="Geometrio" 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/R%C3%BAmfr%C3%A6%C3%B0i" title="Rúmfræði – Icelandic" lang="is" hreflang="is" data-title="Rúmfræði" 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/Geometria" title="Geometria – Italian" lang="it" hreflang="it" data-title="Geometria" 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/%E5%B9%BE%E4%BD%95%E5%AD%A6" title="幾何学 – Japanese" lang="ja" hreflang="ja" data-title="幾何学" 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-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Jaamichri" title="Jaamichri – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Jaamichri" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/G%C3%A9om%C3%A8tri" title="Géomètri – Javanese" lang="jv" hreflang="jv" data-title="Géomètri" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%92%E1%83%94%E1%83%9D%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98%E1%83%90" title="გეომეტრია – Georgian" lang="ka" hreflang="ka" data-title="გეომეტრია" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Geometriya" title="Geometriya – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Geometriya" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tanzeggit" title="Tanzeggit – Kabyle" lang="kab" hreflang="kab" data-title="Tanzeggit" 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%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D0%B5" title="Геометрие – Kabardian" lang="kbd" hreflang="kbd" data-title="Геометрие" data-language-autonym="Адыгэбзэ" data-language-local-name="Kabardian" class="interlanguage-link-target"><span>Адыгэбзэ</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/Sii%C5%8B_l%C9%A9z%CA%8A%CA%8A" title="Siiŋ lɩzʊʊ – Kabiye" lang="kbp" hreflang="kbp" data-title="Siiŋ lɩzʊʊ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/M%C5%A9thun%C5%A9r%C5%A9rio_(geometry)" title="Mũthunũrũrio (geometry) – Kikuyu" lang="ki" hreflang="ki" data-title="Mũthunũrũrio (geometry)" data-language-autonym="Gĩkũyũ" data-language-local-name="Kikuyu" class="interlanguage-link-target"><span>Gĩkũyũ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия – Kazakh" lang="kk" hreflang="kk" data-title="Геометрия" 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%92%E1%9E%9A%E1%9E%8E%E1%9E%B8%E1%9E%98%E1%9E%B6%E1%9E%8F%E1%9F%92%E1%9E%9A" title="ធរណីមាត្រ – Khmer" lang="km" hreflang="km" data-title="ធរណីមាត្រ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B0%E0%B3%87%E0%B2%96%E0%B2%BE%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ರೇಖಾಗಣಿತ – Kannada" lang="kn" hreflang="kn" data-title="ರೇಖಾಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B8%B0%ED%95%98%ED%95%99" title="기하학 – Korean" lang="ko" hreflang="ko" data-title="기하학" 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/Geometr%C3%AE" title="Geometrî – Kurdish" lang="ku" hreflang="ku" data-title="Geometrî" data-language-autonym="Kurdî" data-language-local-name="Kurdish" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Mynsonieth" title="Mynsonieth – Cornish" lang="kw" hreflang="kw" data-title="Mynsonieth" data-language-autonym="Kernowek" data-language-local-name="Cornish" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия – Kyrgyz" lang="ky" hreflang="ky" data-title="Геометрия" 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/Geometria" title="Geometria – Latin" lang="la" hreflang="la" data-title="Geometria" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Geometrie" title="Geometrie – Luxembourgish" lang="lb" hreflang="lb" data-title="Geometrie" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Jeometria" title="Jeometria – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Jeometria" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Essomampimo_(Geometry)" title="Essomampimo (Geometry) – Ganda" lang="lg" hreflang="lg" data-title="Essomampimo (Geometry)" data-language-autonym="Luganda" data-language-local-name="Ganda" class="interlanguage-link-target"><span>Luganda</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Maetk%C3%B3nde" title="Maetkónde – Limburgish" lang="li" hreflang="li" data-title="Maetkónde" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Geometria" title="Geometria – Ligurian" lang="lij" hreflang="lij" data-title="Geometria" data-language-autonym="Ligure" data-language-local-name="Ligurian" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Geometr%C3%ACa" title="Geometrìa – Lombard" lang="lmo" hreflang="lmo" data-title="Geometrìa" 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/Zom%C9%9Bt%C9%9Bl%C3%AD" title="Zomɛtɛlí – Lingala" lang="ln" hreflang="ln" data-title="Zomɛtɛlí" 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%BB%80%E0%BA%A5%E0%BA%82%E0%BA%B2%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94" title="ເລຂາຄະນິດ – Lao" lang="lo" hreflang="lo" data-title="ເລຂາຄະນິດ" 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/Geometrija" title="Geometrija – Lithuanian" lang="lt" hreflang="lt" data-title="Geometrija" 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/%C4%A2eometrija" title="Ģeometrija – Latvian" lang="lv" hreflang="lv" data-title="Ģeometrija" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D1%81%D1%8C" title="Геометриясь – Moksha" lang="mdf" hreflang="mdf" data-title="Геометриясь" data-language-autonym="Мокшень" data-language-local-name="Moksha" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Je%C3%B4metria" title="Jeômetria – Malagasy" lang="mg" hreflang="mg" data-title="Jeômetria" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D0%B9" title="Геометрий – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Геометрий" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Ilmu_ukua" title="Ilmu ukua – Minangkabau" lang="min" hreflang="min" data-title="Ilmu ukua" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Геометрија – Macedonian" lang="mk" hreflang="mk" data-title="Геометрија" 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%9C%E0%B5%8D%E0%B4%AF%E0%B4%BE%E0%B4%AE%E0%B4%BF%E0%B4%A4%E0%B4%BF" title="ജ്യാമിതി – Malayalam" lang="ml" hreflang="ml" data-title="ജ്യാമിതി" 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%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80" title="Геометр – Mongolian" lang="mn" hreflang="mn" data-title="Геометр" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mnw mw-list-item"><a href="https://mnw.wikipedia.org/wiki/%E1%80%82%E1%80%B1%E1%80%9E%E1%80%BC%E1%80%99%E1%80%B1%E1%80%90%E1%80%BC%E1%80%B3" title="ဂေသြမေတြဳ – Mon" lang="mnw" hreflang="mnw" data-title="ဂေသြမေတြဳ" data-language-autonym="ဘာသာမန်" data-language-local-name="Mon" class="interlanguage-link-target"><span>ဘာသာမန်</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AD%E0%A5%82%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A5%80" title="भूमिती – Marathi" lang="mr" hreflang="mr" data-title="भूमिती" 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/Geometri" title="Geometri – Malay" lang="ms" hreflang="ms" data-title="Geometri" 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-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/%C4%A0eometrija" title="Ġeometrija – Maltese" lang="mt" hreflang="mt" data-title="Ġeometrija" data-language-autonym="Malti" data-language-local-name="Maltese" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Geometrie" title="Geometrie – Mirandese" lang="mwl" hreflang="mwl" data-title="Geometrie" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%82%E1%80%BB%E1%80%AE%E1%80%A9%E1%80%99%E1%80%B1%E1%80%90%E1%80%BC%E1%80%AE" title="ဂျီဩမေတြီ – Burmese" lang="my" hreflang="my" data-title="ဂျီဩမေတြီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия – Erzya" lang="myv" hreflang="myv" data-title="Геометрия" data-language-autonym="Эрзянь" data-language-local-name="Erzya" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Geometrie" title="Geometrie – Low German" lang="nds" hreflang="nds" data-title="Geometrie" 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%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="ज्यामिति – Nepali" lang="ne" hreflang="ne" data-title="ज्यामिति" data-language-autonym="नेपाली" data-language-local-name="Nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B0%E0%A5%87%E0%A4%96%E0%A4%BE%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="रेखागणित – Newari" lang="new" hreflang="new" data-title="रेखागणित" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nia mw-list-item"><a href="https://nia.wikipedia.org/wiki/Geometris" title="Geometris – Nias" lang="nia" hreflang="nia" data-title="Geometris" data-language-autonym="Li Niha" data-language-local-name="Nias" class="interlanguage-link-target"><span>Li Niha</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Meetkunde" title="Meetkunde – Dutch" lang="nl" hreflang="nl" data-title="Meetkunde" 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/Geometri" title="Geometri – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Geometri" 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 mw-list-item"><a href="https://no.wikipedia.org/wiki/Geometri" title="Geometri – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Geometri" 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-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Geometria" title="Geometria – Novial" lang="nov" hreflang="nov" data-title="Geometria" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Geometria" title="Geometria – Occitan" lang="oc" hreflang="oc" data-title="Geometria" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Ji%27oomeetirii" title="Ji'oomeetirii – Oromo" lang="om" hreflang="om" data-title="Ji'oomeetirii" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%9C%E0%AD%8D%E0%AD%9F%E0%AC%BE%E0%AC%AE%E0%AC%BF%E0%AC%A4%E0%AC%BF" title="ଜ୍ୟାମିତି – Odia" lang="or" hreflang="or" data-title="ଜ୍ୟାମିତି" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B0%E0%A9%87%E0%A8%96%E0%A8%BE_%E0%A8%97%E0%A8%A3%E0%A8%BF%E0%A8%A4" title="ਰੇਖਾ ਗਣਿਤ – Punjabi" lang="pa" hreflang="pa" data-title="ਰੇਖਾ ਗਣਿਤ" 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/Geometria" title="Geometria – Polish" lang="pl" hreflang="pl" data-title="Geometria" 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/Geometr%C3%ACa" title="Geometrìa – Piedmontese" lang="pms" hreflang="pms" data-title="Geometrìa" 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/%D8%AC%DB%8C%D9%88%D9%85%DB%8C%D9%B9%D8%B1%DB%8C" title="جیومیٹری – Western Punjabi" lang="pnb" hreflang="pnb" data-title="جیومیٹری" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%85%DB%90%DA%86%D9%BE%D9%88%D9%87%D9%86%D9%87" title="مېچپوهنه – Pashto" lang="ps" hreflang="ps" data-title="مېچپوهنه" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Geometria" title="Geometria – Portuguese" lang="pt" hreflang="pt" data-title="Geometria" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Pacha_tupuy" title="Pacha tupuy – Quechua" lang="qu" hreflang="qu" data-title="Pacha tupuy" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Geometrie" title="Geometrie – Romanian" lang="ro" hreflang="ro" data-title="Geometrie" 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%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия – Russian" lang="ru" hreflang="ru" data-title="Геометрия" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D2%90%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F" title="Ґеометрія – Rusyn" lang="rue" hreflang="rue" data-title="Ґеометрія" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия – Yakut" lang="sah" hreflang="sah" data-title="Геометрия" 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-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Giometr%C3%ACa" title="Giometrìa – Sicilian" lang="scn" hreflang="scn" data-title="Giometrìa" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Geometry" title="Geometry – Scots" lang="sco" hreflang="sco" data-title="Geometry" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%AC%D8%A7%D9%85%D9%8A%D9%BD%D8%B1%D9%8A" title="جاميٽري – Sindhi" lang="sd" hreflang="sd" data-title="جاميٽري" data-language-autonym="سنڌي" data-language-local-name="Sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Geometrija" title="Geometrija – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Geometrija" 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-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/As%C9%A3kl" title="Asɣkl – Tachelhit" lang="shi" hreflang="shi" data-title="Asɣkl" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%A2%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B6%B8%E0%B7%92%E0%B6%AD%E0%B7%92%E0%B6%BA" title="ජ්‍යාමිතිය – Sinhala" lang="si" hreflang="si" data-title="ජ්‍යාමිතිය" 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/Geometry" title="Geometry – Simple English" lang="en-simple" hreflang="en-simple" data-title="Geometry" 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/Geometria" title="Geometria – Slovak" lang="sk" hreflang="sk" data-title="Geometria" 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/Geometrija" title="Geometrija – Slovenian" lang="sl" hreflang="sl" data-title="Geometrija" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-smn mw-list-item"><a href="https://smn.wikipedia.org/wiki/Geometria" title="Geometria – Inari Sami" lang="smn" hreflang="smn" data-title="Geometria" data-language-autonym="Anarâškielâ" data-language-local-name="Inari Sami" class="interlanguage-link-target"><span>Anarâškielâ</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Pimachisi" title="Pimachisi – Shona" lang="sn" hreflang="sn" data-title="Pimachisi" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Gjeometria" title="Gjeometria – Albanian" lang="sq" hreflang="sq" data-title="Gjeometria" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Геометрија – Serbian" lang="sr" hreflang="sr" data-title="Геометрија" 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-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Geometrie" title="Geometrie – Saterland Frisian" lang="stq" hreflang="stq" data-title="Geometrie" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/%C3%89lmu_ukur" title="Élmu ukur – Sundanese" lang="su" hreflang="su" data-title="Élmu ukur" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Geometri" title="Geometri – Swedish" lang="sv" hreflang="sv" data-title="Geometri" 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/Jiometri" title="Jiometri – Swahili" lang="sw" hreflang="sw" data-title="Jiometri" 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/Geometryjo" title="Geometryjo – Silesian" lang="szl" hreflang="szl" data-title="Geometryjo" 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%B5%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="வடிவவியல் – Tamil" lang="ta" hreflang="ta" data-title="வடிவவியல்" 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%B0%E0%B1%87%E0%B0%96%E0%B0%BE%E0%B0%97%E0%B0%A3%E0%B0%BF%E0%B0%A4%E0%B0%82" title="రేఖాగణితం – Telugu" lang="te" hreflang="te" data-title="రేఖాగణితం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D2%B2%D0%B0%D0%BD%D0%B4%D0%B0%D1%81%D0%B0" title="Ҳандаса – Tajik" lang="tg" hreflang="tg" data-title="Ҳандаса" data-language-autonym="Тоҷикӣ" data-language-local-name="Tajik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%A3%E0%B8%82%E0%B8%B2%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" title="เรขาคณิต – Thai" lang="th" hreflang="th" data-title="เรขาคณิต" 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/Geometri%C3%BDa" title="Geometriýa – Turkmen" lang="tk" hreflang="tk" data-title="Geometriýa" 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/Geometri" title="Geometri – Turkish" lang="tr" hreflang="tr" data-title="Geometri" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Tinhlayo-vupimi" title="Tinhlayo-vupimi – Tsonga" lang="ts" hreflang="ts" data-title="Tinhlayo-vupimi" data-language-autonym="Xitsonga" data-language-local-name="Tsonga" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия – Tatar" lang="tt" hreflang="tt" data-title="Геометрия" 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-tyv mw-list-item"><a href="https://tyv.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия – Tuvinian" lang="tyv" hreflang="tyv" data-title="Геометрия" data-language-autonym="Тыва дыл" data-language-local-name="Tuvinian" class="interlanguage-link-target"><span>Тыва дыл</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F" title="Геометрія – Ukrainian" lang="uk" hreflang="uk" data-title="Геометрія" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DB%81%D9%86%D8%AF%D8%B3%DB%81" title="ہندسہ – Urdu" lang="ur" hreflang="ur" data-title="ہندسہ" 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/Geometriya" title="Geometriya – Uzbek" lang="uz" hreflang="uz" data-title="Geometriya" 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-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Zeometria" title="Zeometria – Venetian" lang="vec" hreflang="vec" data-title="Zeometria" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Geometrii" title="Geometrii – Veps" lang="vep" hreflang="vep" data-title="Geometrii" 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 mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%ACnh_h%E1%BB%8Dc" title="Hình học – Vietnamese" lang="vi" hreflang="vi" data-title="Hình học" 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/Heyometriya" title="Heyometriya – Waray" lang="war" hreflang="war" data-title="Heyometriya" 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%87%A0%E4%BD%95%E5%AD%A6" title="几何学 – Wu" lang="wuu" hreflang="wuu" data-title="几何学" 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-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%92%E1%83%94%E1%83%9D%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98%E1%83%90" title="გეომეტრია – Mingrelian" lang="xmf" hreflang="xmf" data-title="გეომეტრია" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%92%D7%A2%D7%90%D7%9E%D7%A2%D7%98%D7%A8%D7%99%D7%A2" title="געאמעטריע – Yiddish" lang="yi" hreflang="yi" data-title="געאמעטריע" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-za mw-list-item"><a href="https://za.wikipedia.org/wiki/Gijhozyoz" title="Gijhozyoz – Zhuang" lang="za" hreflang="za" data-title="Gijhozyoz" data-language-autonym="Vahcuengh" data-language-local-name="Zhuang" class="interlanguage-link-target"><span>Vahcuengh</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%9C%E2%B4%B0%E2%B5%8F%E2%B5%A3%E2%B4%B3%E2%B4%B3%E2%B5%89%E2%B5%9C" title="ⵜⴰⵏⵣⴳⴳⵉⵜ – Standard Moroccan Tamazight" lang="zgh" hreflang="zgh" data-title="ⵜⴰⵏⵣⴳⴳⵉⵜ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="Standard Moroccan Tamazight" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%87%A0%E4%BD%95%E5%AD%A6" title="几何学 – Chinese" lang="zh" hreflang="zh" data-title="几何学" 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%B9%BE%E4%BD%95" title="幾何 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="幾何" 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/K%C3%AD-h%C3%B4-ha%CC%8Dk" title="Kí-hô-ha̍k – Minnan" lang="nan" hreflang="nan" data-title="Kí-hô-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%B9%BE%E4%BD%95%E5%AD%B8" title="幾何學 – Cantonese" lang="yue" hreflang="yue" data-title="幾何學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Umchazabukhulu" title="Umchazabukhulu – Zulu" lang="zu" hreflang="zu" data-title="Umchazabukhulu" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q8087#sitelinks-wikipedia" title="Baguhin ang link sa ibang wika" class="wbc-editpage">baguhin ang mga link</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div 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class="mw-content-ltr mw-parser-output" lang="tl" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Teorema_de_desargues.