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="pt" dir="ltr"> <head> <meta charset="UTF-8"> <title>Elipsoide – Wikipédia, a enciclopédia livre</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(/(?:^|; )ptwikimwclientpreferences=([^;]+)/);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":["","janeiro","fevereiro","março","abril","maio","junho","julho","agosto","setembro","outubro","novembro","dezembro"],"wgRequestId":"a9e7dbad-9980-4e65-ba3a-f03a78124c52","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Elipsoide","wgTitle":"Elipsoide","wgCurRevisionId":68369566,"wgRevisionId":68369566,"wgArticleId":46124,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["!Artigos que carecem de notas de rodapé desde outubro de 2012","!Artigos que carecem de notas de rodapé sem indicação de tema","Quádricas","Cartografia","Geodésia","Sólidos geométricos"],"wgPageViewLanguage":"pt","wgPageContentLanguage":"pt","wgPageContentModel":"wikitext","wgRelevantPageName":"Elipsoide","wgRelevantArticleId":46124,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[], "wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"pt","pageLanguageDir":"ltr","pageVariantFallbacks":"pt"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":4000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q190046","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":true,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false, "wgSiteNoticeId":"2.30"};RLSTATE={"ext.gadget.FeedbackHighlight-base":"ready","ext.gadget.keepPDU":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","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","ext.dismissableSiteNotice.styles":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.Topicon","ext.gadget.Metacaixa","ext.gadget.TitleRewrite","ext.gadget.ElementosOcultaveis","ext.gadget.FeedbackHighlight","ext.gadget.ReferenceTooltips", "ext.gadget.NewVillagePump","ext.gadget.wikibugs","ext.gadget.charinsert","ext.gadget.requestForAdminship","ext.gadget.WikiMiniAtlas","ext.gadget.PagesForDeletion","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","oojs-ui.styles.icons-media","oojs-ui-core.icons","wikibase.sidebar.tracking","ext.dismissableSiteNotice"];</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=pt&modules=ext.cite.styles%7Cext.dismissableSiteNotice.styles%7Cext.math.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=pt&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=pt&modules=ext.gadget.FeedbackHighlight-base%2CkeepPDU&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=pt&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <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/9/95/Ellipsoid_3d.jpg"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="960"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/9/95/Ellipsoid_3d.jpg"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="640"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="512"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Elipsoide – Wikipédia, a enciclopédia livre"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//pt.m.wikipedia.org/wiki/Elipsoide"> <link rel="alternate" type="application/x-wiki" title="Editar" href="/w/index.php?title=Elipsoide&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="Wikipédia (pt)"> <link rel="EditURI" type="application/rsd+xml" href="//pt.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://pt.wikipedia.org/wiki/Elipsoide"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.pt"> <link rel="alternate" type="application/atom+xml" title="''Feed'' Atom Wikipédia" href="/w/index.php?title=Especial:Mudan%C3%A7as_recentes&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-Elipsoide rootpage-Elipsoide skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Saltar para o conteúdo</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="Menu principal" > <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">Menu principal</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">Menu principal</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">ocultar</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navegação </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:P%C3%A1gina_principal" title="Visitar a página principal [z]" accesskey="z"><span>Página principal</span></a></li><li id="n-featuredcontent" class="mw-list-item"><a href="/wiki/Portal:Conte%C3%BAdo_destacado"><span>Conteúdo destacado</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Eventos_atuais" title="Informação temática sobre eventos atuais"><span>Eventos atuais</span></a></li><li id="n-villagepump" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Esplanada"><span>Esplanada</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Especial:Aleat%C3%B3ria" title="Carregar página aleatória [x]" accesskey="x"><span>Página aleatória</span></a></li><li id="n-portals" class="mw-list-item"><a href="/wiki/Portal:%C3%8Dndice"><span>Portais</span></a></li><li id="n-bug_in_article" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Informe_um_erro"><span>Informar um erro</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Colaboração </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-welcome" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Boas-vindas"><span>Boas-vindas</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Ajuda:P%C3%A1gina_principal" title="Um local reservado para auxílio."