CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="nl" dir="ltr"> <head> <meta charset="UTF-8"> <title>Meetkunde - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )nlwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":[",\t.",".\t,"],"wgDigitTransformTable":["",""], "wgDefaultDateFormat":"dmy","wgMonthNames":["","januari","februari","maart","april","mei","juni","juli","augustus","september","oktober","november","december"],"wgRequestId":"0033211d-eb1b-4ff2-93a7-01c04c093612","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Meetkunde","wgTitle":"Meetkunde","wgCurRevisionId":68008246,"wgRevisionId":68008246,"wgArticleId":8296,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Meetkunde"],"wgPageViewLanguage":"nl","wgPageContentLanguage":"nl","wgPageContentModel":"wikitext","wgRelevantPageName":"Meetkunde","wgRelevantArticleId":8296,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgRedirectedFrom":"Geometrie","wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{ "pageLanguageCode":"nl","pageLanguageDir":"ltr","pageVariantFallbacks":"nl"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":20000,"wgInternalRedirectTargetUrl":"/wiki/Meetkunde","wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q8087","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading", "ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["mediawiki.action.view.redirect","ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.Direct-link-to-Commons","ext.gadget.ProtectionTemplates","ext.gadget.InterProjectLinks","ext.gadget.hoofdbetekenis-titelwijziging","ext.gadget.switcher","ext.gadget.OpenStreetMapFrame","ext.gadget.subpages","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents", "ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=nl&modules=ext.cite.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=nl&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=nl&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/d/d4/Woman_teaching_geometry.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1326"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Woman_teaching_geometry.jpg/800px-Woman_teaching_geometry.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="884"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Woman_teaching_geometry.jpg/640px-Woman_teaching_geometry.jpg"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="707"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Meetkunde - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//nl.m.wikipedia.org/wiki/Meetkunde"> <link rel="alternate" type="application/x-wiki" title="Bewerken" href="/w/index.php?title=Meetkunde&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (nl)"> <link rel="EditURI" type="application/rsd+xml" href="//nl.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://nl.wikipedia.org/wiki/Meetkunde"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.nl"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom-feed" href="/w/index.php?title=Speciaal:RecenteWijzigingen&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Meetkunde rootpage-Meetkunde skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Naar inhoud springen</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Hoofdmenu" > <label 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">Hoofdmenu</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">Hoofdmenu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">verbergen</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigatie </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Hoofdpagina" title="Naar de hoofdpagina gaan [z]" accesskey="z"><span>Hoofdpagina</span></a></li><li id="n-zoekartikel" class="mw-list-item"><a href="/wiki/Portaal:Navigatie"><span>Vind een artikel</span></a></li><li id="n-today" class="mw-list-item"><a href="/wiki/28_november"><span>Vandaag</span></a></li><li id="n-Etalage" class="mw-list-item"><a href="/wiki/Wikipedia:Etalage"><span>Etalage</span></a></li><li id="n-categories" class="mw-list-item"><a href="/wiki/Categorie:Alles"><span>Categorieën</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Speciaal:RecenteWijzigingen" title="Een lijst met recente wijzigingen in deze wiki. [r]" accesskey="r"><span>Recente wijzigingen</span></a></li><li id="n-newpages" class="mw-list-item"><a href="/wiki/Speciaal:NieuwePaginas"><span>Nieuwe artikelen</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Speciaal:Willekeurig" title="Een willekeurige pagina bekijken [x]" accesskey="x"><span>Willekeurige pagina</span></a></li> </ul> </div> </div> <div id="p-navigation2" class="vector-menu mw-portlet mw-portlet-navigation2" > <div class="vector-menu-heading"> Informatie </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-portal" class="mw-list-item"><a href="/wiki/Portaal:Gebruikersportaal" title="Informatie over het project: wat u kunt doen, waar u dingen kunt vinden"><span>Gebruikersportaal</span></a></li><li id="n-Snelcursus" class="mw-list-item"><a href="/wiki/Wikipedia:Snelcursus"><span>Snelcursus</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Portaal:Hulp_en_beheer" title="Hulpinformatie over deze wiki"><span>Hulp en contact</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Hoofdpagina" 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="de vrije encyclopedie" src="/static/images/mobile/copyright/wikipedia-tagline-nl.svg" width="120" height="13" style="width: 7.5em; 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/Speciaal:Zoeken" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Doorzoek Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Zoeken</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="Doorzoek Wikipedia" aria-label="Doorzoek Wikipedia" autocapitalize="sentences" title="Doorzoek 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="Speciaal:Zoeken"> </div> <button class="cdx-button cdx-search-input__end-button">Zoeken</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Persoonlijke hulpmiddelen"> <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="Uiterlijk"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="De lettergrootte, breedte en kleur van de pagina wijzigen" > <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="Uiterlijk" > <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">Uiterlijk</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_nl.wikipedia.org&uselang=nl" class=""><span>Doneren</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=Speciaal:GebruikerAanmaken&returnto=Meetkunde" title="Registreer u vooral en meld u aan. Dit is echter niet verplicht." class=""><span>Account aanmaken</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=Speciaal:Aanmelden&returnto=Meetkunde" title="U wordt van harte uitgenodigd om aan te melden, maar dit is niet verplicht [o]" accesskey="o" class=""><span>Aanmelden</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="Meer opties" > <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="Persoonlijke hulpmiddelen" > <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">Persoonlijke hulpmiddelen</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Gebruikersmenu" > <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_nl.wikipedia.org&uselang=nl"><span>Doneren</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speciaal:GebruikerAanmaken&returnto=Meetkunde" title="Registreer u vooral en meld u aan. Dit is echter niet verplicht."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Account aanmaken</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speciaal:Aanmelden&returnto=Meetkunde" title="U wordt van harte uitgenodigd om aan te melden, maar dit is niet verplicht [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Aanmelden</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"> Pagina's voor uitgelogde redacteuren <a href="/wiki/Help:Inleiding" aria-label="Meer leren over bewerken"><span>meer lezen</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speciaal:MijnBijdragen" title="Bijdragen IP-adres [y]" accesskey="y"><span>Bijdragen</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speciaal:MijnOverleg" title="Overlegpagina van de anonieme gebruiker van dit IP-adres [n]" accesskey="n"><span>Overleg</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="Site"> <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="Inhoud" 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">Inhoud</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">verbergen</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">Top</div> </a> </li> <li id="toc-Overzicht" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Overzicht"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Overzicht</span> </div> </a> <button aria-controls="toc-Overzicht-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>Overzicht-subkopje inklappen</span> </button> <ul id="toc-Overzicht-sublist" class="vector-toc-list"> <li id="toc-Praktische_meetkunde" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Praktische_meetkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Praktische meetkunde</span> </div> </a> <ul id="toc-Praktische_meetkunde-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Axiomatische_meetkunde" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Axiomatische_meetkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Axiomatische meetkunde</span> </div> </a> <ul id="toc-Axiomatische_meetkunde-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Meetkundige_constructies" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Meetkundige_constructies"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Meetkundige constructies</span> </div> </a> <ul id="toc-Meetkundige_constructies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Analytische_meetkunde" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Analytische_meetkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Analytische meetkunde</span> </div> </a> <ul id="toc-Analytische_meetkunde-sublist" class="vector-toc-list"> <li id="toc-Vectormeetkunde" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Vectormeetkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4.1</span> <span>Vectormeetkunde</span> </div> </a> <ul id="toc-Vectormeetkunde-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Projectieve_meetkunde" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Projectieve_meetkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Projectieve meetkunde</span> </div> </a> <ul id="toc-Projectieve_meetkunde-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Niet-euclidische_meetkunde" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Niet-euclidische_meetkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Niet-euclidische meetkunde</span> </div> </a> <ul