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Teorema_de_desargues.svg/250px-Teorema_de_desargues.svg.png" decoding="async" width="250" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Teorema_de_desargues.svg/375px-Teorema_de_desargues.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Teorema_de_desargues.svg/500px-Teorema_de_desargues.svg.png 2x" data-file-width="300" data-file-height="200" /></a><figcaption>Isang ilustrasyon ng <a href="/w/index.php?title=Teorema_ni_Desargues&action=edit&redlink=1" class="new" title="Teorema ni Desargues (hindi pa naisusulat)">teorema ni Desargues</a> na isang mahalagang resulta ng heometriyang <a href="/w/index.php?title=Heometriyang_Euclidean&action=edit&redlink=1" class="new" title="Heometriyang Euclidean (hindi pa naisusulat)">Euclidyano</a> at <a href="/w/index.php?title=Heometriyang_prohektibo&action=edit&redlink=1" class="new" title="Heometriyang prohektibo (hindi pa naisusulat)">prohektibo</a>.</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 class="mw-selflink selflink">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 collapsed" 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 href="/wiki/Teorema_ni_Pitagoras" title="Teorema ni Pitagoras">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 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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>Ang <b>heometriya</b> o <b>sukgisan</b> (<a href="/wiki/Wikang_Sinaunang_Griyego" title="Wikang Sinaunang Griyego">Sinaunang Griyego</a>: <span lang="grc">γεωμετρία</span>; <i><a href="https://tl.wiktionary.org/wiki/%CE%B3%E1%BF%86" class="extiw" title="wikt:γῆ">geo-</a></i> "daigdig", <i><a href="https://tl.wiktionary.org/wiki/%CE%BC%CE%AD%CF%84%CF%81%CE%BF%CE%BD" class="extiw" title="wikt:μέτρον">-metron</a></i> "pagsukat") ay isang sangay ng <a href="/wiki/Matematika" title="Matematika">matematika</a> na umuukol sa mga tanong ng <a href="/wiki/Hugis" title="Hugis">hugis</a>, <a href="/wiki/Sukat" title="Sukat">sukat</a>, relatibong posisyon ng mga pigura at mga katangian ng <a href="/w/index.php?title=Espasyo&action=edit&redlink=1" class="new" title="Espasyo (hindi pa naisusulat)">espasyo</a>. Ang isang matematiko na gumagawa sa larangan ng heometriya ay tinatawag na <i>heometro</i> (geometer). Ang heometriya ay lumitaw ng independiyente sa isang bilang ng mga sinaunang kultura bilang isang katawan ng praktikal na kaalaman na umuukol sa <a href="/wiki/Haba" title="Haba">haba</a> (length), mga <a href="/wiki/Area" class="mw-redirect" title="Area">area</a>, at mga <a href="/wiki/Bolyum" class="mw-redirect" title="Bolyum">bolyum</a> na ang mga elemento ng isang pormal na agham matematikal ay lumitaw sa Kanluran noong panahon ni <a href="/wiki/Thales" title="Thales">Thales</a> (ika-6 siglo BCE). Noong mga ika-3 siglo BCE, ang heometriya ay inilagay sa isang <a href="/w/index.php?title=Sistemang_aksiyomatiko&action=edit&redlink=1" class="new" title="Sistemang aksiyomatiko (hindi pa naisusulat)">anyong aksiyomatiko</a> ni <a href="/wiki/Euclid" class="mw-redirect" title="Euclid">Euclid</a> na ang pagtatrato na <a href="/w/index.php?title=Heometriyang_Euclidian&action=edit&redlink=1" class="new" title="Heometriyang Euclidian (hindi pa naisusulat)">heometriyang Euclidyano</a> ang nagtakda ng pamantayan para sa mga sumunod na siglo.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Si <a href="/wiki/Archimedes" class="mw-redirect" title="Archimedes">Archimedes</a> ay bumuo ng mga malikhaing pamamaraan para sa pagkukwenta ng mga area at bolyum na sa maraming paraan ay nakakita sa kalkulong <a href="/wiki/Integral" class="mw-redirect" title="Integral">integral</a>. Ang larangan ng <a href="/wiki/Astronomiya" title="Astronomiya">astronomiya</a> lalo na ang pagmamapa ng mga posisyon ng mga <a href="/wiki/Bituin" title="Bituin">bituin</a> at <a href="/wiki/Planeta" title="Planeta">planeta</a> sa sperong kalawakan at sa paglalarawan ng relasyon sa pagitan ng mga galaw ng mga katawang pangkalawakan ay nagsilbi bilang mahalagang pinagkunan ng mga problemang heometriko sa sumunod na isa at kalahating <a href="/wiki/Millenia" class="mw-redirect" title="Millenia">millenia</a>. Ang parehong heometriya at astronomiya ay isinaalang alang sa klasikong daigdig na bahagi ng <a href="/w/index.php?title=Quadrivium&action=edit&redlink=1" class="new" title="Quadrivium (hindi pa naisusulat)">Quadrivium</a> na isang pang-ilalim na mga sining liberal na itinuring na mahalagang madalubhasa ng isang malayang mamamayan. Ang pagpapakilala ng mga <a href="/wiki/Koordinado" class="mw-redirect" title="Koordinado">koordinado</a> ni <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> at ang sabay na mga pag-unlad ng <a href="/wiki/Alhebra" title="Alhebra">alhebra</a> ay nagmarka sa isang bagong yugto ng heometriya dahil ang mga pigurang heometriko gaya ng mga ng mga <a href="/w/index.php?title=Kurbang_plano&action=edit&redlink=1" class="new" title="Kurbang plano (hindi pa naisusulat)">kurbang plano</a> ay maaari na ngayong ikatawan ng <a href="/w/index.php?title=Heometriyang_analitiko&action=edit&redlink=1" class="new" title="Heometriyang analitiko (hindi pa naisusulat)">analitiko</a>. Ito ay gumampan ng isang mahalagang papel sa pag-ahon ng <a href="/w/index.php?title=Kalkulong_inpinetisimal&action=edit&redlink=1" class="new" title="Kalkulong inpinetisimal (hindi pa naisusulat)">kalkulong inpinetisimal</a> noong ika-17 siglo. Sa karagdagan, ang teoriya ng <a href="/w/index.php?title=Perspektibo&action=edit&redlink=1" class="new" title="Perspektibo (hindi pa naisusulat)">perspektibo</a> ay nagpakitang mayroon higit sa heometriya kesa lamang sa mga katangiang metriko ng mga pigura. Ang perspektibo ang pinagmulan ng <a href="/w/index.php?title=Heometriyang_prohektibo&action=edit&redlink=1" class="new" title="Heometriyang prohektibo (hindi pa naisusulat)">heometriyang prohektibo</a>. Ang paksa ng heomeriya ay karagdagang pinayaman ng pag-aaral ng mga likas na istraktura ng mga obhektong heometriko na nagmula kay <a href="/wiki/Euler" class="mw-redirect" title="Euler">Euler</a> at <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a> at tumungo sa pagkakalikha ng <a href="/wiki/Topolohiya" title="Topolohiya">topolohiya</a> at <a href="/wiki/Diperensiyal_na_heometriya" class="mw-redirect" title="Diperensiyal na heometriya">diperensiyal na heometriya</a>. Sa panahon ni Euclid, walang maliwanag na distinksiyon sa pagitan ng espasyong pisikal at espasyong heometrikal. Simula ika-19 siglo, ang pagkakatuklas ng <a href="/w/index.php?title=Heometriyang_hindi_Euclidean&action=edit&redlink=1" class="new" title="Heometriyang hindi Euclidean (hindi pa naisusulat)">heometriyang di-Euclidyano</a> na konsepto ng espasyo ay sumailalim sa isang radikal na transpormasyon at ang tanong ay lumitaw: <i>aling espasyong heometrikal ang mahusay na umaangkop sa espasyong pisikal?</i> Sa paglitaw ng matematikal pormal noong ika-20 siglo, ang <a href="/w/index.php?title=Espasyo&action=edit&redlink=1" class="new" title="Espasyo (hindi pa naisusulat)">espasyo</a>, <a href="/wiki/Punto_(heometriya)" title="Punto (heometriya)">punto</a>, <a href="/wiki/Guhit_(heometriya)" title="Guhit (heometriya)">linya</a> at <a href="/wiki/Plano_(heometriya)" title="Plano (heometriya)">plano</a> ay nawalan rin ng mga nilalamang intuitibo nito kaya ngayon ay kailangan nating itangi ang pagitan ng espasyong pisikal, mga espasyong heometrikal (kung saan ang espasyo, punto etc ay mayroon pa ring kahulugang intuitibo nito) at mga espasyong abstrakto. Ang kontemporaryong heometriya ay nagsaalang alang ng mga <a href="/wiki/Manipoldo" title="Manipoldo">manipoldo</a> na mga espasyong labis na mas abstrakto kesa sa <a href="/wiki/Espasyong_Euclidean" class="mw-redirect" title="Espasyong Euclidean">espasyong Euclidyano</a> na tanging pagtatantiyang katulad ng mga ito sa mga iskalang maliit. Ang mga espasyong ito ay maaaring pagkaloob ng karagdagang istrktura na ang halimbaw ay ang mga ugnayan sa pagitan ng heometriyang <a href="/w/index.php?title=Pseudo-Riemannian&action=edit&redlink=1" class="new" title="Pseudo-Riemannian (hindi pa naisusulat)">pseudo-Riemannian</a> at <a href="/wiki/Pangkalahatang_relatibidad" class="mw-redirect" title="Pangkalahatang relatibidad">pangkalahatang relatibidad</a>. Ang isa sa pinakabatang mga teoriya ng pisika na <a href="/w/index.php?title=Teoriya_ng_tali&action=edit&redlink=1" class="new" title="Teoriya ng tali (hindi pa naisusulat)">teoriya ng tali</a> ay labis na heometriko rin sa lasa. Bagaman ang kalikasang biswal ng heometriya ay gumagawa ritong inisyal na malalapitan kesa sa ibang mga bahagi ng matematika gaya ng <a href="/wiki/Alhebra" title="Alhebra">alhebra</a> o <a href="/wiki/Teoriya_ng_bilang" class="mw-redirect" title="Teoriya ng bilang">teoriya ng bilang</a>, ang wikang heometriko ay ginagamit rin sa kontekstrong malayo sa tradisyonal na probenansiyang Euclidyano (halimbawa sa <a href="/w/index.php?title=Heometriyang_praktal&action=edit&redlink=1" class="new" title="Heometriyang praktal (hindi pa naisusulat)">heometriyang praktal</a>) at <a href="/wiki/Heometriyang_alhebraiko" title="Heometriyang alhebraiko">heometriyang alhebraiko</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Buod">Buod</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=1" title="Baguhin seksiyon: Buod" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=1" title="Edit section's source code: Buod"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Chinese_pythagoras.