><span>Ajuda</span></a></li><li id="n-Páginas-de-testes-públicas" class="mw-list-item"><a href="/wiki/Ajuda:P%C3%A1gina_de_testes"><span>Páginas de testes públicas</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Portal_comunit%C3%A1rio" title="Sobre o projeto"><span>Portal comunitário</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Especial:Mudan%C3%A7as_recentes" title="Uma lista de mudanças recentes nesta wiki [r]" accesskey="r"><span>Mudanças recentes</span></a></li><li id="n-maintenance" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Manuten%C3%A7%C3%A3o"><span>Manutenção</span></a></li><li id="n-createpage" class="mw-list-item"><a href="/wiki/Ajuda:Guia_de_edi%C3%A7%C3%A3o/Como_come%C3%A7ar_uma_p%C3%A1gina"><span>Criar página</span></a></li><li id="n-newpages-description" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginas_novas"><span>Páginas novas</span></a></li><li id="n-contact-description" class="mw-list-item"><a href="/wiki/Wikip%C3%A9dia:Contato"><span>Contato</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Wikip%C3%A9dia:P%C3%A1gina_principal" 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="Wikipédia" src="/static/images/mobile/copyright/wikipedia-wordmark-fr.svg" style="width: 7.4375em; height: 1.125em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-pt.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/Especial:Pesquisar" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Pesquisar na Wikipédia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Busca</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="Pesquisar na Wikipédia" aria-label="Pesquisar na Wikipédia" autocapitalize="sentences" title="Pesquisar na Wikipédia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Especial:Pesquisar"> </div> <button class="cdx-button cdx-search-input__end-button">Pesquisar</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Ferramentas pessoais"> <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="Aspeto"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Aspeto" > <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">Aspeto</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=20120521SB001&uselang=pt" class=""><span>Donativos</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=Especial:Criar_conta&returnto=Elipsoide" title="É encorajado a criar uma conta e iniciar sessão; no entanto, não é obrigatório" class=""><span>Criar uma conta</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=Especial:Entrar&returnto=Elipsoide" title="Aconselhamos-lhe a criar uma conta na Wikipédia, embora tal não seja obrigatório. [o]" accesskey="o" class=""><span>Entrar</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="Mais opções" > <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="Ferramentas pessoais" > <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">Ferramentas pessoais</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Menu do utilizador" > <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=20120521SB001&uselang=pt"><span>Donativos</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Criar_conta&returnto=Elipsoide" title="É encorajado a criar uma conta e iniciar sessão; no entanto, não é obrigatório"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Criar uma conta</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Entrar&returnto=Elipsoide" title="Aconselhamos-lhe a criar uma conta na Wikipédia, embora tal não seja obrigatório. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Entrar</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"> Páginas para editores sem sessão iniciada <a href="/wiki/Ajuda:Introduction" aria-label="Saiba mais sobre edição"><span>saber mais</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/Especial:Minhas_contribui%C3%A7%C3%B5es" title="Uma lista de edições feitas a partir deste endereço IP [y]" accesskey="y"><span>Contribuições</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:Minha_discuss%C3%A3o" title="Discussão sobre edições feitas a partir deste endereço IP [n]" accesskey="n"><span>Discussão</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 id="mw-dismissablenotice-anonplace"></div><script>(function(){var