id="toc-Niet-euclidische_meetkunde-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Symmetrie" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Symmetrie"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.7</span> <span>Symmetrie</span> </div> </a> <ul id="toc-Symmetrie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Moderne_meetkunde" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Moderne_meetkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.8</span> <span>Moderne meetkunde</span> </div> </a> <ul id="toc-Moderne_meetkunde-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Geschiedenis_van_de_meetkunde" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Geschiedenis_van_de_meetkunde"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Geschiedenis van de meetkunde</span> </div> </a> <ul id="toc-Geschiedenis_van_de_meetkunde-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externe_link" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externe_link"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Externe link</span> </div> </a> <ul id="toc-Externe_link-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voetnoten" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voetnoten"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Voetnoten</span> </div> </a> <ul id="toc-Voetnoten-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="Inhoud" 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="Inhoudsopgave omschakelen" > <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">Inhoudsopgave omschakelen</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">Meetkunde</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="Ga naar een artikel in een andere taal. Beschikbaar in 179 talen" > <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 talen</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 – Zwitserduits" lang="gsw" hreflang="gsw" data-title="Geometrie" data-language-autonym="Alemannisch" data-language-local-name="Zwitserduits" 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 – Amhaars" lang="am" hreflang="am" data-title="ጂዎሜትሪ" data-language-autonym="አማርኛ" data-language-local-name="Amhaars" 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 – Aragonees" lang="an" hreflang="an" data-title="Cheometría" data-language-autonym="Aragonés" data-language-local-name="Aragonees" 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 – Arabisch" lang="ar" hreflang="ar" data-title="هندسة رياضية" data-language-autonym="العربية" data-language-local-name="Arabisch" 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 – Marokkaans Arabisch" lang="ary" hreflang="ary" data-title="تسطار" data-language-autonym="الدارجة" data-language-local-name="Marokkaans Arabisch" 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 – Assamees" lang="as" hreflang="as" data-title="জ্যামিতি" data-language-autonym="অসমীয়া" data-language-local-name="Assamees" 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 – Asturisch" lang="ast" hreflang="ast" data-title="Xeometría" data-language-autonym="Asturianu" data-language-local-name="Asturisch" 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 – Azerbeidzjaans" lang="az" hreflang="az" data-title="Həndəsə" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" 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 – Basjkiers" lang="ba" hreflang="ba" data-title="Геометрия" data-language-autonym="Башҡортса" data-language-local-name="Basjkiers" 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 – Samogitisch" lang="sgs" hreflang="sgs" data-title="Geuometrėjė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitisch" 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 – Belarussisch" lang="be" hreflang="be" data-title="Геаметрыя" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" 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 – Bulgaars" lang="bg" hreflang="bg" data-title="Геометрия" data-language-autonym="Български" data-language-local-name="Bulgaars" 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 – Bengaals" lang="bn" hreflang="bn" data-title="জ্যামিতি" data-language-autonym="বাংলা" data-language-local-name="Bengaals" 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། – Tibetaans" lang="bo" hreflang="bo" data-title="དབྱིབས་རྩིས་རིག་པ།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetaans" 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 – Bretons" lang="br" hreflang="br" data-title="Mentoniezh" data-language-autonym="Brezhoneg" data-language-local-name="Bretons" 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 – Bosnisch" lang="bs" hreflang="bs" data-title="Geometrija" data-language-autonym="Bosanski" data-language-local-name="Bosnisch" 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 – Catalaans" lang="ca" hreflang="ca" data-title="Geometria" data-language-autonym="Català" data-language-local-name="Catalaans" 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 – Soranî" lang="ckb" hreflang="ckb" data-title="ئەندازە" data-language-autonym="کوردی" data-language-local-name="Soranî" 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 – Corsicaans" lang="co" hreflang="co" data-title="Geumitria" data-language-autonym="Corsu" data-language-local-name="Corsicaans" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs badge-Q17437798 badge-goodarticle mw-list-item" title="goed artikel"><a href="https://cs.wikipedia.org/wiki/Geometrie" title="Geometrie – Tsjechisch" lang="cs" hreflang="cs" data-title="Geometrie" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" 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 – Tsjoevasjisch" lang="cv" hreflang="cv" data-title="Геометри" data-language-autonym="Чӑвашла" data-language-local-name="Tsjoevasjisch" 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 – Deens" lang="da" hreflang="da" data-title="Geometri" data-language-autonym="Dansk" data-language-local-name="Deens" 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 – Duits" lang="de" hreflang="de" data-title="Geometrie" data-language-autonym="Deutsch" data-language-local-name="Duits" 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 – Grieks" lang="el" hreflang="el" data-title="Γεωμετρία" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" 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 – Engels" lang="en" hreflang="en" data-title="Geometry" data-language-autonym="English" data-language-local-name="Engels" 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 – Spaans" lang="es" hreflang="es" data-title="Geometría" data-language-autonym="Español" data-language-local-name="Spaans" 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 – Estisch" lang="et" hreflang="et" data-title="Geomeetria" data-language-autonym="Eesti" data-language-local-name="Estisch" 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 – Baskisch" lang="eu" hreflang="eu" data-title="Geometria" data-language-autonym="Euskara" data-language-local-name="Baskisch" 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 – Extremeens" lang="ext" hreflang="ext" data-title="Geometria" data-language-autonym="Estremeñu" data-language-local-name="Extremeens" 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 – Perzisch" lang="fa" hreflang="fa" data-title="هندسه" data-language-autonym="فارسی" data-language-local-name="Perzisch" 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 – Fins" lang="fi" hreflang="fi" data-title="Geometria" data-language-autonym="Suomi" data-language-local-name="Fins" 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 – Fijisch" lang="fj" hreflang="fj" data-title="Geometry" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijisch" 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 – Faeröers" lang="fo" hreflang="fo" data-title="Geometri" data-language-autonym="Føroyskt" data-language-local-name="Faeröers" 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 – Frans" lang="fr" hreflang="fr" data-title="Géométrie" data-language-autonym="Français" data-language-local-name="Frans" 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 – Noord-Fries" lang="frr" hreflang="frr" data-title="Geometrii" data-language-autonym="Nordfriisk" data-language-local-name="Noord-Fries" 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 – Iers" lang="ga" hreflang="ga" data-title="Geoiméadracht" data-language-autonym="Gaeilge" data-language-local-name="Iers" 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 – Ganyu" lang="gan" hreflang="gan" data-title="幾何學" data-language-autonym="贛語" data-language-local-name="Ganyu" 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 – Schots-Gaelisch" lang="gd" hreflang="gd" data-title="Geoimeatras" data-language-autonym="Gàidhlig" data-language-local-name="Schots-Gaelisch" 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 – Galicisch" lang="gl" hreflang="gl" data-title="Xeometría" data-language-autonym="Galego" data-language-local-name="Galicisch" 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 – Guaraní" lang="gn" hreflang="gn" data-title="Ysajarekokuaa" data-language-autonym="Avañe'ẽ" data-language-local-name="Guaraní" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-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" lang="hak" hreflang="hak" data-title="Kí-hò-ho̍k" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka" 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 – Hebreeuws" lang="he" hreflang="he" data-title="גאומטריה" data-language-autonym="עברית" data-language-local-name="Hebreeuws" 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 – Fijisch Hindi" lang="hif" hreflang="hif" data-title="Geometry" data-language-autonym="Fiji Hindi" data-language-local-name="Fijisch 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 – Kroatisch" lang="hr" hreflang="hr" data-title="Geometrija" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" 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 – Haïtiaans Creools" lang="ht" hreflang="ht" data-title="Jewometri" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haïtiaans Creools" 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 – Hongaars" lang="hu" hreflang="hu" data-title="Geometria" data-language-autonym="Magyar" data-language-local-name="Hongaars" 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 – Armeens" lang="hy" hreflang="hy" data-title="Երկրաչափություն" data-language-autonym="Հայերեն" data-language-local-name="Armeens" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia badge-Q17437796 badge-featuredarticle mw-list-item" title="uitgelicht artikel"><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 – Indonesisch" lang="id" hreflang="id" data-title="Geometri" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" 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 – IJslands" lang="is" hreflang="is" data-title="Rúmfræði" data-language-autonym="Íslenska" data-language-local-name="IJslands" 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 – Italiaans" lang="it" hreflang="it" data-title="Geometria" data-language-autonym="Italiano" data-language-local-name="Italiaans" 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 – Japans" lang="ja" hreflang="ja" data-title="幾何学" data-language-autonym="日本語" data-language-local-name="Japans" 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 – Jamaicaans Creools" lang="jam" hreflang="jam" data-title="Jaamichri" data-language-autonym="Patois" data-language-local-name="Jamaicaans Creools" 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 – Javaans" lang="jv" hreflang="jv" data-title="Géomètri" data-language-autonym="Jawa" data-language-local-name="Javaans" 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 – Georgisch" lang="ka" hreflang="ka" data-title="გეომეტრია" data-language-autonym="ქართული" data-language-local-name="Georgisch" 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 – Karakalpaks" lang="kaa" hreflang="kaa" data-title="Geometriya" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Karakalpaks" 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 – Kabylisch" lang="kab" hreflang="kab" data-title="Tanzeggit" data-language-autonym="Taqbaylit" data-language-local-name="Kabylisch" 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 – Kabardisch" lang="kbd" hreflang="kbd" data-title="Геометрие" data-language-autonym="Адыгэбзэ" data-language-local-name="Kabardisch" 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) – Gikuyu" lang="ki" hreflang="ki" data-title="Mũthunũrũrio (geometry)" data-language-autonym="Gĩkũyũ" data-language-local-name="Gikuyu" 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 – Kazachs" lang="kk" hreflang="kk" data-title="Геометрия" data-language-autonym="Қазақша" data-language-local-name="Kazachs" 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 – Koreaans" lang="ko" hreflang="ko" data-title="기하학" data-language-autonym="한국어" data-language-local-name="Koreaans" 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 – Koerdisch" lang="ku" hreflang="ku" data-title="Geometrî" data-language-autonym="Kurdî" data-language-local-name="Koerdisch" 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 – Kirgizisch" lang="ky" hreflang="ky" data-title="Геометрия" data-language-autonym="Кыргызча" data-language-local-name="Kirgizisch" 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 – Latijn" lang="la" hreflang="la" data-title="Geometria" data-language-autonym="Latina" data-language-local-name="Latijn" 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 – Luxemburgs" lang="lb" hreflang="lb" data-title="Geometrie" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxemburgs" 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) – Luganda" lang="lg" hreflang="lg" data-title="Essomampimo (Geometry)" data-language-autonym="Luganda" data-language-local-name="Luganda" 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 – Limburgs" lang="li" hreflang="li" data-title="Maetkónde" data-language-autonym="Limburgs" data-language-local-name="Limburgs" 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 – Ligurisch" lang="lij" hreflang="lij" data-title="Geometria" data-language-autonym="Ligure" data-language-local-name="Ligurisch" 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 – Lombardisch" lang="lmo" hreflang="lmo" data-title="Geometrìa" data-language-autonym="Lombard" data-language-local-name="Lombardisch" 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 – Laotiaans" lang="lo" hreflang="lo" data-title="ເລຂາຄະນິດ" data-language-autonym="ລາວ" data-language-local-name="Laotiaans" 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 – Litouws" lang="lt" hreflang="lt" data-title="Geometrija" data-language-autonym="Lietuvių" data-language-local-name="Litouws" 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 – Lets" lang="lv" hreflang="lv" data-title="Ģeometrija" data-language-autonym="Latviešu" data-language-local-name="Lets" 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 – Moksja" lang="mdf" hreflang="mdf" data-title="Геометриясь" data-language-autonym="Мокшень" data-language-local-name="Moksja" 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 – Malagassisch" lang="mg" hreflang="mg" data-title="Jeômetria" data-language-autonym="Malagasy" data-language-local-name="Malagassisch" 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 – Macedonisch" lang="mk" hreflang="mk" data-title="Геометрија" data-language-autonym="Македонски" data-language-local-name="Macedonisch" 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 – Mongools" lang="mn" hreflang="mn" data-title="Геометр" data-language-autonym="Монгол" data-language-local-name="Mongools" 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 – Maleis" lang="ms" hreflang="ms" data-title="Geometri" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" 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 – Maltees" lang="mt" hreflang="mt" data-title="Ġeometrija" data-language-autonym="Malti" data-language-local-name="Maltees" 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 – Mirandees" lang="mwl" hreflang="mwl" data-title="Geometrie" data-language-autonym="Mirandés" data-language-local-name="Mirandees" 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 – Birmaans" lang="my" hreflang="my" data-title="ဂျီဩမေတြီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Birmaans" 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 – Erzja" lang="myv" hreflang="myv" data-title="Геометрия" data-language-autonym="Эрзянь" data-language-local-name="Erzja" 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 – Nedersaksisch" lang="nds" hreflang="nds" data-title="Geometrie" data-language-autonym="Plattdüütsch" data-language-local-name="Nedersaksisch" 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 – Nepalees" lang="ne" hreflang="ne" data-title="ज्यामिति" data-language-autonym="नेपाली" data-language-local-name="Nepalees" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Geometri" title="Geometri – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Geometri" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - 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 – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Geometri" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - 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 – Occitaans" lang="oc" hreflang="oc" data-title="Geometria" data-language-autonym="Occitan" data-language-local-name="Occitaans" 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 – Afaan Oromo" lang="om" hreflang="om" data-title="Ji'oomeetirii" data-language-autonym="Oromoo" data-language-local-name="Afaan 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 – Pools" lang="pl" hreflang="pl" data-title="Geometria" data-language-autonym="Polski" data-language-local-name="Pools" 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 – Piëmontees" lang="pms" hreflang="pms" data-title="Geometrìa" data-language-autonym="Piemontèis" data-language-local-name="Piëmontees" 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 – Pasjtoe" lang="ps" hreflang="ps" data-title="مېچپوهنه" data-language-autonym="پښتو" data-language-local-name="Pasjtoe" 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 – Portugees" lang="pt" hreflang="pt" data-title="Geometria" data-language-autonym="Português" data-language-local-name="Portugees" 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 – Roemeens" lang="ro" hreflang="ro" data-title="Geometrie" data-language-autonym="Română" data-language-local-name="Roemeens" 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 – Russisch" lang="ru" hreflang="ru" data-title="Геометрия" data-language-autonym="Русский" data-language-local-name="Russisch" 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 – Roetheens" lang="rue" hreflang="rue" data-title="Ґеометрія" data-language-autonym="Русиньскый" data-language-local-name="Roetheens" 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 – Jakoets" lang="sah" hreflang="sah" data-title="Геометрия" data-language-autonym="Саха тыла" data-language-local-name="Jakoets" 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 – Siciliaans" lang="scn" hreflang="scn" data-title="Giometrìa" data-language-autonym="Sicilianu" data-language-local-name="Siciliaans" 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 – Schots" lang="sco" hreflang="sco" data-title="Geometry" data-language-autonym="Scots" data-language-local-name="Schots" 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 – Servo-Kroatisch" lang="sh" hreflang="sh" data-title="Geometrija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Servo-Kroatisch" 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 – Tashelhiyt" lang="shi" hreflang="shi" data-title="Asɣkl" data-language-autonym="Taclḥit" data-language-local-name="Tashelhiyt" 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 – Singalees" lang="si" hreflang="si" data-title="ජ්‍යාමිතිය" data-language-autonym="සිංහල" data-language-local-name="Singalees" 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 – Slowaaks" lang="sk" hreflang="sk" data-title="Geometria" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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 – Sloveens" lang="sl" hreflang="sl" data-title="Geometrija" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" 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-Samisch" lang="smn" hreflang="smn" data-title="Geometria" data-language-autonym="Anarâškielâ" data-language-local-name="Inari-Samisch" 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 – Albanees" lang="sq" hreflang="sq" data-title="Gjeometria" data-language-autonym="Shqip" data-language-local-name="Albanees" 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 – Servisch" lang="sr" hreflang="sr" data-title="Геометрија" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" 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 – Saterfries" lang="stq" hreflang="stq" data-title="Geometrie" data-language-autonym="Seeltersk" data-language-local-name="Saterfries" 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 – Soendanees" lang="su" hreflang="su" data-title="Élmu ukur" data-language-autonym="Sunda" data-language-local-name="Soendanees" 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 – Zweeds" lang="sv" hreflang="sv" data-title="Geometri" data-language-autonym="Svenska" data-language-local-name="Zweeds" 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 – Silezisch" lang="szl" hreflang="szl" data-title="Geometryjo" data-language-autonym="Ślůnski" data-language-local-name="Silezisch" 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 – Tadzjieks" lang="tg" hreflang="tg" data-title="Ҳандаса" data-language-autonym="Тоҷикӣ" data-language-local-name="Tadzjieks" 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 – Turkmeens" lang="tk" hreflang="tk" data-title="Geometriýa" data-language-autonym="Türkmençe" data-language-local-name="Turkmeens" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Heometriya" title="Heometriya – Tagalog" lang="tl" hreflang="tl" data-title="Heometriya" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Geometri" title="Geometri – Turks" lang="tr" hreflang="tr" data-title="Geometri" data-language-autonym="Türkçe" data-language-local-name="Turks" 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 – Tataars" lang="tt" hreflang="tt" data-title="Геометрия" data-language-autonym="Татарча / tatarça" data-language-local-name="Tataars" 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 – Toevaans" lang="tyv" hreflang="tyv" data-title="Геометрия" data-language-autonym="Тыва дыл" data-language-local-name="Toevaans" 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 – Oekraïens" lang="uk" hreflang="uk" data-title="Геометрія" data-language-autonym="Українська" data-language-local-name="Oekraïens" 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 – Oezbeeks" lang="uz" hreflang="uz" data-title="Geometriya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" 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 – Venetiaans" lang="vec" hreflang="vec" data-title="Zeometria" data-language-autonym="Vèneto" data-language-local-name="Venetiaans" 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 – Wepsisch" lang="vep" hreflang="vep" data-title="Geometrii" data-language-autonym="Vepsän kel’" data-language-local-name="Wepsisch" 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 – Vietnamees" lang="vi" hreflang="vi" data-title="Hình học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" 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 – Wuyu" lang="wuu" hreflang="wuu" data-title="几何学" data-language-autonym="吴语" data-language-local-name="Wuyu" 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 – Mingreels" lang="xmf" hreflang="xmf" data-title="გეომეტრია" data-language-autonym="მარგალური" data-language-local-name="Mingreels" 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 – Jiddisch" lang="yi" hreflang="yi" data-title="געאמעטריע" data-language-autonym="ייִדיש" data-language-local-name="Jiddisch" 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 – Standaard Marokkaanse Tamazight" lang="zgh" hreflang="zgh" data-title="ⵜⴰⵏⵣⴳⴳⵉⵜ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="Standaard Marokkaanse 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 – Chinees" lang="zh" hreflang="zh" data-title="几何学" data-language-autonym="中文" data-language-local-name="Chinees" 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 – Klassiek Chinees" lang="lzh" hreflang="lzh" data-title="幾何" data-language-autonym="文言" data-language-local-name="Klassiek Chinees" 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 – Minnanyu" lang="nan" hreflang="nan" data-title="Kí-hô-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnanyu" 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 – Kantonees" lang="yue" hreflang="yue" data-title="幾何學" data-language-autonym="粵語" data-language-local-name="Kantonees" 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 – Zoeloe" lang="zu" hreflang="zu" data-title="Umchazabukhulu" data-language-autonym="IsiZulu" data-language-local-name="Zoeloe" 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="Taalkoppelingen bewerken" class="wbc-editpage">Koppelingen bewerken</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Naamruimten"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Meetkunde" title="Inhoudspagina bekijken [c]" accesskey="c"><span>Artikel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Overleg:Meetkunde" rel="discussion" title="Overleg over deze pagina [t]" accesskey="t"><span>Overleg</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Taalvariant wijzigen" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Nederlands</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Weergaven"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Meetkunde"><span>Lezen</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Meetkunde&veaction=edit" title="Deze pagina bewerken [v]" accesskey="v"><span>Bewerken</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Meetkunde&action=edit" title="Broncode van deze pagina bewerken [e]" accesskey="e"><span>Brontekst bewerken</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Meetkunde&action=history" title="Eerdere versies van deze pagina [h]" accesskey="h"><span>Geschiedenis weergeven</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Paginahulpmiddelen"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Hulpmiddelen" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Hulpmiddelen</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Hulpmiddelen</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">verbergen</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Meer opties" > <div class="vector-menu-heading"> Handelingen </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Meetkunde"><span>Lezen</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Meetkunde&veaction=edit" title="Deze pagina bewerken [v]" accesskey="v"><span>Bewerken</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Meetkunde&action=edit" title="Broncode van deze pagina bewerken [e]" accesskey="e"><span>Brontekst bewerken</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Meetkunde&action=history"><span>Geschiedenis weergeven</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Algemeen </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciaal:VerwijzingenNaarHier/Meetkunde" title="Lijst met alle pagina's die naar deze pagina verwijzen [j]" accesskey="j"><span>Links naar deze pagina</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciaal:RecenteWijzigingenGelinkt/Meetkunde" rel="nofollow" title="Recente wijzigingen in pagina's waar deze pagina naar verwijst [k]" accesskey="k"><span>Gerelateerde wijzigingen</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=nl" title="Bestanden uploaden [u]" accesskey="u"><span>Bestand uploaden</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speciaal:SpecialePaginas" title="Lijst met alle speciale pagina's [q]" accesskey="q"><span>Speciale pagina's</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Meetkunde&oldid=68008246" title="Permanente koppeling naar deze versie van deze pagina"><span>Permanente koppeling</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Meetkunde&action=info" title="Meer informatie over deze pagina"><span>Paginagegevens</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speciaal:Citeren&page=Meetkunde&id=68008246&wpFormIdentifier=titleform" title="Informatie over hoe u deze pagina kunt citeren"><span>Deze pagina citeren</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciaal:UrlShortener&url=https%3A%2F%2Fnl.wikipedia.org%2Fwiki%2FMeetkunde"><span>Verkorte URL verkrijgen</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciaal:QrCode&url=https%3A%2F%2Fnl.wikipedia.org%2Fwiki%2FMeetkunde"><span>QR-code downloaden</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Afdrukken/exporteren </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speciaal:Boek&bookcmd=book_creator&referer=Meetkunde"><span>Boek aanmaken</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciaal:DownloadAsPdf&page=Meetkunde&action=show-download-screen"><span>Downloaden als PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Meetkunde&printable=yes" title="Printvriendelijke versie van deze pagina [p]" accesskey="p"><span>Afdrukversie</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In andere projecten </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Geometry" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q8087" title="Koppeling naar item in verbonden gegevensrepository [g]" accesskey="g"><span>Wikidata-item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Paginahulpmiddelen"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Uiterlijk"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Uiterlijk</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">verbergen</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Uit Wikipedia, de vrije encyclopedie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Doorverwezen vanaf <a href="/w/index.php?title=Geometrie&redirect=no" class="mw-redirect" title="Geometrie">Geometrie</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="nl" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Woman_teaching_geometry.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Woman_teaching_geometry.jpg/260px-Woman_teaching_geometry.jpg" decoding="async" width="260" height="287" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Woman_teaching_geometry.jpg/390px-Woman_teaching_geometry.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Woman_teaching_geometry.jpg/520px-Woman_teaching_geometry.jpg 2x" data-file-width="1039" data-file-height="1148" /></a><figcaption>Een vrouw onderwijst studenten in de meetkunde. In de <a href="/wiki/Middeleeuwen" title="Middeleeuwen">middeleeuwen</a> was het ongewoon dat een vrouw afgebeeld werd als lerares, vooral omdat de afgebeelde studenten waarschijnlijk monniken zijn. Het is mogelijk dat de vrouw een personificatie van de meetkunde is.</figcaption></figure> <p>De <b>meetkunde</b>, ook wel <b>geometrie</b> (van <a href="/wiki/Oudgrieks" title="Oudgrieks">Oudgrieks</a>: γεωμετρία, γῆ "aarde", μέτρον "maat"), het "meten van de aarde", is het onderdeel van de <a href="/wiki/Wiskunde" title="Wiskunde">wiskunde</a>, dat zich bezighoudt met het bepalen van afmetingen, vormen, de relatieve positie van figuren en de eigenschappen van die figuren en van de <a href="/wiki/Ruimte_(wiskunde)" title="Ruimte (wiskunde)">ruimte</a> waarin ze geplaatst zijn. De specifiek Nederlandse term <i>meetkunde</i> werd rond 1600 door de Vlaamse wiskundige <a href="/wiki/Simon_Stevin" title="Simon Stevin">Simon Stevin</a> geïntroduceerd.