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Chinese_pythagoras.jpg/300px-Chinese_pythagoras.jpg" decoding="async" width="300" height="164" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Chinese_pythagoras.jpg/450px-Chinese_pythagoras.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Chinese_pythagoras.jpg/600px-Chinese_pythagoras.jpg 2x" data-file-width="871" data-file-height="475" /></a><figcaption><a href="/w/index.php?title=Patunay_(matematika)&action=edit&redlink=1" class="new" title="Patunay (matematika) (hindi pa naisusulat)">Patunay</a> na biswal ng <a href="/wiki/Teoremang_Pythagorean" class="mw-redirect" title="Teoremang Pythagorean">teoremang Pythagorean</a> para sa tatsulok na (3, 4, 5) gaya ng sa <a href="/w/index.php?title=Chou_Pei_Suan_Ching&action=edit&redlink=1" class="new" title="Chou Pei Suan Ching (hindi pa naisusulat)">Chou Pei Suan Ching</a>.</figcaption></figure> <p>Ang itinalang pag-unlad ng heometriya ay sumasaklaw sa higit sa dalawang <a href="/wiki/Millenia" class="mw-redirect" title="Millenia">millenia</a>. Bahagyang nakapagtataka na ang mga persepsiyon kung ano ang bumubuo sa heometriya ay nag-ebolb sa loob ng mga panahon. </p> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_praktikal">Heometriyang praktikal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=2" title="Baguhin seksiyon: Heometriyang praktikal" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=2" title="Edit section's source code: Heometriyang praktikal"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang heometriya ay nagmula sa isang praktikal na agham na umuukol sa pagsu-survey, pagsukat, mga area at bolyum. Sa mga kilalang nagawa, ang isa ay makahahanap ng mga pormula para sa mga <a href="/wiki/Haba" title="Haba">haba</a>, <a href="/wiki/Area" class="mw-redirect" title="Area">area</a> at <a href="/wiki/Bolyum" class="mw-redirect" title="Bolyum">bolyum</a> gaya ng sa <a href="/wiki/Teoremang_Pythagorean" class="mw-redirect" title="Teoremang Pythagorean">teoremang Pythagorean</a>, <a href="/wiki/Sirkumperensiya" title="Sirkumperensiya">sirkumperensiya</a> at <a href="/w/index.php?title=Area_ng_disko&action=edit&redlink=1" class="new" title="Area ng disko (hindi pa naisusulat)">area ng disko</a>, area ng <a href="/wiki/Tatsulok" title="Tatsulok">tatsulok</a>, bolyum ng isang silindro, spero at pyramid. Ang isang paraan ng pagkukwenta ng ilang mga hindi makukuhang distansiya o taas ay batay sa pagkakapareho ng mga pigurang heometriko ay itinuro kay <a href="/wiki/Thales" title="Thales">Thales</a>. Ang pag-unlad ng astronomiya ay tumungo sa paglitaw ng <a href="/wiki/Trigonometriya" title="Trigonometriya">trigonometriya</a> at <a href="/w/index.php?title=Trigonometriyang_sperikal&action=edit&redlink=1" class="new" title="Trigonometriyang sperikal (hindi pa naisusulat)">trigonometriyang sperikal</a> kasama ng tumutulong na mga pamamaraang komputasyonal. </p> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_aksiyomatiko">Heometriyang aksiyomatiko</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=3" title="Baguhin seksiyon: Heometriyang aksiyomatiko" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=3" title="Edit section's source code: Heometriyang aksiyomatiko"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Parallel_postulate_en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Parallel_postulate_en.svg/220px-Parallel_postulate_en.svg.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Parallel_postulate_en.svg/330px-Parallel_postulate_en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Parallel_postulate_en.svg/440px-Parallel_postulate_en.svg.png 2x" data-file-width="800" data-file-height="600" /></a><figcaption>Isang ilustrasyon ng <a href="/w/index.php?title=Postuladong_parallelo&action=edit&redlink=1" class="new" title="Postuladong parallelo (hindi pa naisusulat)">postuladong parallelo</a> ni <a href="/wiki/Euclid" class="mw-redirect" title="Euclid">Euclid</a>.</figcaption></figure> <div role="note" class="hatnote navigation-not-searchable">Tingnan din: <a href="/w/index.php?title=Heometriyang_Euclidean&action=edit&redlink=1" class="new" title="Heometriyang Euclidean (hindi pa naisusulat)">Heometriyang Euclidean</a></div> <p>Si <a href="/wiki/Euclid" class="mw-redirect" title="Euclid">Euclid</a> ay kumuha ng isang mas abstraktong pakikitungo sa kanyang akdang <i><a href="/wiki/Mga_Elemento_ni_Euclid" class="mw-redirect" title="Mga Elemento ni Euclid">Mga Elemento</a></i> na isa sa pinakamaimpluwensiya <i>(influential)</i> na mga aklat na kailanman isinulat. Ipinakilala ni Euclid ang ilang mga <a href="/wiki/Aksiyoma" class="mw-disambig" title="Aksiyoma">aksiyoma</a> o mga <a href="/w/index.php?title=Postulado&action=edit&redlink=1" class="new" title="Postulado (hindi pa naisusulat)">postulado</a> na naghahayag ng pangunahin o ebidente sa sariling mga katangian ng mga punto, linya at plano. Siya ay nagpatuloy sa mahigpit na paghihinuha ng ibang mga katangian sa pamamagitan ng pangangatwirang matematikal. Ang natatanging katangian ng pakikitungo ni Euclid ay ang pagiging mahigpit nito at ito ay nakilala bilang heometriyang aksiyomatiko o <a href="/w/index.php?title=Heometriyang_sintetiko&action=edit&redlink=1" class="new" title="Heometriyang sintetiko (hindi pa naisusulat)">heometriyang sintetiko</a>. Sa simula nang ika-19 siglo, ang pagkakatuklas ng mga <a href="/w/index.php?title=Heometriyang_hindi_Euclidean&action=edit&redlink=1" class="new" title="Heometriyang hindi Euclidean (hindi pa naisusulat)">heometriyang di-Euclidyano</a> nina <a href="/w/index.php?title=Gauss&action=edit&redlink=1" class="new" title="Gauss (hindi pa naisusulat)">Gauss</a>, <a href="/w/index.php?title=Lobachevsky&action=edit&redlink=1" class="new" title="Lobachevsky (hindi pa naisusulat)">Lobachevsky</a>, <a href="/w/index.php?title=Bolyai&action=edit&redlink=1" class="new" title="Bolyai (hindi pa naisusulat)">Bolyai</a> at iba pa ay tumungo sa muling pagbuhay ng interes at noong ika-20 siglo, si <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a> ay gumamit ng pangangatwirang aksiyomatiko sa pagtatangka sa magbigay ng isang modernong saligan ng heometriya. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Geometry_Lessons.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Geometry_Lessons.jpg/220px-Geometry_Lessons.jpg" decoding="async" width="220" height="277" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Geometry_Lessons.jpg/330px-Geometry_Lessons.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Geometry_Lessons.jpg/440px-Geometry_Lessons.jpg 2x" data-file-width="4517" data-file-height="5692" /></a><figcaption>Mga aralin ng heometriya noong ika-20 siglo.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Mga_konstruksiyong_heometriko">Mga konstruksiyong heometriko</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=4" title="Baguhin seksiyon: Mga konstruksiyong heometriko" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=4" title="Edit section's source code: Mga konstruksiyong heometriko"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang mga klasikong heometro ay nagbigay ng espesyal na atensiyon sa pagtatayo ng mga obhektong heometriko na inilarawan sa ibang paraan. Sa klasiko, ang tanging mga instrumentong pinayagan sa mga konstruksiyong heometriko ang <a href="/w/index.php?title=Kompas&action=edit&redlink=1" class="new" title="Kompas (hindi pa naisusulat)">kompas</a> at <a href="/w/index.php?title=Ruler&action=edit&redlink=1" class="new" title="Ruler (hindi pa naisusulat)">ruler</a>. Gayundin, ang bawat konstruksiyon ay dapat kumpleto sa isang may hangganang bilang ng mga hakbang. Gayunpaman, ang ilang mga problema ay lumabas na mahirap o imposibleng malutas ng tanging mga paraang ito at ang mga malikhaing konstruksiyon gamit ang mga <a href="/wiki/Parabola" class="mw-redirect" title="Parabola">parabola</a> at iba pang mga kurba gayundin din ang mga kasangkapang mekanikal ay natagpuan. </p> <div class="mw-heading mw-heading3"><h3 id="Mga_bilang_sa_heometriya">Mga bilang sa heometriya</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=5" title="Baguhin seksiyon: Mga bilang sa heometriya" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=5" title="Edit section's source code: Mga bilang sa heometriya"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sa <a href="/wiki/Sinaunang_Gresya" title="Sinaunang Gresya">sinaunang Gresya</a>, ang <a href="/w/index.php?title=Mga_Pythagorran&action=edit&redlink=1" class="new" title="Mga Pythagorran (hindi pa naisusulat)">mga Pythagorran</a> ay nagsaalang alang ng papel ng mga bilang sa heometriya. Gayunpaman, ang pagkakatuklas ng mga <a href="/w/index.php?title=Komensurabilidad_(matematika)&action=edit&redlink=1" class="new" title="Komensurabilidad (matematika) (hindi pa naisusulat)">hindi komensurableng</a> mga haba na sumalungat sa kanilang mga pananaw pilosopikal ay gumawa sa kanilang lumisan sa mga abstraktong bilang at pumabor sa mga konkretong kantidad na heometriko gaya ng haba at area ng mga pigura. Ang mga bilang ay muling ipinakilala sa heometriya sa anyo ng mga <a href="/wiki/Koordinado" class="mw-redirect" title="Koordinado">koordinado</a> ni <a href="/w/index.php?title=Descartes&action=edit&redlink=1" class="new" title="Descartes (hindi pa naisusulat)">Descartes</a> na nakatanto na ang pag-aaral ng mga hugis heometriko ay maaaring tumulong sa