node=document.getElementById("mw-dismissablenotice-anonplace");if(node){node.outerHTML="\u003Cdiv class=\"mw-dismissable-notice\"\u003E\u003Cdiv class=\"mw-dismissable-notice-close\"\u003E[\u003Ca tabindex=\"0\" role=\"button\"\u003Eocultar\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv id=\"localNotice\" data-nosnippet=\"\"\u003E\u003Cdiv class=\"anonnotice\" lang=\"pt\" dir=\"ltr\"\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></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="Conteúdo" 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">Conteúdo</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ocultar</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">Início</div> </a> </li> <li id="toc-Volume" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Volume"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Volume</span> </div> </a> <ul id="toc-Volume-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Área_da_superfície" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Área_da_superfície"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Área da superfície</span> </div> </a> <ul id="toc-Área_da_superfície-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Transformações_lineares" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Transformações_lineares"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Transformações lineares</span> </div> </a> <ul id="toc-Transformações_lineares-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aplicação_em_cartografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplicação_em_cartografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Aplicação em cartografia</span> </div> </a> <ul id="toc-Aplicação_em_cartografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ver_também" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ver_também"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Ver também</span> </div> </a> <ul id="toc-Ver_também-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referências" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referências"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Referências</span> </div> </a> <ul id="toc-Referências-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ligações_externas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ligações_externas"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Ligações externas</span> </div> </a> <ul id="toc-Ligações_externas-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="Conteúdo" 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="Alternar o índice" > <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">Alternar o índice</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">Elipsoide</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="Ir para um artigo noutra língua. Disponível em 54 línguas" > <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-54" 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">54 línguas</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B3%D8%B7%D8%AD_%D9%86%D8%A7%D9%82%D8%B5%D9%8A" title="سطح ناقصي — árabe" lang="ar" hreflang="ar" data-title="سطح ناقصي" data-language-autonym="العربية" data-language-local-name="árabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Elipsoide_de_revoluci%C3%B3n" title="Elipsoide de revolución — asturiano" lang="ast" hreflang="ast" data-title="Elipsoide de revolución" data-language-autonym="Asturianu" data-language-local-name="asturiano" 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/Ellipsoid" title="Ellipsoid — azerbaijano" lang="az" hreflang="az" data-title="Ellipsoid" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BB%D1%96%D0%BF%D1%81%D0%BE%D1%96%D0%B4" title="Эліпсоід — bielorrusso" lang="be" hreflang="be" data-title="Эліпсоід" data-language-autonym="Беларуская" data-language-local-name="bielorrusso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Елипсоид — búlgaro" lang="bg" hreflang="bg" data-title="Елипсоид" data-language-autonym="Български" data-language-local-name="búlgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/El%C2%B7lipsoide" title="El·lipsoide — catalão" lang="ca" hreflang="ca" data-title="El·lipsoide" data-language-autonym="Català" data-language-local-name="catalão" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Elipsoid" title="Elipsoid — checo" lang="cs" hreflang="cs" data-title="Elipsoid" data-language-autonym="Čeština" data-language-local-name="checo" 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%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Эллипсоид — chuvash" lang="cv" hreflang="cv" data-title="Эллипсоид" data-language-autonym="Чӑвашла" data-language-local-name="chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Elipsoid" title="Elipsoid — galês" lang="cy" hreflang="cy" data-title="Elipsoid" data-language-autonym="Cymraeg" data-language-local-name="galês" 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/Ellipsoide" title="Ellipsoide — dinamarquês" lang="da" hreflang="da" data-title="Ellipsoide" data-language-autonym="Dansk" data-language-local-name="dinamarquês" 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/Ellipsoid" title="Ellipsoid — alemão" lang="de" hreflang="de" data-title="Ellipsoid" data-language-autonym="Deutsch" data-language-local-name="alemão" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BB%CE%BB%CE%B5%CE%B9%CF%88%CE%BF%CE%B5%CE%B9%CE%B4%CE%AE" title="Ελλειψοειδή — grego" lang="el" hreflang="el" data-title="Ελλειψοειδή" data-language-autonym="Ελληνικά" data-language-local-name="grego" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid — inglês" lang="en" hreflang="en" data-title="Ellipsoid" data-language-autonym="English" data-language-local-name="inglês" 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/Elipsoido" title="Elipsoido — esperanto" lang="eo" hreflang="eo" data-title="Elipsoido" 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/Elipsoide" title="Elipsoide — espanhol" lang="es" hreflang="es" data-title="Elipsoide" data-language-autonym="Español" data-language-local-name="espanhol" 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/Ellipsoid" title="Ellipsoid — estónio" lang="et" hreflang="et" data-title="Ellipsoid" data-language-autonym="Eesti" data-language-local-name="estónio" 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/Elipsoide" title="Elipsoide — basco" lang="eu" hreflang="eu" data-title="Elipsoide" data-language-autonym="Euskara" data-language-local-name="basco" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%DB%8C%D8%B6%DB%8C%E2%80%8C%DA%AF%D9%88%D9%86" title="بیضی‌گون — persa" lang="fa" hreflang="fa" data-title="بیضی‌گون" data-language-autonym="فارسی" data-language-local-name="persa" 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/Ellipsoidi" title="Ellipsoidi — finlandês" lang="fi" hreflang="fi" data-title="Ellipsoidi" data-language-autonym="Suomi" data-language-local-name="finlandês" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Ellipso%C3%AFde" title="Ellipsoïde — francês" lang="fr" hreflang="fr" data-title="Ellipsoïde" data-language-autonym="Français" data-language-local-name="francês" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/%C3%89ileaps%C3%B3ideach" title="Éileapsóideach — irlandês" lang="ga" hreflang="ga" data-title="Éileapsóideach" data-language-autonym="Gaeilge" data-language-local-name="irlandês" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9C%D7%99%D7%A4%D7%A1%D7%95%D7%90%D7%99%D7%93" title="אליפסואיד — hebraico" lang="he" hreflang="he" data-title="אליפסואיד" data-language-autonym="עברית" data-language-local-name="hebraico" 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%A6%E0%A5%80%E0%A4%B0%E0%A5%8D%E0%A4%98%E0%A4%B5%E0%A5%83%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BE%E0%A4%AD" title="दीर्घवृत्ताभ — hindi" lang="hi" hreflang="hi" data-title="दीर्घवृत्ताभ" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Ellipszoid" title="Ellipszoid — húngaro" lang="hu" hreflang="hu" data-title="Ellipszoid" data-language-autonym="Magyar" data-language-local-name="húngaro" 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%B7%D5%AC%D5%AB%D5%BA%D5%BD%D5%B8%D5%AB%D5%A4" title="Էլիպսոիդ — arménio" lang="hy" hreflang="hy" data-title="Էլիպսոիդ" data-language-autonym="Հայերեն" data-language-local-name="arménio" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Elipsoid" title="Elipsoid — indonésio" lang="id" hreflang="id" data-title="Elipsoid" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Sporvala" title="Sporvala — islandês" lang="is" hreflang="is" data-title="Sporvala" data-language-autonym="Íslenska" data-language-local-name="islandês" 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/Ellissoide" title="Ellissoide — italiano" lang="it" hreflang="it" data-title="Ellissoide" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%A5%95%E5%86%86%E4%BD%93" title="楕円体 — japonês" lang="ja" hreflang="ja" data-title="楕円体" data-language-autonym="日本語" data-language-local-name="japonês" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%94%E1%83%9A%E1%83%98%E1%83%A4%E1%83%A1%E1%83%9D%E1%83%98%E1%83%93%E1%83%98" title="ელიფსოიდი — georgiano" lang="ka" hreflang="ka" data-title="ელიფსოიდი" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Эллипсоид — cazaque" lang="kk" hreflang="kk" data-title="Эллипсоид" data-language-autonym="Қазақша" data-language-local-name="cazaque" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%83%80%EC%9B%90%EB%A9%B4" title="타원면 — coreano" lang="ko" hreflang="ko" data-title="타원면" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Эллипсоид — quirguiz" lang="ky" hreflang="ky" data-title="Эллипсоид" data-language-autonym="Кыргызча" data-language-local-name="quirguiz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid — luxemburguês" lang="lb" hreflang="lb" data-title="Ellipsoid" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemburguês" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Elipso%C4%ABds" title="Elipsoīds — letão" lang="lv" hreflang="lv" data-title="Elipsoīds" data-language-autonym="Latviešu" data-language-local-name="letão" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Ellipso%C3%AFde" title="Ellipsoïde — neerlandês" lang="nl" hreflang="nl" data-title="Ellipsoïde" data-language-autonym="Nederlands" data-language-local-name="neerlandês" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Ellipsoide" title="Ellipsoide — norueguês nynorsk" lang="nn" hreflang="nn" data-title="Ellipsoide" data-language-autonym="Norsk nynorsk" data-language-local-name="norueguês 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/Ellipsoide" title="Ellipsoide — norueguês bokmål" lang="nb" hreflang="nb" data-title="Ellipsoide" data-language-autonym="Norsk bokmål" data-language-local-name="norueguês bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Elipsoida" title="Elipsoida — polaco" lang="pl" hreflang="pl" data-title="Elipsoida" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Elipsoid" title="Elipsoid — romeno" lang="ro" hreflang="ro" data-title="Elipsoid" data-language-autonym="Română" data-language-local-name="romeno" 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%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Эллипсоид — russo" lang="ru" hreflang="ru" data-title="Эллипсоид" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid — Simple English" lang="en-simple" hreflang="en-simple" data-title="Ellipsoid" 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/Elipsoid" title="Elipsoid — eslovaco" lang="sk" hreflang="sk" data-title="Elipsoid" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" 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/Elipsoid" title="Elipsoid — esloveno" lang="sl" hreflang="sl" data-title="Elipsoid" data-language-autonym="Slovenščina" data-language-local-name="esloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Elipsoidi" title="Elipsoidi — albanês" lang="sq" hreflang="sq" data-title="Elipsoidi" data-language-autonym="Shqip" data-language-local-name="albanês" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid — sueco" lang="sv" hreflang="sv" data-title="Ellipsoid" data-language-autonym="Svenska" data-language-local-name="sueco" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AF%80%E0%AE%B3%E0%AF%8D%E0%AE%B5%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%BF%E0%AE%A3%E0%AF%8D%E0%AE%AE%E0%AE%AE%E0%AF%8D" title="நீள்வட்டத்திண்மம் — tâmil" lang="ta" hreflang="ta" data-title="நீள்வட்டத்திண்மம்" data-language-autonym="தமிழ்" data-language-local-name="tâmil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%A3%E0%B8%B5" title="ทรงรี — tailandês" lang="th" hreflang="th" data-title="ทรงรี" data-language-autonym="ไทย" data-language-local-name="tailandês" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Elipsoit" title="Elipsoit — turco" lang="tr" hreflang="tr" data-title="Elipsoit" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BB%D1%96%D0%BF%D1%81%D0%BE%D1%97%D0%B4" title="Еліпсоїд — ucraniano" lang="uk" hreflang="uk" data-title="Еліпсоїд" data-language-autonym="Українська" data-language-local-name="ucraniano" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid — usbeque" lang="uz" hreflang="uz" data-title="Ellipsoid" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbeque" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid — vietnamita" lang="vi" hreflang="vi" data-title="Ellipsoid" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%A4%AD%E7%90%83" title="椭球 — chinês" lang="zh" hreflang="zh" data-title="椭球" data-language-autonym="中文" data-language-local-name="chinês" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%A9%A2%E7%90%83" title="橢球 — cantonês" lang="yue" hreflang="yue" data-title="橢球" data-language-autonym="粵語" data-language-local-name="cantonês" class="interlanguage-link-target"><span>粵語</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/Q190046#sitelinks-wikipedia" title="Editar hiperligações interlínguas" class="wbc-editpage">Editar hiperligações</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="Espaços nominais"> <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/Elipsoide" title="Ver a página de conteúdo [c]" accesskey="c"><span>Artigo</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Discuss%C3%A3o:Elipsoide" rel="discussion" title="Discussão sobre o conteúdo da página [t]" accesskey="t"><span>Discussão</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="Mudar a variante da língua" > <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">português</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="Vistas"> <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/Elipsoide"><span>Ler</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Elipsoide&veaction=edit" title="Editar esta página [v]" accesskey="v"><span>Editar</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Elipsoide&action=edit" title="Editar o código-fonte desta página [e]" accesskey="e"><span>Editar código-fonte</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Elipsoide&action=history" title="Edições anteriores desta página. [h]" accesskey="h"><span>Ver histórico</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Ferramentas de página"> <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="Ferramentas" > <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">Ferramentas</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">Ferramentas</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ocultar</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Mais opções" > <div class="vector-menu-heading"> Operações </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/Elipsoide"><span>Ler</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Elipsoide&veaction=edit" title="Editar esta página [v]" accesskey="v"><span>Editar</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Elipsoide&action=edit" title="Editar o código-fonte desta página [e]" accesskey="e"><span>Editar código-fonte</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Elipsoide&action=history"><span>Ver histórico</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Geral </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginas_afluentes/Elipsoide" title="Lista de todas as páginas que contêm hiperligações para esta [j]" accesskey="j"><span>Páginas afluentes</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:Altera%C3%A7%C3%B5es_relacionadas/Elipsoide" rel="nofollow" title="Mudanças recentes nas páginas para as quais esta contém hiperligações [k]" accesskey="k"><span>Alterações relacionadas</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:Carregar_ficheiro" title="Carregar ficheiros [u]" accesskey="u"><span>Carregar ficheiro</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A1ginas_especiais" title="Lista de páginas especiais [q]" accesskey="q"><span>Páginas especiais</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Elipsoide&oldid=68369566" title="Hiperligação permanente para esta revisão desta página"><span>Hiperligação permanente</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Elipsoide&action=info" title="Mais informações sobre esta página"><span>Informações da página</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citar&page=Elipsoide&id=68369566&wpFormIdentifier=titleform" title="Informação sobre como citar esta página"><span>Citar esta página</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:UrlShortener&url=https%3A%2F%2Fpt.wikipedia.org%2Fwiki%2FElipsoide"><span>Obter URL encurtado</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrCode&url=https%3A%2F%2Fpt.wikipedia.org%2Fwiki%2FElipsoide"><span>Descarregar código QR</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"> Imprimir/exportar </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=Especial:Livro&bookcmd=book_creator&referer=Elipsoide"><span>Criar um livro</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Especial:DownloadAsPdf&page=Elipsoide&action=show-download-screen"><span>Descarregar como PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Elipsoide&printable=yes" title="Versão para impressão desta página [p]" accesskey="p"><span>Versão para impressão</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"> Noutros projetos </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:Ellipsoids" 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/Q190046" title="Hiperligação para o elemento do repositório de dados [g]" accesskey="g"><span>Elemento Wikidata</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="Ferramentas de página"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspeto"> <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">Aspeto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mover para a barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ocultar</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">Origem: Wikipédia, a enciclopédia livre.