<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> Een wiskundige die op het gebied van de meetkunde werkt, wordt een meetkundige genoemd. </p><p>De meetkunde is een van de oudste wetenschappen. Aanvankelijk begonnen als een geheel van praktische kennis over <a href="/wiki/Lengte_(meetkunde)" title="Lengte (meetkunde)">lengten</a>, <a href="/wiki/Oppervlakte" title="Oppervlakte">oppervlakten</a> en <a href="/wiki/Inhoud_(volume)" title="Inhoud (volume)">volumen</a> werd de meetkunde in de 3e eeuw v.Chr. door <a href="/wiki/Euclides_van_Alexandri%C3%AB" title="Euclides van Alexandrië">Euclides van Alexandrië</a> van een <a href="/wiki/Axioma" title="Axioma">axiomatisch</a> fundament voorzien. Al in het klassieke <a href="/wiki/Griekenland" title="Griekenland">Griekenland</a> werden de eerste axioma's geformuleerd (waaronder de <a href="/wiki/Postulaten_van_Euclides" title="Postulaten van Euclides">postulaten van Euclides</a>), waar later de gehele meetkunde zich uit heeft ontwikkeld. De axioma's werden gebruikt voor de wiskundige definitie van <a href="/wiki/Punt_(wiskunde)" title="Punt (wiskunde)">punten</a>, rechte <a href="/wiki/Lijn_(meetkunde)" title="Lijn (meetkunde)">lijnen</a>, <a href="/wiki/Kromme" title="Kromme">krommen</a> en <a href="/wiki/Vlak_(meetkunde)" title="Vlak (meetkunde)">vlakken</a>. Euclides' behandeling van de meetkunde – de <a href="/wiki/Euclidische_meetkunde" title="Euclidische meetkunde">euclidische meetkunde</a> – was bijna 2000 jaar de norm, waaraan al het andere werk werd afgemeten. </p> <dl><dt>Opmerkingen</dt></dl> <ul><li><i>De</i> meetkunde is een deelwetenschap van de wiskunde. Evenwel, ook de onderwerpen die in de meetkunde worden bestudeerd (de meetkundige structuren), worden <i>meetkunde</i> genoemd: zo'n onderwerp is dan <i>een</i> meetkunde; zie het hierna volgende overzicht waarin enkele van die meetkundes worden genoemd.</li> <li>Daarnaast wordt meetkunde ook <a href="/wiki/Metonymie" title="Metonymie">metonymisch</a> gebruikt: les krijgen in de meetkunde ("het volgende lesuur hebben we meetkunde").</li> <li>De beschrijving van ruimtelijke objecten, zoals wegen en gebouwen, wordt vaak de geometrie van zo'n object genoemd. Betreft dat gebouwen, dan spreekt men van <i>pandgeometrie</i>.<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></li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overzicht">Overzicht</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=1" title="Bewerk dit kopje: Overzicht" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=1" title="De broncode bewerken van de sectie: Overzicht"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De ons bekende ontwikkeling van de meetkunde omspant meer dan twee <a href="/wiki/Millennium" title="Millennium">millennia</a>. De opvatting wat men precies onder meetkunde verstaat heeft door de eeuwen heen een evolutie doorgemaakt. </p> <div class="mw-heading mw-heading3"><h3 id="Praktische_meetkunde">Praktische meetkunde</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=2" title="Bewerk dit kopje: Praktische meetkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=2" title="De broncode bewerken van de sectie: Praktische meetkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Regelmatig_achtvlak.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Regelmatig_achtvlak.png/260px-Regelmatig_achtvlak.png" decoding="async" width="260" height="261" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Regelmatig_achtvlak.png/390px-Regelmatig_achtvlak.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Regelmatig_achtvlak.png/520px-Regelmatig_achtvlak.png 2x" data-file-width="524" data-file-height="526" /></a><figcaption>Een regelmatig achtvlak is een meetkundig figuur</figcaption></figure> <p>Er bestaat weinig twijfel dat de meetkunde is ontstaan als een <i>praktische</i> wetenschap, die zich bezighield met <a href="/wiki/Landmeetkunde" title="Landmeetkunde">landmeten</a>, afmetingen van voorwerpen, <a href="/wiki/Oppervlakte" title="Oppervlakte">oppervlakte</a> en <a href="/wiki/Inhoud_(volume)" title="Inhoud (volume)">volumen</a>. Onder de opmerkelijke prestaties vindt men de formules voor het berekenen van <a href="/wiki/Lengte_(meetkunde)" title="Lengte (meetkunde)">lengten</a>, oppervlakten en inhoud (volume), zoals de <a href="/wiki/Stelling_van_Pythagoras" title="Stelling van Pythagoras">stelling van Pythagoras</a>, <a href="/wiki/Omtrek" title="Omtrek">omtrek</a> en oppervlakte van een cirkel, oppervlakte van een <a href="/wiki/Driehoek_(meetkunde)" title="Driehoek (meetkunde)">driehoek</a>, het volume van een <a href="/wiki/Cilinder_(meetkunde)" title="Cilinder (meetkunde)">cilinder</a>, <a href="/wiki/Sfeer_(wiskunde)" title="Sfeer (wiskunde)">sfeer</a> of <a href="/wiki/Piramide_(ruimtelijke_figuur)" title="Piramide (ruimtelijke figuur)">piramide</a>. Ontwikkelingen in de <a href="/wiki/Astronomie" title="Astronomie">astronomie</a> hebben samen met de daarmee gepaard gaande computationele technieken tot de opkomst van de <a href="/wiki/Goniometrie" title="Goniometrie">trigonometrie</a> (goniometrie) en de <a href="/wiki/Boldriehoeksmeting" title="Boldriehoeksmeting">boldriehoeksmeetkunde</a> geleid. </p> <div class="mw-heading mw-heading3"><h3 id="Axiomatische_meetkunde">Axiomatische meetkunde</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=3" title="Bewerk dit kopje: Axiomatische meetkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=3" title="De broncode bewerken van de sectie: Axiomatische meetkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Een methode om bepaalde ontoegankelijke afstanden en hoogten te berekenen op basis van <a href="/wiki/Gelijkvormigheid_(meetkunde)" title="Gelijkvormigheid (meetkunde)">gelijkvormigheid</a> van meetkundige figuren wordt toegeschreven aan <a href="/wiki/Thales_van_Milete" title="Thales van Milete">Thales van Milete</a>. Deze methode liep vooruit op de meer abstracte benadering van de meetkunde, zoals door <a href="/wiki/Euclides_van_Alexandri%C3%AB" title="Euclides van Alexandrië">Euclides van Alexandrië</a> uiteen werd gezet in zijn <a href="/wiki/Elementen_van_Euclides" class="mw-redirect" title="Elementen van Euclides">Elementen</a>. Euclides voerde bepaalde <a href="/wiki/Axioma" title="Axioma">axioma</a>'s (ook postulaten genoemd) in, op basis waarvan hij primaire of vanzelfsprekende eigenschappen van punten, lijnen en vlakken formuleerde. Daarna ging hij over tot een strenge <a href="/wiki/Deductie" title="Deductie">deductie</a> van andere eigenschappen van deze <a href="/wiki/Wiskundig_object" class="mw-redirect" title="Wiskundig object">wiskundige objecten</a> met behulp van wiskundige en logische redeneringen. Het karakteristieke kenmerk van de aanpak van Euclides van de meetkunde was haar strengheid. In het begin van de 20e eeuw gebruikte <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a> een eigen <a href="/wiki/Hilberts_axiomasysteem_van_de_euclidische_meetkunde" title="Hilberts axiomasysteem van de euclidische meetkunde">axiomatisch systeem</a> in zijn poging om Euclides' werk te updaten en zo een modern fundament voor de meetkunde te leggen. </p> <div class="mw-heading mw-heading3"><h3 id="Meetkundige_constructies">Meetkundige constructies</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=4" title="Bewerk dit kopje: Meetkundige constructies" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=4" title="De broncode bewerken van de sectie: Meetkundige constructies"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote" style="margin-bottom:0.5em; padding:0.5em 0 0.5em 1.6em; font-size:95%;" role="note"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/15px-1rightarrow_blue.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/23px-1rightarrow_blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/30px-1rightarrow_blue.svg.png 2x" data-file-width="480" data-file-height="480" /></span></span> <i>Zie <a href="/wiki/Constructie_met_passer_en_liniaal" title="Constructie met passer en liniaal">Constructie met passer en liniaal</a> voor het hoofdartikel over dit onderwerp.</i></div> <p>In de Griekse oudheid besteedden wiskundigen bijzondere aandacht aan de constructie van reeds bekende meetkundige objecten. Klassieke instrumenten die werden toegestaan in de meetkundige constructies waren de <a href="/wiki/Passer_(gereedschap)" title="Passer (gereedschap)">passer</a> en een <a href="/wiki/Liniaal" title="Liniaal">liniaal</a> zonder schaalverdeling; dat laatste omdat er nog geen symbolische notatie van getallen was. Getalwaarden werden weergegeven door geconstrueerde lengten en oppervlakten. Sommige problemen bleken echter moeilijk of onmogelijk met deze middelen alleen op te lossen. Men vond ingenieuze constructies met behulp van parabolen en andere krommen, zelfs mechanische apparaten. De aanpak van meetkundige problemen met meetkundige of mechanische middelen staat bekend als de <a href="/wiki/Synthetische_meetkunde" title="Synthetische meetkunde">synthetische meetkunde</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Analytische_meetkunde">Analytische meetkunde</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=5" title="Bewerk dit kopje: Analytische meetkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=5" title="De broncode bewerken van de sectie: Analytische meetkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote" style="margin-bottom:0.5em; padding:0.5em 0 0.5em 1.6em; font-size:95%;" role="note"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/15px-1rightarrow_blue.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/23px-1rightarrow_blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/30px-1rightarrow_blue.svg.png 2x" data-file-width="480" data-file-height="480" /></span></span> <i>Zie <a href="/wiki/Analytische_meetkunde" title="Analytische meetkunde">Analytische meetkunde</a> voor het hoofdartikel over dit onderwerp.