representasyong alhebraiko ng mga ito at siyang pinangalanan ng <a href="/w/index.php?title=Planong_Cartesian&action=edit&redlink=1" class="new" title="Planong Cartesian (hindi pa naisusulat)">planong Cartesian</a>. Ang <a href="/w/index.php?title=Heometriyang_analitiko&action=edit&redlink=1" class="new" title="Heometriyang analitiko (hindi pa naisusulat)">heometriyang analitiko</a> ay naglalapat ng mga pamamaraan ng alhebra sa mga tanong na heometriko na karaniwan sa pamamagitan ng pag-uugnay ng mga kurbang heometriko at mga ekwasyong alhebraiko. Ang mga ideyang ito ay gumampan ng isang mahalagang papel sa pagpapaunlad ng <a href="/wiki/Kalkulo" class="mw-redirect" title="Kalkulo">kalkulo</a> noong ika-17 siglo at tumungo sa pagkakatuklas ng maraming mga bagong katangian ng mga kurbang plano. Ang modernong <a href="/wiki/Heometriyang_alhebraiko" title="Heometriyang alhebraiko">heometriyang alhebraiko</a> ay nagsasaalang alang ng parehong mga tanong sa isang malawak na mas abstraktong lebel. </p> <div class="mw-heading mw-heading3"><h3 id="Heometriya_ng_posisyon">Heometriya ng posisyon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=6" title="Baguhin seksiyon: Heometriya ng posisyon" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=6" title="Edit section's source code: Heometriya ng posisyon"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote navigation-not-searchable">Mga pangunahing artikulo: <a href="/w/index.php?title=Heometriyang_prohektibo&action=edit&redlink=1" class="new" title="Heometriyang prohektibo (hindi pa naisusulat)">Heometriyang prohektibo</a> at <a href="/wiki/Topolohiya" title="Topolohiya">Topolohiya</a></div> <p>Kahit sa mga sinaunang panahon, ang mga heometro ay nagsaalang alang ng mga tanong ng relatibong posisyon o relasyong pang-espasyo ng mga pigura at hugis na heometriko. Ang ilang mga halimbawa ay ibinigay ng mga naka inskriba at nakasirkumskribang mga bilog ng mga <a href="/wiki/Poligon" title="Poligon">poligon</a>, mga linyang bumabagtas at <a href="/wiki/Tangent" title="Tangent">tangent</a> sa mga <a href="/w/index.php?title=Seksiyong_koniko&action=edit&redlink=1" class="new" title="Seksiyong koniko (hindi pa naisusulat)">seksiyong koniko</a> at mga konpigurasyong Pappus at Menelaus ng mga punto at linya. Sa Gitnang mga Panahon, ang bago at mas komplikadong mga tanong ng uring ito ay isinaalang alang:<i>Ano ang maksimum na bilang ng mga spero na sabay na humihipo sa isang ibinigay na spero ng parehong radius</i>? (<a href="/w/index.php?title=Problemang_humahalik_na_bilang&action=edit&redlink=1" class="new" title="Problemang humahalik na bilang (hindi pa naisusulat)">problemang humahalik na bilang</a>) <i>Ano ang pinakasiksik na <a href="/w/index.php?title=Pagpapake_ng_spero&action=edit&redlink=1" class="new" title="Pagpapake ng spero (hindi pa naisusulat)">pagpapake ng spero</a> ng magkatumbas na sukat sa espasyo?</i> (<a href="/w/index.php?title=Konhekturang_Kepler&action=edit&redlink=1" class="new" title="Konhekturang Kepler (hindi pa naisusulat)">konhekturang Kepler</a>) Ang karamihan sa mga tanong na ito ay kinasasangkutan ng mga mahigpit na hugis heometrikal gaya ng mga linya o spero. Ang heometriyang <a href="/w/index.php?title=Heometriyang_prohektibo&action=edit&redlink=1" class="new" title="Heometriyang prohektibo (hindi pa naisusulat)">prohektibo</a>, <a href="/w/index.php?title=Heometriyang_konbeks&action=edit&redlink=1" class="new" title="Heometriyang konbeks (hindi pa naisusulat)">konbeks</a> at <a href="/wiki/Heometriyang_diskreto" class="mw-redirect" title="Heometriyang diskreto">diskreto</a> ang tatlong mga pang-ilalim na mga disiplina sa loob ng kasalukuyang heometriya na umuukol sa mga ito at mga kaugnay na tanong. Si <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> sa kanyang pag-aaral ng mga problema tulad ng <a href="/w/index.php?title=Mga_Pitong_Tulay_ng_K%C3%B6nigsberg&action=edit&redlink=1" class="new" title="Mga Pitong Tulay ng Königsberg (hindi pa naisusulat)">Mga Pitong Tulay ng Königsberg</a> ay nagsaalang alang ng pinaka pundamental na mga katangian ng mga pigurang heometrika na batay lamang sa hugis na hindi nakasalalay sa mga katangiang metriko ng mga ito. Tinawag ni Euler ang bagong sangay na ito ng heometriya na <i>geometria situs</i> (heometriya ng lugar) na kilala na ngayon bilang <a href="/w/index.php?title=Topolihiya&action=edit&redlink=1" class="new" title="Topolihiya (hindi pa naisusulat)">topolihiya</a>. Ito ay hindi nagtatangi sa pagitan ng mga obheto na maaaring tuloy tuloy na ideporma sa bawat isa. Gayunpaman, ang mga obhekto ay nagpapanatili ng ilang heometriya gaya ng sa kaso ng mga <a href="/w/index.php?title=Buhol_na_hiperboliko&action=edit&redlink=1" class="new" title="Buhol na hiperboliko (hindi pa naisusulat)">buhol na hiperboliko</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_lagpas_kay_Euclid">Heometriyang lagpas kay Euclid</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=7" title="Baguhin seksiyon: Heometriyang lagpas kay Euclid" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=7" title="Edit section's source code: Heometriyang lagpas kay Euclid"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Hyperbolic_triangle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Hyperbolic_triangle.svg/220px-Hyperbolic_triangle.svg.png" decoding="async" width="220" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Hyperbolic_triangle.svg/330px-Hyperbolic_triangle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/89/Hyperbolic_triangle.svg/440px-Hyperbolic_triangle.svg.png 2x" data-file-width="809" data-file-height="559" /></a><figcaption>Ang <a href="/wiki/Diperensiyal_na_heometriya" class="mw-redirect" title="Diperensiyal na heometriya">diperensiyal na heometriya</a> ay gumagamit ng mga kasangkapan mula sa <a href="/wiki/Kalkulo" class="mw-redirect" title="Kalkulo">kalkulo</a> upang pag-aralan ang mga problema sa heometriya.</figcaption></figure> <p>Sa halos mga dalawang libong taon mula kay Euclid, bagaman ang saklaw ng mga tanong heometrikal na itinanong at sinagot ay hindi maiiwasang lumawig, ang basikong pagkaunawa ng espasyo ay nanatiling likas na pareho. Si <a href="/wiki/Immanuel_Kant" title="Immanuel Kant">Immanuel Kant</a> ay nangatwirang may isa lamang absolutong heometriya na alam na totoong <a href="/w/index.php?title=A_prior&action=edit&redlink=1" class="new" title="A prior (hindi pa naisusulat)">a prior</a> ng isang panloob na pakultad ng isip: ang heometriyang Euclidyano ay sintetiko a prior.<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> Ang nananaig na pananaw na ito ay pinataob ng rebolusyonaryong pagkakatuklas ng <a href="/w/index.php?title=Heometriyang_hindi_Euclidean&action=edit&redlink=1" class="new" title="Heometriyang hindi Euclidean (hindi pa naisusulat)">heometriyang hindi Euclidyano</a> sa mga akda ni <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a> (na hindi kailanman naglimbag ng kanyang teoriya) gayundin nina <a href="/w/index.php?title=Bolyai&action=edit&redlink=1" class="new" title="Bolyai (hindi pa naisusulat)">Bolyai</a> at <a href="/w/index.php?title=Lobachevsky&action=edit&redlink=1" class="new" title="Lobachevsky (hindi pa naisusulat)">Lobachevsky</a> na nagpakitang ang ordinaryong <a href="/wiki/Espasyong_Euclidean" class="mw-redirect" title="Espasyong Euclidean">espasyong Euclidyano</a> ang tanging isang posibilidad para sa pag-unlad ng heometriya. Ang isang malawak na pangitain ng paksa ng heometriya ay inihayag ni <a href="/w/index.php?title=Riemann&action=edit&redlink=1" class="new" title="Riemann (hindi pa naisusulat)">Riemann</a> sa kanyang inaugurasyong pagtuturo noong 1867 na <i>Über die Hypothesen, welche der Geometrie zu Grunde liegen</i> (Tungkol sa mga hipotesis kung saan ang heometriyay nakabatay)<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> na inilimbag lamang pagkatapos ng kanyang kamatayan. Ang bagong ideya ni Riemann ng espasyo ay napatunayang mahalaga sa <a href="/wiki/Pangkalahatang_relatibidad" class="mw-redirect" title="Pangkalahatang relatibidad">pangkalahatang relatibidad</a> ni <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> at ang <a href="/wiki/Heometriyang_Riemannian" class="mw-redirect" title="Heometriyang Riemannian">heometriyang Riemannian</a> na nagsasaalang alang ng labis na pangkalahatang mga espasyo kung saan ang nosyon ng haba ay inilalarawan ay saligan ng modernong heometriya. </p> <div class="mw-heading mw-heading3"><h3 id="Dimensiyon">Dimensiyon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=8" title="Baguhin seksiyon: Dimensiyon" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=8" title="Edit section's source code: Dimensiyon"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kung saan ang tradisyonal na heometriya ay pumapayag sa mga dimensiyong 1 (isang <a href="/wiki/Linya" class="mw-redirect mw-disambig" title="Linya">linya</a>), 2 (isang <a href="/wiki/Plano" class="mw-disambig" title="Plano">plano</a>) at 3 (ating daigdig na naunawaan bilang <a href="/wiki/Tatlong_dimensiyonal" class="mw-redirect" title="Tatlong dimensiyonal">tatlong dimensiyonal</a> na espasyo), ang mga matematiko ay gumamit ng mga <a href="/w/index.php?title=Mas_mataas_na_dimensiyon&action=edit&redlink=1" class="new" title="Mas mataas na dimensiyon (hindi pa naisusulat)">mas mataas na dimensiyon</a> sa loob ng halos 200 siglo. Ang dimensiyon ay sumailalim sa mga yugto ng pagiging anumang <a href="/wiki/Natural_na_bilang" class="mw-redirect" title="Natural na bilang">natural na bilang</a> na <i>n</i> na posibleng walang hangganan sa pagpapakilala ng <a href="/wiki/Espasyong_Hilbert" title="Espasyong Hilbert">espasyong