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="pt" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r68971778">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}.mw-parser-output .cmbox{margin:3px 0;border-collapse:collapse;border:1px solid #a2a9b1;background-color:#dfe8ff;box-sizing:border-box;color:var(--color-base)}.mw-parser-output .cmbox-speedy{border:4px solid #b32424;background-color:#ffdbdb}.mw-parser-output .cmbox-delete{background-color:#ffdbdb}.mw-parser-output .cmbox-content{background-color:#ffe7ce}.mw-parser-output .cmbox-style{background-color:#fff9db}.mw-parser-output .cmbox-move{background-color:#e4d8ff}.mw-parser-output .cmbox-protection{background-color:#efefe1}.mw-parser-output .cmbox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .cmbox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .cmbox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .cmbox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .cmbox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .cmbox{margin:3px 10%}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .cmbox{background-color:#0d1a27}html.skin-theme-clientpref-night .mw-parser-output .cmbox-speedy,html.skin-theme-clientpref-night .mw-parser-output .cmbox-delete{background-color:#300}html.skin-theme-clientpref-night .mw-parser-output .cmbox-content{background-color:#331a00}html.skin-theme-clientpref-night .mw-parser-output .cmbox-style{background-color:#332b00}html.skin-theme-clientpref-night .mw-parser-output .cmbox-move{background-color:#08001a}html.skin-theme-clientpref-night .mw-parser-output .cmbox-protection{background-color:#212112}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cmbox{background-color:#0d1a27}html.skin-theme-clientpref-os .mw-parser-output .cmbox-speedy,html.skin-theme-clientpref-os .mw-parser-output .cmbox-delete{background-color:#300}html.skin-theme-clientpref-os .mw-parser-output .cmbox-content{background-color:#331a00}html.skin-theme-clientpref-os .mw-parser-output .cmbox-style{background-color:#332b00}html.skin-theme-clientpref-os .mw-parser-output .cmbox-move{background-color:#08001a}html.skin-theme-clientpref-os .mw-parser-output .cmbox-protection{background-color:#212112}}.mw-parser-output .fmbox{clear:both;margin:0.2em 0;width:100%;border:1px solid #a2a9b1;background-color:var(--background-color-interactive-subtle,#f8f9fa);box-sizing:border-box;color:var(--color-base,#202122)}.mw-parser-output .fmbox-warning{border:1px solid #bb7070;background-color:#ffdbdb}.mw-parser-output .fmbox-editnotice{background-color:transparent}.mw-parser-output .fmbox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .fmbox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .fmbox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .fmbox .mbox-invalid-type{text-align:center}@media screen{html.skin-theme-clientpref-night .mw-parser-output .fmbox-warning{background-color:#683131}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .fmbox-warning{background-color:#683131}}.mw-parser-output .imbox{margin:4px 0;border-collapse:collapse;border:3px solid #36c;background-color:var(--background-color-interactive-subtle,#f8f9fa);box-sizing:border-box}.mw-parser-output .imbox .mbox-text .imbox{margin:0 -0.5em;display:block}.mw-parser-output .imbox-speedy{border:3px solid #b32424;background-color:#fee7e6}.mw-parser-output .imbox-delete{border:3px solid #b32424}.mw-parser-output .imbox-content{border:3px solid #f28500}.mw-parser-output .imbox-style{border:3px solid #fc3}.mw-parser-output .imbox-move{border:3px solid #9932cc}.mw-parser-output .imbox-protection{border:3px solid #a2a9b1}.mw-parser-output .imbox-license{border:3px solid #88a}.mw-parser-output .imbox-featured{border:3px solid #cba135}.mw-parser-output .imbox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .imbox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .imbox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .imbox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .imbox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .imbox{margin:4px 10%}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .imbox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .imbox-speedy{background-color:#310402}}.mw-parser-output .ombox{margin:4px 0;border-collapse:collapse;background-color:var(--background-color-neutral-subtle,#f8f9fa);box-sizing:border-box;border:1px solid #a2a9b1;color:var(--color-base,#202122)}.mw-parser-output .ombox.mbox-small{font-size:88%;line-height:1.25em}.mw-parser-output .ombox-speedy{border:2px solid #b32424;background-color:#fee7e6}.mw-parser-output .ombox-delete{border:2px solid #b32424}.mw-parser-output .ombox-content{border:1px solid #f28500}.mw-parser-output .ombox-style{border:1px solid #fc3}.mw-parser-output .ombox-move{border:1px solid #9932cc}.mw-parser-output .ombox-protection{border:2px solid #a2a9b1}.mw-parser-output .ombox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .ombox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .ombox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .ombox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ombox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .ombox{margin:4px 