</i></div> <p>De <a href="/wiki/Pythagorisme_(Pythagoras)" title="Pythagorisme (Pythagoras)">Pythagoreërs</a> beschouwden reeds de rol van <a href="/wiki/Getal_(wiskunde)" title="Getal (wiskunde)">getallen</a> in de meetkunde. De ontdekking van de <a href="/wiki/Commensurabiliteit_(wiskunde)" class="mw-redirect" title="Commensurabiliteit (wiskunde)">incommensurabele</a> lengten, die volkomen in strijd waren met hun filosofische opvattingen, zorgde echter voor een crisis en leidde ertoe dat men de studie van de (abstracte) getallen verliet ten gunste van (concrete) meetkundige grootheden, zoals de lengte en de oppervlakte van figuren. Getallen werden in de vorm van <a href="/wiki/Co%C3%B6rdinatenstelsel" title="Coördinatenstelsel">coördinaten</a> pas opnieuw in de meetkunde geïntroduceerd door <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a>, die besefte dat de studie van meetkundige vormen door hun <a href="/wiki/Algebra" title="Algebra">algebraïsche</a> weergave kan worden vergemakkelijkt. De <a href="/wiki/Analytische_meetkunde" title="Analytische meetkunde">analytische meetkunde</a> past algebraïsche methoden toe op de meetkundige vragen, typisch door meetkundige <a href="/wiki/Kromme" title="Kromme">krommen</a> en algebraïsche <a href="/wiki/Vergelijking_(wiskunde)" title="Vergelijking (wiskunde)">vergelijkingen</a> aan elkaar te relateren. Deze ideeën speelden in de 17e eeuw een belangrijke rol in de ontwikkeling van de <a href="/wiki/Analyse_(wiskunde)" title="Analyse (wiskunde)">analyse</a> en leidden tot de ontdekking van vele nieuwe eigenschappen van <a href="/wiki/Kromme" title="Kromme">krommen</a>. De moderne <a href="/wiki/Algebra%C3%AFsche_meetkunde" title="Algebraïsche meetkunde">algebraïsche meetkunde</a> beschouwt gelijksoortige vragen, maar dan op een veel abstracter niveau. </p> <div class="mw-heading mw-heading4"><h4 id="Vectormeetkunde">Vectormeetkunde</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=6" title="Bewerk dit kopje: Vectormeetkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=6" title="De broncode bewerken van de sectie: Vectormeetkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Meetkunde met behulp van <a href="/wiki/Vector_(wiskunde)" title="Vector (wiskunde)">vectoren</a> en vectorvoorstellingen. Door vectoren uit te drukken als de coördinaten van hun eindpunten, kan vectormeetkunde herleid worden tot analytische meetkunde. Allerlei meetkundige grootheden, waarvan afstanden en lengten slechts de eenvoudigste voorbeelden zijn, kunnen zo overzichtelijk worden berekend, in twee, drie of (veel) meer dimensies. Ingewikkelde fysische problemen kunnen zo met methodes uit de analytische meetkunde worden berekend, terwijl andersom meetkundige inzichten langs deze weg kunnen worden toegepast op algebraïsche en fysische problemen. </p> <div class="mw-heading mw-heading3"><h3 id="Projectieve_meetkunde">Projectieve meetkunde</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=7" title="Bewerk dit kopje: Projectieve meetkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=7" title="De broncode bewerken van de sectie: Projectieve meetkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote" style="margin-bottom:0.5em; padding:0.5em 0 0.5em 1.6em; font-size:95%;" role="note"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/15px-1rightarrow_blue.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/23px-1rightarrow_blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/30px-1rightarrow_blue.svg.png 2x" data-file-width="480" data-file-height="480" /></span></span> <i>Zie <a href="/wiki/Projectieve_meetkunde" title="Projectieve meetkunde">Projectieve meetkunde</a> voor het hoofdartikel over dit onderwerp.</i></div> <p>Meetkundigen beschouwden in de <a href="/wiki/Klassieke_oudheid" title="Klassieke oudheid">klassieke oudheid</a> vragen van relatieve posities of de ruimtelijke relatie van meetkundige figuren en vormen. Enkele voorbeelden worden gegeven door <a href="/wiki/Ingeschreven_cirkel" title="Ingeschreven cirkel">ingeschreven-</a> en <a href="/wiki/Omgeschreven_cirkel" title="Omgeschreven cirkel">omgeschreven cirkels</a> van <a href="/wiki/Veelhoek" title="Veelhoek">veelhoeken</a>, lijnen die <a href="/wiki/Kegelsnede" title="Kegelsnede">kegelsneden</a> doorsnijden en raken, de <a href="/wiki/Stelling_van_Pappos" title="Stelling van Pappos">stellingen van Pappos</a> en <a href="/wiki/Stelling_van_Menelaos" title="Stelling van Menelaos">Menelaos</a> configuraties van punten en lijnen. In de middeleeuwen werden nieuwe en ingewikkeldere onderwerpen van dit type bestudeerd: zoals voor <a href="/wiki/Sfeer_(wiskunde)" title="Sfeer (wiskunde)">bollen</a> het <a href="/wiki/Kusgetal" title="Kusgetal">kusgetal</a>, de <a href="/wiki/Dichtste_bolstapeling" title="Dichtste bolstapeling">dichtste stapeling</a> en het <a href="/wiki/Vermoeden_van_Kepler" title="Vermoeden van Kepler">vermoeden van Kepler</a>. De meeste van deze vragen betreffen 'vaste' meetkundige vormen, zoals lijnen of bollen. <a href="/wiki/Projectieve_meetkunde" title="Projectieve meetkunde">Projectieve</a>, <a href="/wiki/Convexe_meetkunde" title="Convexe meetkunde">convexe</a> en <a href="/wiki/Discrete_wiskunde" title="Discrete wiskunde">discrete meetkunde</a> zijn drie subdisciplines binnen de huidige meetkunde, die zich met deze en aanverwante vragen bezighouden. </p><p>Een nieuw hoofdstuk in <i>Geometria situs</i> werd door <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> geopend, die metrische eigenschappen van meetkundige figuren opmerkte en hun meest fundamentele meetkundige structuren louter en alleen op basis van vorm bestudeerde. <a href="/wiki/Topologie" title="Topologie">Topologie</a> kwam voort uit de meetkunde, maar veranderde in een groot onafhankelijk deelgebied van de wiskunde, waar geen onderscheid wordt gemaakt tussen wiskundige objecten die door een continue transformatie in elkaar over kunnen gaan. De objecten kunnen evenwel nog enige meetkundige eigenschappen bewaren, zoals in het geval van hyperbolische knopen. </p> <div class="mw-heading mw-heading3"><h3 id="Niet-euclidische_meetkunde">Niet-euclidische meetkunde</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=8" title="Bewerk dit kopje: Niet-euclidische meetkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=8" title="De broncode bewerken van de sectie: Niet-euclidische meetkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote" style="margin-bottom:0.5em; padding:0.5em 0 0.5em 1.6em; font-size:95%;" role="note"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/15px-1rightarrow_blue.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/23px-1rightarrow_blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/30px-1rightarrow_blue.svg.png 2x" data-file-width="480" data-file-height="480" /></span></span> <i>Zie <a href="/wiki/Niet-euclidische_meetkunde" title="Niet-euclidische meetkunde">Niet-euclidische meetkunde</a> voor het hoofdartikel over dit onderwerp.</i></div> <p>In de meer dan tweeduizend jaar sinds Euclides bleef het basisbegrip van de <a href="/wiki/Ruimte_(wiskunde)" title="Ruimte (wiskunde)">ruimte</a> in essentie onveranderd. Dit hoewel het bereik van de gestelde en beantwoorde meetkundige vragen zich in deze tijd onvermijdelijk sterk uitbreidde. <a href="/wiki/Immanuel_Kant" title="Immanuel Kant">Immanuel Kant</a> voerde aan dat er slechts een, <i>absolute</i>, meetkunde bestond, die door een innerlijke faculteit van de geest als <i><a href="/wiki/A_priori" title="A priori">a priori</a></i> voor waar aangezien werd: <a href="/wiki/Euclidische_meetkunde" title="Euclidische meetkunde">euclidische meetkunde</a> was <a href="/wiki/Analytisch_oordeel" class="mw-redirect" title="Analytisch oordeel">synthetisch a priori</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Deze dominante opvatting werd op zijn kop gezet door de revolutionaire ontdekking van de niet-euclidische meetkunde in de werken van <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a> (die deze theorie overigens nooit publiceerde), <a href="/wiki/J%C3%A1nos_Bolyai" title="János Bolyai">Bolyai</a>, en <a href="/wiki/Nikolaj_Lobatsjevski" title="Nikolaj Lobatsjevski">Lobatsjevski</a>, die heeft aangetoond dat de gewone <a href="/wiki/Euclidische_ruimte" title="Euclidische ruimte">euclidische ruimte</a> slechts een van de mogelijke bases voor de ontwikkeling van een meetkunde is. Een brede visie op het onderwerp van de meetkunde werd vervolgens door <a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Bernhard Riemann</a> tot uitdrukking gebracht in zijn inaugurele college <i>Über die hypothesen, welche der Geometrie zu Grunde liegen</i> (Over de hypotheses, die ten grondslag liggen aan de meetkunde), dat pas na zijn dood werd gepubliceerd. Riemanns nieuwe ideeën over de ruimte bleken van cruciaal belang in de ontwikkeling van de <a href="/wiki/Albert_Einstein" title="Albert Einstein">Einsteins</a> <a href="/wiki/Algemene_relativiteitstheorie" title="Algemene relativiteitstheorie">algemene relativiteitstheorie</a> en de <a href="/wiki/Riemann-meetkunde" title="Riemann-meetkunde">Riemann-meetkunde</a>, waarin zeer algemene ruimten worden beschouwd, waarin het begrip lengte is gedefinieerd. </p> <div class="mw-heading mw-heading3"><h3 id="Symmetrie">Symmetrie</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=9" title="Bewerk dit kopje: Symmetrie" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=9" title="De broncode bewerken van de sectie: Symmetrie"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote" style="margin-bottom:0.5em; padding:0.5em 0 0.5em 1.6em; font-size:95%;" role="note"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/15px-1rightarrow_blue.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/23px-1rightarrow_blue.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/1rightarrow_blue.svg/30px-1rightarrow_blue.svg.png 2x" data-file-width="480" data-file-height="480" /></span></span> <i>Zie <a href="/wiki/Symmetrie" title="Symmetrie">Symmetrie</a> voor het hoofdartikel over dit onderwerp.</i></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Bestand:3-7_kisrhombille.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/3-7_kisrhombille.svg/120px-3-7_kisrhombille.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7c/3-7_kisrhombille.svg/180px-3-7_kisrhombille.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7c/3-7_kisrhombille.svg/240px-3-7_kisrhombille.svg.png 2x" data-file-width="2000" data-file-height="2000" /></a><figcaption>Een <a href="/wiki/Betegeling" title="Betegeling">betegeling</a> van het <a href="/w/index.php?title=Hyperbolisch_vlak&action=edit&redlink=1" class="new" title="Hyperbolisch vlak (de pagina bestaat niet)">hyperbolische vlak</a></figcaption></figure> <p>Het thema van <a href="/wiki/Symmetrie" title="Symmetrie">symmetrie</a> in de meetkunde is bijna zo oud als de wetenschap van de meetkunde zelf. De <a href="/wiki/Cirkel" title="Cirkel">cirkel</a>, de <a href="/wiki/Regelmatige_veelhoek" title="Regelmatige veelhoek">regelmatige veelhoeken</a> en <a href="/wiki/Regelmatig_veelvlak" title="Regelmatig veelvlak">regelmatige veelvlakken</a> of platonische lichamen bezaten voor vele antieke filosofen een diepe betekenis en werden in de tijd van Euclides in detail onderzocht. Symmetrische patronen komen in de natuur voor en werden kunstzinnig in een veelheid van vormen weergegeven, waaronder de in wiskundige kringen bijzonder geliefde grafieken van <a href="/wiki/Maurits_Cornelis_Escher" title="Maurits Cornelis Escher">Escher</a>. Toch was het pas in de tweede helft van de 19e eeuw dat de verbindende rol van symmetrie in de grondslagen van de meetkunde werd herkend. <a href="/wiki/Felix_Klein" title="Felix Klein">Felix Kleins</a> <a href="/wiki/Erlanger_Programm" title="Erlanger Programm">Erlanger Programm</a> verklaarde dat, in een zeer precieze betekenis, symmetrie, uitgedrukt via de notie van een transformatie<a href="/wiki/Groep_(wiskunde)" title="Groep (wiskunde)">groep</a>, bepaalt