Hilbert</a> at anumang positibong real na bilang sa <a href="/w/index.php?title=Heometriyang_praktal&action=edit&redlink=1" class="new" title="Heometriyang praktal (hindi pa naisusulat)">heometriyang praktal</a>. Ang <a href="/w/index.php?title=Teoriyang_dimensiyon&action=edit&redlink=1" class="new" title="Teoriyang dimensiyon (hindi pa naisusulat)">teoriyang dimensiyon</a> ay isang ideyang teknikal na sa simula ay sa loob ng <a href="/w/index.php?title=Pangkalahatang_topolohiya&action=edit&redlink=1" class="new" title="Pangkalahatang topolohiya (hindi pa naisusulat)">pangkalahatang topolohiya</a> na tumatalakay sa mga depinisyon. Sang ayon sa karamihang mga ideyang matematikal, ang dimensiyon ay inilalarawan na ngayon imbis na isang intuisyon. Ang konektadong mga <a href="/w/index.php?title=Manipoldong_topolohikal&action=edit&redlink=1" class="new" title="Manipoldong topolohikal (hindi pa naisusulat)">manipoldong topolohikal</a> ay may isang mahusay na nilalarawang dimensiyon. Ito ang teorema ng <a href="/w/index.php?title=Inbariansa_ng_sakop&action=edit&redlink=1" class="new" title="Inbariansa ng sakop (hindi pa naisusulat)">inbariansa ng sakop</a> kesa sa anumang <i>a priori</i>. Ang isyu ng dimensiyon ay mahalaga pa rin sa heometriya sa kawalan ng mga kompletong sagot sa mga klasikong tanong. Ang mga dimensiyong 3 ng espasyo at 4 ng <a href="/wiki/Espasyo-panahon" title="Espasyo-panahon">espasyo-panahon</a> ay mga espesyal na kaso sa <a href="/w/index.php?title=Topolohiyang_heometriko&action=edit&redlink=1" class="new" title="Topolohiyang heometriko (hindi pa naisusulat)">topolohiyang heometriko</a>. Ang dimensiyong 10 o 11 ay isang mahalagang bilang sa <a href="/w/index.php?title=Teoriya_ng_tali&action=edit&redlink=1" class="new" title="Teoriya ng tali (hindi pa naisusulat)">teoriya ng tali</a>. Ang pagsasaliksik ay maaaring magdala ng isang nakasasapat na dahilang heometriko para sa kahalagahan mga dimensiyong 10 o 11. </p> <div class="mw-heading mw-heading3"><h3 id="Simetriya">Simetriya</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=9" title="Baguhin seksiyon: Simetriya" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=9" title="Edit section's source code: Simetriya"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Order-3_heptakis_heptagonal_tiling.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Order-3_heptakis_heptagonal_tiling.png/220px-Order-3_heptakis_heptagonal_tiling.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Order-3_heptakis_heptagonal_tiling.png/330px-Order-3_heptakis_heptagonal_tiling.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Order-3_heptakis_heptagonal_tiling.png/440px-Order-3_heptakis_heptagonal_tiling.png 2x" data-file-width="800" data-file-height="800" /></a><figcaption>Isang <a href="/w/index.php?title=Order-3_na_bisektadong_tiling&action=edit&redlink=1" class="new" title="Order-3 na bisektadong tiling (hindi pa naisusulat)">tiling</a> ng <a href="/w/index.php?title=Heometriyang_hiperboliko&action=edit&redlink=1" class="new" title="Heometriyang hiperboliko (hindi pa naisusulat)">planong hiperboliko</a>.</figcaption></figure> <p>Ang tema ng <a href="/wiki/Simetriya" title="Simetriya">simetriya</a> sa heometriya ay halos kasing tanda ng mismong agham ng heometriya. Ang mga hugis simetriko gaya ng <a href="/wiki/Bilog" title="Bilog">bilog</a>, mga <a href="/wiki/Regular_na_poligon" title="Regular na poligon">regular na poligon</a> at mga <a href="/w/index.php?title=Solidong_platoniko&action=edit&redlink=1" class="new" title="Solidong platoniko (hindi pa naisusulat)">solidong platoniko</a> ay humawak ng malalim na kahalagahan para sa maraming mga sinaunang pilosopo at inimbestighan sa detalye bago ang panahon ni Euclid. Ang mga paternong simetriko ay nangyayari sa kalikasan at artistikong iginuhit sa maraming mga anyo kabilang ang mga grapika ni <a href="/w/index.php?title=M._C._Escher&action=edit&redlink=1" class="new" title="M. C. Escher (hindi pa naisusulat)">M. C. Escher</a>. Gayunpaman, hanggang sa ikalawang kalahati ng ika-19 siglo lamang nang ang nagpapaisang papel ng simetriya sa mga pundasyon ng heometriya ay nakilala. Ang <a href="/w/index.php?title=Programang_Erlangen&action=edit&redlink=1" class="new" title="Programang Erlangen (hindi pa naisusulat)">programang Erlangen</a> ni <a href="/wiki/Felix_Klein" title="Felix Klein">Felix Klein</a> ay naghayag na sa isang napaka tumpak na kahulugan, ang simetriya na inihayag sa pamamagitan ng nosyon ng isang transpormasyong <a href="/wiki/Grupo_(matematika)" title="Grupo (matematika)">grupo</a> ay tumutukoy sa kung ano ang heometriya. Ang simetriya sa klasikong <a href="/w/index.php?title=Heometriyang_Euclidean&action=edit&redlink=1" class="new" title="Heometriyang Euclidean (hindi pa naisusulat)">heometriyang Euclidyano</a> ay kinakatawan ng mga <a href="/w/index.php?title=Kongruensa_(heometriya)&action=edit&redlink=1" class="new" title="Kongruensa (heometriya) (hindi pa naisusulat)">kongruensa</a> at mga matibay na mosyon samantalang ang <a href="/w/index.php?title=Heometriyang_prohektibo&action=edit&redlink=1" class="new" title="Heometriyang prohektibo (hindi pa naisusulat)">heometriyang prohektibo</a> na analogosong papel na ginamapanan ng mga <a href="/w/index.php?title=Kolineayasyon&action=edit&redlink=1" class="new" title="Kolineayasyon (hindi pa naisusulat)">kolineayasyon</a> na mga transpormasyong heometriko na kumukuha ng mga linyang tuwid. Gayunpaman, sa mga bagong heometriya nina Bolyai at Lobachevsky, Riemann, <a href="/w/index.php?title=William_Kingdon_Clifford&action=edit&redlink=1" class="new" title="William Kingdon Clifford (hindi pa naisusulat)">Clifford</a> at Klein, at <a href="/w/index.php?title=Sophus_Lie&action=edit&redlink=1" class="new" title="Sophus Lie (hindi pa naisusulat)">Sophus Lie</a> na ang ideya ni Klein upang ilarawan ang heometriya sa pamaamgitan ng mga <a href="/w/index.php?title=Grupong_simetriya&action=edit&redlink=1" class="new" title="Grupong simetriya (hindi pa naisusulat)">grupong simetriya</a> nito ay napatunayang napakamaimpluwensiya <i>(influential)</i>. Ang parehong mga simetriyang diskreto at tuloy tuloy ay gumagampan ng mga papel sa heometriya, ang una ay sa <a href="/wiki/Topolohiya" title="Topolohiya">topolohiya</a> at <a href="/w/index.php?title=Teoriyang_grupong_heometriko&action=edit&redlink=1" class="new" title="Teoriyang grupong heometriko (hindi pa naisusulat)">teoriyang grupong heometriko</a> at ang huli ay sa <a href="/wiki/Teoriyang_Lie" class="mw-redirect" title="Teoriyang Lie">teoriyang Lie</a> at <a href="/wiki/Heometriyang_Riemannian" class="mw-redirect" title="Heometriyang Riemannian">heometriyang Riemannian</a>. Ang isang ibang uri ng simetriya ang prinsipyo ng dualidad sa <a href="/w/index.php?title=Heometriyang_prohektibo&action=edit&redlink=1" class="new" title="Heometriyang prohektibo (hindi pa naisusulat)">heometriyang prohektibo</a> kasama ng ibang mga larangan. Ang meta-phenomenon na ito ay halos mailalarawan bilang sumusunod: sa anumang teorema, ipalit ang <i>punto</i> sa <i>plano</i>, <i>pagsanib</i> sa <i>pagtatagpo</i>, <i>nasa</i> sa <i>naglalaman</i> at ikaw ay makakakuha ng magkatumbas na totoong teorema. Ang isang katulad at malapit na kaugnay na anyo ng dualidad ay umiiral sa pagitan ng isang <a href="/wiki/Espasyong_bektor" title="Espasyong bektor">espasyong bektor</a> at espasyong dual nito. </p> <div class="mw-heading mw-heading2"><h2 id="Kontemporaryong_heometriya">Kontemporaryong heometriya</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=10" title="Baguhin seksiyon: Kontemporaryong heometriya" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=10" title="Edit section's source code: Kontemporaryong heometriya"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_Euclidyano">Heometriyang Euclidyano</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=11" title="Baguhin seksiyon: Heometriyang Euclidyano" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=11" title="Edit section's source code: Heometriyang Euclidyano"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:E8Petrie.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/120px-E8Petrie.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/180px-E8Petrie.