wat meetkunde <i>is</i>. In de klassieke <a href="/wiki/Euclidische_meetkunde" title="Euclidische meetkunde">euclidische meetkunde</a> wordt symmetrie vertegenwoordigd door <a href="/wiki/Congruentie_(meetkunde)" title="Congruentie (meetkunde)">congruenties</a> en vaste bewegingen, terwijl in de <a href="/wiki/Projectieve_meetkunde" title="Projectieve meetkunde">projectieve meetkunde</a> een analoge rol wordt gespeeld door <a href="/w/index.php?title=Collineatie&action=edit&redlink=1" class="new" title="Collineatie (de pagina bestaat niet)">collineaties</a>, meetkundige transformaties die rechte lijnen in rechte lijnen transformeren. Het was echter in de nieuwe meetkunden van Bolyai en Lobatsjevski, Riemann, <a href="/wiki/William_Kingdon_Clifford" title="William Kingdon Clifford">Clifford</a> en Klein, en <a href="/wiki/Sophus_Lie" title="Sophus Lie">Sophus Lie</a> dat Kleins idee om een 'meetkunde te definiëren via haar <a href="/wiki/Symmetriegroep" title="Symmetriegroep">symmetriegroep</a>' het meest invloedrijk bleek. Zowel discrete als continue symmetrieën spelen een prominente rol in de meetkunde, de eerste in de <a href="/wiki/Topologie" title="Topologie">topologie</a> en <a href="/wiki/Meetkundige_groepentheorie" title="Meetkundige groepentheorie">meetkundige groepentheorie</a>, de laatste in de <a href="/wiki/Lie-theorie" title="Lie-theorie">Lie-theorie</a> en de <a href="/wiki/Riemann-meetkunde" title="Riemann-meetkunde">Riemann-meetkunde</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Moderne_meetkunde">Moderne meetkunde</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=10" title="Bewerk dit kopje: Moderne meetkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=10" title="De broncode bewerken van de sectie: Moderne meetkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Moderne meetkunde</i> is de titel van een populair handboek door Dubrovin, <a href="/wiki/Sergej_Novikov_(wiskundige)" title="Sergej Novikov (wiskundige)">Novikov</a> en Fomenko, waarvan de eerste editie in 1979 (in het Russisch) werd gepubliceerd. Het bijna 1000 pagina's dikke boek heeft een belangrijke leidraad: meetkundige structuren van verschillende typen <a href="/wiki/Vari%C3%ABteit_(wiskunde)" title="Variëteit (wiskunde)">variëteiten</a> en hun toepassingen in de hedendaagse <a href="/wiki/Theoretische_natuurkunde" title="Theoretische natuurkunde">theoretische natuurkunde</a>. Een kwart eeuw na haar publicatie blijven de <a href="/wiki/Differentiaalmeetkunde" title="Differentiaalmeetkunde">differentiaalmeetkunde</a>, <a href="/wiki/Algebra%C3%AFsche_meetkunde" title="Algebraïsche meetkunde">algebraïsche meetkunde</a>, <a href="/wiki/Symplectische_meetkunde" title="Symplectische meetkunde">symplectische meetkunde</a> en <a href="/wiki/Lie-theorie" title="Lie-theorie">Lie-theorie</a>, die in dit boek worden behandeld, tot de meest zichtbare gebieden van de moderne meetkunde behoren, met meerdere verbindingen naar andere deelgebieden van de wiskunde en de natuurkunde. </p> <div class="mw-heading mw-heading2"><h2 id="Geschiedenis_van_de_meetkunde">Geschiedenis van de meetkunde</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=11" title="Bewerk dit kopje: Geschiedenis van de meetkunde" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=11" title="De broncode bewerken van de sectie: Geschiedenis van de meetkunde"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>De <a href="/wiki/Landmeetkunde" title="Landmeetkunde">landmeetkunde</a> ontwikkelde zich bij de <a href="/wiki/Oude_Egypte" title="Oude Egypte">oude Egyptenaren</a>: ieder jaar stroomde de <a href="/wiki/Nijl" title="Nijl">Nijl</a> over en veranderde het land. Met hun nieuwe inzicht konden zij de meetkunde gebruiken in de <a href="/wiki/Architectuur" title="Architectuur">architectuur</a>, de <a href="/wiki/Astronomie" title="Astronomie">astronomie</a> en de <a href="/wiki/Landbouw" title="Landbouw">landbouw</a>. </p><p>De <a href="/wiki/Elementen_van_Euclides" class="mw-redirect" title="Elementen van Euclides">Elementen</a> van <a href="/wiki/Euclides_van_Alexandri%C3%AB" title="Euclides van Alexandrië">Euclides</a> van omstreeks <a href="/wiki/300_v.Chr." title="300 v.Chr.">300 v.Chr.</a>, was een van de belangrijkste vroege teksten over de meetkunde. In dit werk presenteerde Euclides de meetkunde in een ideale <a href="/wiki/Axioma" title="Axioma">axiomatische</a> vorm die bekend kwam te staan als de <a href="/wiki/Euclidische_meetkunde" title="Euclidische meetkunde">euclidische meetkunde</a>. De verhandeling is niet, zoals soms wordt gedacht, een compendium van alles wat de <a href="/wiki/Hellenisme" title="Hellenisme">Hellenistische</a> wiskundigen op dat moment over de meetkunde wisten, maar veeleer is het een elementaire inleiding tot de toenmalige wiskunde,<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> die voor een groot deel overeenkomt met wat wij tegenwoordig meetkunde noemen. Euclides schreef zelf acht meer geavanceerde boeken over de meetkunde. We weten uit verwijzingen in andere klassieke werken dat de Elementen niet het eerste elementaire meetkundige leerboek was, maar na het verschijnen van het werk van Euclides, raakten de eerdere werken in onbruik en omdat zij niet meer gekopieerd werden, gingen zij op den duur verloren. </p><p>Gedurende lange tijd was de meetkunde de studie van vlakke en ruimtelijke figuren. </p><p>In het begin van de 17e eeuw vonden er twee belangrijke ontwikkelingen in de meetkunde plaats. De eerste, en belangrijkste, was de formulering van de <a href="/wiki/Analytische_meetkunde" title="Analytische meetkunde">analytische meetkunde</a>, of meetkunde met <a href="/wiki/Co%C3%B6rdinatenstelsel" title="Coördinatenstelsel">coördinaten</a> en <a href="/wiki/Vergelijking_(wiskunde)" title="Vergelijking (wiskunde)">vergelijkingen</a> door <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> (1596-1650) en <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a> (1601-1665). In deze analytische meetkunde voerde men een rechthoekig assenstelsel in, waarmee meetkundige objecten met behulp van getallen en vergelijkingen konden worden beschreven. </p><p>Dit was een noodzakelijke voorloper van de ontwikkeling van de <a href="/wiki/Analyse_(wiskunde)" title="Analyse (wiskunde)">analyse</a> en een exacte kwantitatieve <a href="/wiki/Natuurkunde" title="Natuurkunde">natuurwetenschap</a>. De tweede meetkundige ontwikkeling in deze periode was de systematische studie van de <a href="/wiki/Projectieve_meetkunde" title="Projectieve meetkunde">projectieve meetkunde</a> door <a href="/wiki/Girard_Desargues" title="Girard Desargues">Girard Desargues</a> (1591-1661). Projectieve meetkunde is de studie van de meetkunde zonder metingen, alleen de manier hoe punten zich ten opzichte van elkaar verhouden wordt bestudeerd. </p><p>Ook in de 19e eeuw veranderden twee ontwikkelingen in de meetkunde de manier, waarop de meetkunde werd bestudeerd. Dit waren de ontdekking van de niet-euclidische meetkundes door <a href="/wiki/Nikolaj_Lobatsjevski" title="Nikolaj Lobatsjevski">Lobatsjevski</a>, <a href="/wiki/J%C3%A1nos_Bolyai" title="János Bolyai">Bolyai</a> en <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a> en de formulering van het begrip <a href="/wiki/Symmetrie" title="Symmetrie">symmetrie</a> als de centrale overweging in het <a href="/wiki/Erlanger_Programm" title="Erlanger Programm">Erlanger Programm</a> van <a href="/wiki/Felix_Klein" title="Felix Klein">Felix Klein</a>. </p><p>De aanleiding voor de niet-euclidische meetkunde was een heel praktische: de klassieke tweedimensionale euclidische meetkunde is niet op het aardoppervlak van toepassing; op het <a href="/wiki/Kromming_(meetkunde)" title="Kromming (meetkunde)">gekromde</a> vlak geldt het <a href="/wiki/Parallellenpostulaat" title="Parallellenpostulaat">parallellenpostulaat</a> van Euclides niet. Langzaamaan ontstonden er meer verschillende niet-euclidische meetkundes. Deze meetkunden bleken bijvoorbeeld zeer goed bruikbaar bij de beschrijving van de <a href="/wiki/Ruimte_(natuurkunde)" title="Ruimte (natuurkunde)">ruimte</a> volgens de <a href="/wiki/Algemene_relativiteitstheorie" title="Algemene relativiteitstheorie">algemene relativiteitstheorie</a> van <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>. Tegenwoordig blijft de meetkunde dus zeker niet meer alleen beperkt tot het <a href="/wiki/Vlak_(meetkunde)" title="Vlak (meetkunde)">platte vlak</a>; een ruimte kan veel meer <a href="/wiki/Dimensie_(algemeen)" title="Dimensie (algemeen)">dimensies</a> hebben, en bijvoorbeeld ook oprekbaar zijn. Zie bijvoorbeeld de <a href="/wiki/Topologie" title="Topologie">topologie</a>, ofwel de meetkunde van rekbare <a href="/wiki/Oppervlak_(topologie)" title="Oppervlak (topologie)">oppervlakken</a>. De <a href="/wiki/Ruimtemeetkunde" title="Ruimtemeetkunde">stereometrie</a> is de meetkunde in drie dimensies. </p><p>Klein veralgemeende de euclidische en de niet-euclidische meetkundes. Twee van de belangrijkste meetkundigen van de 19e eeuw waren <a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Bernhard Riemann</a>, die voornamelijk met instrumenten uit de <a href="/wiki/Analyse_(wiskunde)" title="Analyse (wiskunde)">wiskundige analyse</a> werkte en die het <a href="/wiki/Riemann-oppervlak" title="Riemann-oppervlak">Riemann-oppervlak</a> introduceerde, en <a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a>, de man die de <a href="/wiki/Algebra%C3%AFsche_topologie" title="Algebraïsche topologie">algebraïsche topologie</a> en de meetkundige theorie van <a href="/wiki/Dynamisch_systeem" title="Dynamisch systeem">dynamische systemen</a> introduceerde. </p><p>Tegelijk, aan het begin van de 19e eeuw werd door <a href="/wiki/Gaspard_Monge" title="Gaspard Monge">Gaspard Monge</a> de <a href="/wiki/Beschrijvende_meetkunde" title="Beschrijvende meetkunde">beschrijvende meetkunde</a> ontwikkeld. </p> <div class="mw-heading mw-heading2"><h2 id="Externe_link">Externe link</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=12" title="Bewerk dit kopje: Externe link" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=12" title="De broncode bewerken van de sectie: Externe link"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a class="external text" href="https://nl.wikibooks.org/wiki/Vectormeetkunde">Wikiboek: Vectormeetkunde</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voetnoten">Voetnoten</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkunde&veaction=edit&section=13" title="Bewerk dit kopje: Voetnoten" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkunde&action=edit&section=13" title="De broncode bewerken van de sectie: Voetnoten"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"><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">Margriet van der Heijden. <i>Oerknal: dat is pas klare taal</i>. <a href="/wiki/NRC_Handelsblad" class="mw-redirect" title="NRC Handelsblad">NRC Handelsblad</a>, 15 mei 2021.