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/E8Petrie.svg/240px-E8Petrie.svg.png 2x" data-file-width="512" data-file-height="514" /></a><figcaption>Ang <a href="/w/index.php?title=4_21_politopo&action=edit&redlink=1" class="new" title="4 21 politopo (hindi pa naisusulat)">4<sub>21</sub>politopo</a> na ortogonal na minapa sa <a href="/w/index.php?title=E8_(matematika)&action=edit&redlink=1" class="new" title="E8 (matematika) (hindi pa naisusulat)">E<sub>8</sub></a> <a href="/w/index.php?title=Grupong_Lie&action=edit&redlink=1" class="new" title="Grupong Lie (hindi pa naisusulat)">grupong Lie</a> <a href="/w/index.php?title=Planong_Coxeter&action=edit&redlink=1" class="new" title="Planong Coxeter (hindi pa naisusulat)">planong Coxeter</a></figcaption></figure> <p>Ang heometriyang Euclidyano ay naging malapit na kaugnay ng <a href="/w/index.php?title=Heometriyang_komputasyonal&action=edit&redlink=1" class="new" title="Heometriyang komputasyonal (hindi pa naisusulat)">heometriyang komputasyonal</a>, <a href="/w/index.php?title=Grapikang_kompyuter&action=edit&redlink=1" class="new" title="Grapikang kompyuter (hindi pa naisusulat)">grapikang kompyuter</a>, <a href="/w/index.php?title=Heometriyang_konbeks&action=edit&redlink=1" class="new" title="Heometriyang konbeks (hindi pa naisusulat)">heometriyang konbeks</a>, <a href="/wiki/Heometriyang_diskreto" class="mw-redirect" title="Heometriyang diskreto">heometriyang diskreto</a> at ilang mga sakop ng <a href="/wiki/Kombinatorika" title="Kombinatorika">kombinatorika</a>. Ang momentum ay ibinigay sa karagdagang akda sa heometriyang Euclidyano at ang mga grupong Euclidyano ng <a href="/wiki/Kristalograpiya" class="mw-redirect" title="Kristalograpiya">kristalograpiya</a> at sa akda ni <a href="/w/index.php?title=H._S._M._Coxeter&action=edit&redlink=1" class="new" title="H. S. M. Coxeter (hindi pa naisusulat)">H. S. M. Coxeter</a> at maaaring makita sa mga teoriya ng nga <a href="/w/index.php?title=Grupong_Coxeter&action=edit&redlink=1" class="new" title="Grupong Coxeter (hindi pa naisusulat)">grupong Coxeter</a> at mga politopo. Ang <a href="/w/index.php?title=Teoriyang_grupong_heometriko&action=edit&redlink=1" class="new" title="Teoriyang grupong heometriko (hindi pa naisusulat)">teoriyang grupong heometriko</a> ay isang lumalawig na sakop ng teoriya ng mas pangkalahatang mga <a href="/w/index.php?title=Grupong_diskreto&action=edit&redlink=1" class="new" title="Grupong diskreto (hindi pa naisusulat)">grupong diskreto</a> na humahango sa mga modelong heometriko at mga pamamaraang alhebraiko. </p> <div class="mw-heading mw-heading3"><h3 id="Heometriyang_diperensiyal">Heometriyang diperensiyal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=12" title="Baguhin seksiyon: Heometriyang diperensiyal" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=12" title="Edit section's source code: Heometriyang diperensiyal"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ang <a href="/wiki/Diperensiyal_na_heometriya" class="mw-redirect" title="Diperensiyal na heometriya">heometriyang diperensiyal</a> ay naging ng tumataas na kahalagahan sa <a href="/wiki/Pisikang_matematikal" class="mw-redirect" title="Pisikang matematikal">pisikang matematikal</a> sanhi ng postulasyon ng <a href="/wiki/Pangkalahatang_relatibidad" class="mw-redirect" title="Pangkalahatang relatibidad">pangkalahatang relatibidad</a> ni <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a> na ang <a href="/wiki/Uniberso" title="Uniberso">uniberso</a> ay naka-kurba. Ang kontemporaryong heometriyang diperensiyal ay likas na nangangahulugang ang mga espasyong isinasaalang alang nito ay mga <a href="/w/index.php?title=Manipoldong_makinis&action=edit&redlink=1" class="new" title="Manipoldong makinis (hindi pa naisusulat)">manipoldong makinis</a> ang istrakturang heometriko ay pinangangasiwaan ng isang <a href="/w/index.php?title=Metrikong_Riemannian&action=edit&redlink=1" class="new" title="Metrikong Riemannian (hindi pa naisusulat)">metrikong Riemannian</a> na tumutukoy sa kung paanong ang mga distansiya ay nasusukat malapit sa bawat punto at hindi ang mga bahaging a priori ng ilang pangkapaligirang patag na espasyong Euclidyano. </p> <div class="mw-heading mw-heading3"><h3 id="Topolohiya_at_heometriya">Topolohiya at heometriya</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=13" title="Baguhin seksiyon: Topolohiya at heometriya" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=13" title="Edit section's source code: Topolohiya at heometriya"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Trefoil_knot_arb.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Trefoil_knot_arb.png/120px-Trefoil_knot_arb.png" decoding="async" width="120" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Trefoil_knot_arb.png/180px-Trefoil_knot_arb.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Trefoil_knot_arb.png/240px-Trefoil_knot_arb.png 2x" data-file-width="1024" data-file-height="768" /></a><figcaption>Ang pagkapal ng isang <a href="/w/index.php?title=Buhol_na_trefoil&action=edit&redlink=1" class="new" title="Buhol na trefoil (hindi pa naisusulat)">buhol na trefoil</a>.</figcaption></figure> <p>Ang larangan ng <a href="/wiki/Topolohiya" title="Topolohiya">topolohiya</a> na nakakita ng malaking pag-unlad noong ika-20 siglo ay sa teknikal na kahulugan isang uri ng <a href="/w/index.php?title=Heometriyang_transpormasyon&action=edit&redlink=1" class="new" title="Heometriyang transpormasyon (hindi pa naisusulat)">heometriyang transpormasyon</a> kung saan ang mga transpormasyon ay mga <a href="/w/index.php?title=Homeomorpismo&action=edit&redlink=1" class="new" title="Homeomorpismo (hindi pa naisusulat)">homeomorpismo</a>. Ito ay kadalasang inihahayag sa anyo ng dictum na 'ang topolohiya ay isang heometriyang gomang kumot'. Ang kontemporaryong <a href="/w/index.php?title=Topolohiyang_heometriko&action=edit&redlink=1" class="new" title="Topolohiyang heometriko (hindi pa naisusulat)">topolohiyang heometriko</a> at <a href="/wiki/Topolohiyang_diperensiyal" class="mw-redirect" title="Topolohiyang diperensiyal">topolohiyang diperensiyal</a> at mga partikular na pang-ilalim na larangan gaya ng <a href="/w/index.php?title=Teoriyang_Morse&action=edit&redlink=1" class="new" title="Teoriyang Morse (hindi pa naisusulat)">teoriyang Morse</a> ay mabibilang ng karamihang mga matematiko bilang bahagi ng heometriya. Ang <a href="/w/index.php?title=Topolohiyang_alhebraiko&action=edit&redlink=1" class="new" title="Topolohiyang alhebraiko (hindi pa naisusulat)">topolohiyang alhebraiko</a> at <a href="/w/index.php?title=Pangkalahatang_topolohiya&action=edit&redlink=1" class="new" title="Pangkalahatang topolohiya (hindi pa naisusulat)">pangkalahatang topolohiya</a> ay tumungo sa kanilang mga sariling landas. </p> <div class="mw-heading mw-heading3"><h3 id="Heometrikang_alhebraiko">Heometrikang alhebraiko</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Heometriya&veaction=edit&section=14" title="Baguhin seksiyon: Heometrikang alhebraiko" class="mw-editsection-visualeditor"><span>baguhin</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Heometriya&action=edit&section=14" title="Edit section's source code: Heometrikang alhebraiko"><span>baguhin ang wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Talaksan:Calabi_yau.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Calabi_yau.jpg/120px-Calabi_yau.jpg" decoding="async" width="120" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Calabi_yau.jpg/180px-Calabi_yau.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Calabi_yau.jpg/240px-Calabi_yau.jpg 2x" data-file-width="1432" data-file-height="1493" /></a><figcaption>Kwintikong <a href="/w/index.php?title=Manipoldong_Calabi%E2%80%93Yau&action=edit&redlink=1" class="new" title="Manipoldong Calabi–Yau (hindi pa naisusulat)">manipoldong Calabi–Yau</a></figcaption></figure> <p>Ang larangan ng <a href="/w/index.php?title=Heometrikang_alhebraiko&action=edit&redlink=1" class="new" title="Heometrikang alhebraiko (hindi pa naisusulat)">heometrikang alhebraiko</a> ang modernong inkarnasyon ng <a href="/w/index.php?title=Heomeriyang_Cartesian&action=edit&redlink=1" class="new" title="Heomeriyang Cartesian (hindi pa naisusulat)">heomeriyang Cartesian</a> ng mga <a href="/wiki/Koordinado" class="mw-redirect" title="Koordinado">koordinado</a>. Mula huli hanggang 1950 hanggang gitna nang 1970, ito ay sumailalim sa malaking mga pang pundasyong pag-unlad na malaking sanhi ng akda nina <a href="/w/index.php?title=Jean-Pierre_Serre&action=edit&redlink=1" class="new" title="Jean-Pierre Serre (hindi pa naisusulat)">Jean-Pierre Serre</a> at <a href="/w/index.php?title=Alexander_Grothendieck&action=edit&redlink=1" class="new" title="Alexander Grothendieck (hindi pa naisusulat)">Alexander Grothendieck</a>. Ito ay tumungo sa pagpapakilala ng <a href="/w/index.php?title=Skema_(heometriyang_alhebraiko)&action=edit&redlink=1" class="new" title="Skema (heometriyang alhebraiko) (hindi pa naisusulat)">mga skema</a> at mas malaking pagbibigay diin sa mga pamamaraang <a href="/w/index.php?title=Topolohiyang_alhebraiko&action=edit&redlink=1" class="new" title="Topolohiyang alhebraiko (hindi pa naisusulat)">topolohikal</a> kabilang ang iba't ibang mga <a href="/w/index.php?title=Teoriyang_cohomolohiya&action=edit&redlink=1" class="new" title="Teoriyang cohomolohiya (hindi pa naisusulat)">teoriyang cohomolohiya</a>. Ang pag-aaral ng mababang dimensiyonal na mga bariedad na alhebraiko na mga <a href="/w/index.php?title=Kurbang_alhebraiko&action=edit&redlink=1" class="new" title="Kurbang alhebraiko (hindi pa naisusulat)">kurbang alhebraiko</a>, mga surpasyong alhebraiko at mga bariedad na alhebraiko ng dimensiyong 3 ay isinulong. Ang teoriyang <a href="/w/index.php?title=Basehang_Gr%C3%B6bner&action=edit&redlink=1" class="new" title="Basehang Gröbner (hindi pa naisusulat)">basehang Gröbner</a> at <a href="/w/index.php?title=Real_na_heometriyang_alhebraiko&action=edit&redlink=1" class="new" title="Real na heometriyang alhebraiko (hindi pa naisusulat)">real na heometriyang alhebraiko</a> ay kasama sa mga mas nilalapat na pang-ilalim na larangan ng modernong heometriyang alhebraiko. Ang heometriyang aritmetiko ay isang aktibong larangan na nagsasama ng heometriyang alhebraiko at <a href="/wiki/Teoriya_ng_bilang" class="mw-redirect" title="Teoriya ng bilang">teoriya ng bilang</a>. Ang ibang mga direksiyon ng pagsasaliksik ay kinasasangkutan ng mga <a href="/w/index.php?title=Espasyong_moduli&action=edit&redlink=1" class="new" title="Espasyong moduli (hindi pa naisusulat)">espasyong moduli</a> at heometriyang kompleks. Ang mga pamamaraang alhebro-heometriko ay karaniwang inilalapat sa <a href="/w/index.php?title=Teoriya_ng_tali&action=edit&redlink=1" class="new" title="Teoriya ng tali (hindi pa naisusulat)">teoriya ng tali</a> at <a href="/w/index.php?title=Teoriya_ng_brano&action=edit&redlink=1" class="new" title="Teoriya ng brano (hindi pa naisusulat)">teoriya ng brano</a>. </p> <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=Heometriya&veaction=edit&section=15" 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=Heometriya&action=edit&section=15" 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"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Martin J. Turner,Jonathan M. Blackledge,Patrick R. Andrews (1998). "<i><a rel="nofollow" class="external text" href="http://books.google.com/books?id=oLXgFdfKp78C&pg=PA1&dq&hl=en#v=onepage&q=&f=false">Fractal geometry in digital imaging</a></i>". <a href="/w/index.php?title=Academic_Press&action=edit&redlink=1" class="new" title="Academic Press (hindi pa naisusulat)">Academic Press</a>. p.1. <a href="/wiki/Natatangi:Mga_pinagmulang_aklat/0127039708" class="internal mw-magiclink-isbn">ISBN 0-12-703970-8</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">It is quite common in algebraic geometry to speak about <i>geometry of <a href="/w/index.php?title=Algebraic_variety&action=edit&redlink=1" class="new" title="Algebraic variety (hindi pa naisusulat)">algebraic varieties</a> over <a href="/w/index.php?title=Finite_field&action=edit&redlink=1" class="new" title="Finite field (hindi pa naisusulat)">finite fields</a></i>, possibly <a href="/w/index.php?title=Singularity_theory&action=edit&redlink=1" class="new" title="Singularity theory (hindi pa naisusulat)">singular</a>. From a naïve perspective, these objects are just finite sets of points, but by invoking powerful geometric imagery and using well developed geometric techniques, it is possible to find structure and establish properties that make them somewhat analogous to the ordinary <a href="/w/index.php?title=Sphere&action=edit&redlink=1" class="new" title="Sphere (hindi pa naisusulat)">spheres</a> or <a href="/w/index.php?title=Cone_(geometry)&action=edit&redlink=1" class="new" title="Cone (geometry) (hindi pa naisusulat)">cones</a>.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Kline (1972) "Mathematical thought from ancient to modern times", Oxford University Press, p. 1032. Kant did not reject the logical (analytic a priori) <i>possibility</i> of non-Euclidean geometry, see <a href="/w/index.php?title=Jeremy_Gray&action=edit&redlink=1" class="new" title="Jeremy Gray (hindi pa naisusulat)">Jeremy Gray</a>, "Ideas of Space Euclidean, Non-Euclidean, and Relativistic", Oxford, 1989; p. 85. Some have implied that, in light of this, Kant had in fact <i>predicted</i> the development of non-Euclidean geometry, cf. Leonard Nelson, "Philosophy and Axiomatics," Socratic Method and Critical Philosophy, Dover, 1965; p.164.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external free" href="http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/">http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/</a></span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r2023235">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol 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mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1843287"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-tingnan"><a href="/w/index.php?title=Padron:Areas_of_mathematics&action=edit&redlink=1" class="new" title="Padron:Areas of mathematics (hindi pa naisusulat)"><abbr title="Tingnan ang padron">t</abbr></a></li><li class="nv-usapan"><a href="/w/index.php?title=Usapang_padron:Areas_of_mathematics&action=edit&redlink=1" class="new" title="Usapang padron:Areas of mathematics (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:Areas_of_mathematics&action=edit"><abbr title="Baguhin ang padron">b</abbr></a></li></ul></div><div id="Matematika_(sipnayan)" 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pangkat">pangkat</a></li> <li><a href="/w/index.php?title=Teorya_ng_uri&action=edit&redlink=1" class="new" title="Teorya ng uri (hindi pa naisusulat)">uri</a></li></ul></li> <li><a href="/wiki/Lohikang_matematikal" title="Lohikang matematikal">Lohika</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Alhebra" title="Alhebra">Alhebra</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alhebrang_basal" title="Alhebrang basal">Basal</a></li> <li><a href="/wiki/Alhebrang_elementaryo" title="Alhebrang elementaryo">Elementaryo</a></li> <li><a href="/w/index.php?title=Alhebrang_homolohika&action=edit&redlink=1" class="new" title="Alhebrang homolohika (hindi pa naisusulat)">Homolohika</a></li> <li><a href="/w/index.php?title=Alhebrang_komutatibo&action=edit&redlink=1" class="new" title="Alhebrang komutatibo (hindi pa naisusulat)">Komutatibo</a></li> <li><a href="/wiki/Alhebrang_linyar" title="Alhebrang linyar">Linyar</a> <ul><li><a href="/wiki/Alhebrang_multilinyar" title="Alhebrang multilinyar">multi</a></li></ul></li> <li><a href="/w/index.php?title=Alhebrang_pangkalahatan&action=edit&redlink=1" class="new" title="Alhebrang pangkalahatan (hindi pa naisusulat)">Pangkalahatan</a></li> <li><a href="/wiki/Teorya_ng_grupo" title="Teorya ng grupo">Teorya ng grupo</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Pagsusuring_matematikal" title="Pagsusuring matematikal">Pagsusuri</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ekwasyong_diperensiyal" title="Ekwasyong diperensiyal">Ekwasyong diperensiyal</a></li> <li><a href="/wiki/Kalkulo" class="mw-redirect" title="Kalkulo">Kalkulo</a></li> <li><i>Pagsusuring...</i> <ul><li><a href="/w/index.php?title=Pagsusuring_harmoniko&action=edit&redlink=1" class="new" title="Pagsusuring harmoniko (hindi pa naisusulat)">harmoniko</a></li> <li><a href="/w/index.php?title=Pagsusuring_komplikado&action=edit&redlink=1" class="new" title="Pagsusuring komplikado (hindi pa naisusulat)">komplikado</a> <ul><li><a href="/w/index.php?title=Pagsusuring_hiperkomplikado&action=edit&redlink=1" class="new" title="Pagsusuring hiperkomplikado (hindi pa naisusulat)">hiper</a></li></ul></li> <li><a href="/wiki/Pagsusuring_punsiyonal" title="Pagsusuring punsiyonal">punsiyon</a></li> <li><a href="/w/index.php?title=Pagsusuring_tunay&action=edit&redlink=1" class="new" title="Pagsusuring tunay (hindi pa naisusulat)">tunay</a></li></ul></li> <li><a href="/wiki/Sukat_(matematika)" title="Sukat (matematika)">Teorya ng sukat</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matematikang_diskreto" title="Matematikang diskreto">Diskreto</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kombinatorika" title="Kombinatorika">Kombinatorika</a></li> <li><i>Teorya ng...</i> <ul><li><a href="/w/index.php?title=Teorya_ng_ayos&action=edit&redlink=1" class="new" title="Teorya ng ayos (hindi pa naisusulat)">ayos</a></li> <li><a href="/wiki/Teorya_ng_grap" title="Teorya ng grap">grap</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">Heometriya</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Heometriyang_alhebraiko" title="Heometriyang alhebraiko">Alhebraiko</a></li> <li><a href="/w/index.php?title=Heometriyang_aritmetiko&action=edit&redlink=1" class="new" title="Heometriyang aritmetiko (hindi pa naisusulat)">Aritmetiko</a></li> <li><a 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title="Alhebraikong teorya ng bilang (hindi pa naisusulat)">Alhebraiko</a></li> <li><a href="/wiki/Aritmetika" title="Aritmetika">Aritmetika</a></li> <li><a href="/w/index.php?title=Heometriyang_diopantika&action=edit&redlink=1" class="new" title="Heometriyang diopantika (hindi pa naisusulat)">Heometriyang diopantika</a></li> <li><a href="/w/index.php?title=Pasuring_teorya_ng_bilang&action=edit&redlink=1" class="new" title="Pasuring teorya ng bilang (hindi pa naisusulat)">Pasuri</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Topolohiya" title="Topolohiya">Topolohiya</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Topolohiyang_alhebraiko&action=edit&redlink=1" class="new" title="Topolohiyang alhebraiko (hindi pa naisusulat)">Alhebraiko</a></li> <li><a href="/wiki/Topolohiyang_diperensiyal" class="mw-redirect" title="Topolohiyang diperensiyal">Diperensiyal</a></li> <li><a href="/w/index.php?title=Topolohiyang_heometriko&action=edit&redlink=1" class="new" title="Topolohiyang heometriko (hindi pa naisusulat)">Heometriko</a></li> <li><a href="/w/index.php?title=Homotopiya&action=edit&redlink=1" class="new" title="Homotopiya (hindi pa naisusulat)">Homotopiya</a> <ul><li><a href="/w/index.php?title=Teorya_ng_homotopiya&action=edit&redlink=1" class="new" title="Teorya ng homotopiya (hindi pa naisusulat)">teorya</a></li></ul></li> <li><a href="/w/index.php?title=Topolohiyang_pangkalahatan&action=edit&redlink=1" class="new" title="Topolohiyang pangkalahatan (hindi pa naisusulat)">Pangkalahatan</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Matematikang_nalalapat" class="mw-redirect" title="Matematikang nalalapat">Nalalapat</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Agham_pansistema&action=edit&redlink=1" class="new" title="Agham pansistema (hindi pa naisusulat)">Agham pansistema</a> <ul><li><a href="/w/index.php?title=Pananaliksik_pang-operasyon&action=edit&redlink=1" class="new" title="Pananaliksik pang-operasyon (hindi pa naisusulat)">pananaliksik pang-operasyon</a></li> <li><i>teorya ng...</i> <ul><li><a href="/wiki/Teorya_ng_kontrol" title="Teorya ng kontrol">kontrol</a></li> <li><a href="/wiki/Teorya_ng_laro" title="Teorya ng laro">laro</a></li></ul></li></ul></li> <li><a href="/wiki/Estadistika" title="Estadistika">Estadistika</a></li> <li><i>Matematikang...</i> <ul><li><a href="/wiki/Matematikang_pangbiolohiya" title="Matematikang pangbiolohiya">biolohiya</a></li> <li><a href="/wiki/Matematikang_pang-ekonomika" title="Matematikang pang-ekonomika">ekonomika</a></li> <li><a href="/w/index.php?title=Matematikang_pang-estadistika&action=edit&redlink=1" class="new" title="Matematikang 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