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://maxius.nl/wet-basisregistraties-adressen-en-gebouwen/artikel7">Wet Basisregistraties adressen en gebouwen (BAG), art. 7</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20231022124327/https://maxius.nl/wet-basisregistraties-adressen-en-gebouwen/artikel7">Gearchiveerd</a> op 22 oktober 2023.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><span style="font-variant:small-caps;"><a href="/wiki/Morris_Kline" title="Morris Kline">Kline</a></span> (1972), <i>Mathematical thought from ancient to modern times</i>, Oxford University Press, blz. 1032. Kant verwierp de logische (analytische a priori) <i>mogelijkheid</i> van de niet-euclidische meetkunde niet, zie <a href="/w/index.php?title=Jeremy_Gray&action=edit&redlink=1" class="new" title="Jeremy Gray (de pagina bestaat niet)">Jeremy Gray</a>, "Ideas of Space Euclidean, Non-Euclidean, and Relativistic", Oxford, 1989; blz. 85. Sommigen hebben geïmpliceerd dat, in dit licht, Kant in feite de ontwikkeling van de niet-euclidische meetkunde had <i>voorspeld</i>, zie Leonard Nelson, "Philosophy and Axiomatics" (Filosofie en axiomatiek), 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"><style data-mw-deduplicate="TemplateStyles:r67679320">.mw-parser-output .taalaanduiding{font-family:sans-serif;font-size:85%;cursor:help;color:var(--color-subtle,#555)}.mw-parser-output .taalaanduiding span{border-bottom:1px dotted var(--color-subtle,#555)}</style><span class="taalaanduiding" title="Taal: Engels">(<span>en</span>) </span> <span style="font-variant:small-caps;"><a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer">Carl Boyer</a></span> (1991), hfdst.: Euclid of Alexandria, blz 104: The Elements was not, as is sometimes thought, a compendium of all geometric knowledge; it was instead an introductory textbook covering all elementary mathematics.</span> </li> </ol></div></div> <style data-mw-deduplicate="TemplateStyles:r67837862">.mw-parser-output .navigatie{position:relative;clear:both;overflow:auto;margin:1em auto -0.5em;padding:2px;background-color:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);text-align:center;font-size:87%}.mw-parser-output .navigatie-bewerken{margin-left:0.5em}.mw-parser-output .navigatie-bewerken .mw-ui-icon::before{background-size:0.9em}.mw-parser-output .navigatie-afb-links,.mw-parser-output .navigatie-afb-rechts{position:absolute}.mw-parser-output .navigatie-afb-rechts{right:2px}.mw-parser-output .navigatie-afb-groot{float:right;padding-left:0.5em}.mw-parser-output .navigatie-titel{background-color:#ddeef8;padding:2px 5.5em;font-weight:bold}.mw-parser-output .navigatie-inhoud{padding:0.5em}.mw-parser-output .navigatie-inhoud p:first-child{margin:0}.mw-parser-output .navigatie div[style*="background-color"],.mw-parser-output .navigatie div[style*="background"]{color:inherit}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navigatie-titel{background-color:var(--background-color-interactive,#eaecf0)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navigatie-titel{background-color:var(--background-color-interactive,#eaecf0)!important}}</style> <div class="navigatie" role="navigation" aria-labelledby="Wiskunde"> <div class="navigatie-afb-links noviewer"><div class="navigatie-bewerken show-autoconfirmed nomobile"><span class="nowrap skin-invert-image"><span typeof="mw:File"><a href="/wiki/Sjabloon:Navigatie_wiskunde" title="Sjabloon:Navigatie wiskunde"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/OOjs_UI_icon_article-ltr.svg/16px-OOjs_UI_icon_article-ltr.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/OOjs_UI_icon_article-ltr.svg/24px-OOjs_UI_icon_article-ltr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/OOjs_UI_icon_article-ltr.svg/32px-OOjs_UI_icon_article-ltr.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span> · <span class="ui-state-disabled" typeof="mw:File"><span title="Overleg sjabloon (de pagina bestaat niet)"><img alt="Overleg sjabloon (de pagina bestaat niet)" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/OOjs_UI_icon_speechBubbles-ltr.svg/16px-OOjs_UI_icon_speechBubbles-ltr.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/OOjs_UI_icon_speechBubbles-ltr.svg/24px-OOjs_UI_icon_speechBubbles-ltr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/OOjs_UI_icon_speechBubbles-ltr.svg/32px-OOjs_UI_icon_speechBubbles-ltr.svg.png 2x" data-file-width="20" data-file-height="20" /></span></span> · <span typeof="mw:File"><a href="//nl.wikipedia.org/w/index.php?title=Sjabloon:Navigatie_wiskunde&action=edit" title="Sjabloon bewerken"><img alt="Sjabloon bewerken" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/16px-OOjs_UI_icon_edit-ltr.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/24px-OOjs_UI_icon_edit-ltr.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr.svg/32px-OOjs_UI_icon_edit-ltr.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></span></div></div> <div id="Wiskunde" class="navigatie-titel"><a href="/wiki/Wiskunde" title="Wiskunde">Wiskunde</a></div> <div class="navigatie-inhoud"> <p><a href="/wiki/Algebra_(hoofdbetekenis)" class="mw-redirect" title="Algebra (hoofdbetekenis)">algebra</a> · <a href="/wiki/Lineaire_algebra" title="Lineaire algebra">lineaire algebra</a> · <a class="mw-selflink selflink">meetkunde</a> · <a href="/wiki/Goniometrie" title="Goniometrie">goniometrie</a> · <a href="/wiki/Rekenen" title="Rekenen">rekenkunde</a> · <a href="/wiki/Integraalrekening" title="Integraalrekening">integraalrekening</a> · <a href="/wiki/Getaltheorie" title="Getaltheorie">getaltheorie</a> · <a href="/wiki/Speltheorie" title="Speltheorie">speltheorie</a> · <a href="/wiki/Groepentheorie" title="Groepentheorie">groepentheorie</a> · <a href="/wiki/Verzamelingenleer" title="Verzamelingenleer">verzamelingenleer</a> · <a href="/wiki/Statistiek" title="Statistiek">statistiek</a> · <a href="/wiki/Kansrekening" title="Kansrekening">kansrekening</a> · <a href="/wiki/Topologie" title="Topologie">topologie</a> </p> </div></div> <div class="interProject commons mw-list-item" style="display:none;"><a href="https://commons.wikimedia.org/wiki/Category:Geometry#mw-subcategories" class="extiw" title="commons:Category:Geometry">Mediabestanden</a></div> <div class="interProjectTemplate interProject-groot toccolours" style="display:flex; gap:1em; align-items:center; clear:both; margin:1em 0 -0.5em 0;"> <div style="min-width:max-content;"><span class="noviewer noresize" typeof="mw:File"><a href="/wiki/Bestand:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/25px-Commons-logo.svg.png" decoding="async" width="25" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/38px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/50px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div>Zie de categorie <i><b><a href="https://commons.wikimedia.org/wiki/Category:Geometry#mw-subcategories" class="extiw" title="commons:Category:Geometry">Geometry</a></b></i> van <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a> voor mediabestanden over dit onderwerp.</div> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Overgenomen van "<a dir="ltr" href="https://nl.wikipedia.org/w/index.php?title=Meetkunde&oldid=68008246">https://nl.wikipedia.org/w/index.php?title=Meetkunde&oldid=68008246</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Categorie:Alles" title="Categorie:Alles">Categorie</a>: <ul><li><a href="/wiki/Categorie:Meetkunde" title="Categorie:Meetkunde">Meetkunde</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Deze pagina is voor het laatst bewerkt op 23 aug 2024 om 15:58.</li> <li id="footer-info-copyright">De tekst is beschikbaar onder de licentie <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.nl">Creative Commons Naamsvermelding/Gelijk delen</a>, er kunnen aanvullende voorwaarden van toepassing zijn. Zie de <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use/nl">gebruiksvoorwaarden</a> voor meer informatie.<br /> Wikipedia® is een geregistreerd handelsmerk van de <a rel="nofollow" class="external text" href="https://www.wikimediafoundation.org">Wikimedia Foundation, Inc.</a>, een organisatie zonder winstoogmerk.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacybeleid</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia">Over Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:Algemeen_voorbehoud">Disclaimers</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Gedragscode</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Ontwikkelaars</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/nl.wikipedia.org">Statistieken</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookieverklaring</a></li> <li id="footer-places-mobileview"><a href="//nl.m.wikipedia.org/w/index.php?title=Meetkunde&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobiele weergave</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-7fc47fc68d-997xx","wgBackendResponseTime":160,"wgPageParseReport":{"limitreport":{"cputime":"0.100","walltime":"0.165","ppvisitednodes":{"value":809,"limit":1000000},"postexpandincludesize":{"value":8903,"limit":2097152},"templateargumentsize":{"value":1252,"limit":2097152},"expansiondepth":{"value":10,"limit":100},"expensivefunctioncount":{"value":1,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":4402,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 96.936 1 -total"," 34.59% 33.534 1 Sjabloon:Commonscat"," 31.36% 30.397 1 Sjabloon:References"," 30.40% 29.464 1 Sjabloon:Zusterproject_box"," 22.47% 21.779 1 Sjabloon:Navigatie_wiskunde"," 18.43% 17.868 1 Sjabloon:Navigatie"," 10.09% 9.780 1 Sjabloon:En"," 9.75% 9.454 5 Sjabloon:Zie_hoofdartikel"," 8.51% 8.248 2 Sjabloon:First_non_empty"," 6.96% 6.746 1 Sjabloon:Taalaanduiding"]},"scribunto":{"limitreport-timeusage":{"value":"0.005","limit":"10.000"},"limitreport-memusage":{"value":638351,"limit":52428800}},"cachereport":{"origin":"mw-web.eqiad.main-5dc8bcfc84-nljtt","timestamp":"20241112071754","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Meetkunde","url":"https:\/\/nl.wikipedia.org\/wiki\/Meetkunde","sameAs":"http:\/\/www.wikidata.org\/entity\/Q8087","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q8087","author":{"@type":"Organization","name":"Bijdragers aan Wikimedia-projecten"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2003-02-07T21:09:46Z","dateModified":"2024-08-23T14:58:35Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/d\/d4\/Woman_teaching_geometry.jpg","headline":"onderdeel van de wiskunde, dat zich richt op de eigenschappen van de ruimte"}</script> </body> </html>