10%}.mw-parser-output .ombox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}body.skin--responsive .mw-parser-output table.ombox img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .ombox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ombox-speedy{background-color:#310402}}.mw-parser-output .tmbox{margin:4px 0;border-collapse:collapse;border:1px solid #c0c090;background-color:#f8eaba;box-sizing:border-box}.mw-parser-output .tmbox.mbox-small{font-size:88%;line-height:1.25em}.mw-parser-output .tmbox-speedy{border:2px solid #b32424;background-color:#fee7e6}.mw-parser-output .tmbox-delete{border:2px solid #b32424}.mw-parser-output .tmbox-content{border:1px solid #c0c090}.mw-parser-output .tmbox-style{border:2px solid #fc3}.mw-parser-output .tmbox-move{border:2px solid #9932cc}.mw-parser-output .tmbox .mbox-text{border:none;padding:0.25em 0.9em;width:100%}.mw-parser-output .tmbox .mbox-image{border:none;padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .tmbox .mbox-imageright{border:none;padding:2px 0.9em 2px 0;text-align:center}.mw-parser-output .tmbox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .tmbox .mbox-invalid-type{text-align:center}@media(min-width:720px){.mw-parser-output .tmbox{margin:4px 10%}.mw-parser-output .tmbox.mbox-small{clear:right;float:right;margin:4px 0 4px 1em;width:238px}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-night .mw-parser-output .tmbox-speedy{background-color:#310402}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmbox{background-color:#2e2505}html.skin-theme-clientpref-os .mw-parser-output .tmbox-speedy{background-color:#310402}}body.skin--responsive .mw-parser-output table.tmbox img{max-width:none!important}</style><table class="box-Mais_notas plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/Ficheiro:Question_book-new.svg" class="mw-file-description"><img alt="Esta página cita fontes, mas não cobrem todo o conteúdo" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">Esta página <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Cite_as_fontes" title="Wikipédia:Livro de estilo/Cite as fontes">cita fontes</a>, mas que <b><a href="/wiki/Wikip%C3%A9dia:V" class="mw-redirect" title="Wikipédia:V">não cobrem</a> todo o conteúdo</b>.<span class="hide-when-compact"> Ajude a <a href="/wiki/Wikip%C3%A9dia:Livro_de_estilo/Refer%C3%AAncias_e_notas_de_rodap%C3%A9" title="Wikipédia:Livro de estilo/Referências e notas de rodapé">inserir referências</a> (<small><i>Encontre fontes:</i> <span class="plainlinks"><a rel="nofollow" class="external text" href="https://wikipedialibrary.wmflabs.org/">ABW</a>  •  <a rel="nofollow" class="external text" href="https://www.periodicos.capes.gov.br">CAPES</a>  •  <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&as_epq=Elipsoide">Google</a> (<a rel="nofollow" class="external text" href="https://www.google.com/search?hl=pt&tbm=nws&q=Elipsoide&oq=Elipsoide">N</a> • <a rel="nofollow" class="external text" href="http://books.google.com/books?&as_brr=0&as_epq=Elipsoide">L</a> • <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?hl=pt&q=Elipsoide">A</a>)</span></small>).</span> <small class="date-container"><i>(<span class="date">Outubro de 2012</span>)</i></small></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Ellipsoid_3d.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/95/Ellipsoid_3d.jpg/291px-Ellipsoid_3d.jpg" decoding="async" width="291" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/95/Ellipsoid_3d.jpg 1.5x" data-file-width="300" data-file-height="240" /></a><figcaption>Imagem tridimensional de um elipsoide</figcaption></figure> <p>Em <a href="/wiki/Matem%C3%A1tica" title="Matemática">matemática</a>, um <b>elipsoide</b> (pré-<a href="/wiki/Acordo_Ortogr%C3%A1fico_de_1990" title="Acordo Ortográfico de 1990">AO 1990</a>: elipsóide) é uma superfície cuja equação num sistema de <a href="/wiki/Coordenada" class="mw-redirect mw-disambig" title="Coordenada">coordenadas</a> cartesianas <i>x</i>-<i>y</i>-<i>z</i> é </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {x^{2} \over a^{2}}+{y^{2} \over b^{2}}+{z^{2} \over c^{2}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {x^{2} \over a^{2}}+{y^{2} \over b^{2}}+{z^{2} \over c^{2}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/303573ace88047e7932c90d55d2c691d44ce2d39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:19.193ex; height:6.009ex;" alt="{\displaystyle {x^{2} \over a^{2}}+{y^{2} \over b^{2}}+{z^{2} \over c^{2}}=1}"></span></dd></dl> <p>onde <i>a</i>, <i>b</i> e <i>c</i> são <a href="/wiki/N%C3%BAmero_real" title="Número real">números reais</a> positivos que determinam as dimensões e forma do elipsoide. Se dois dos números são iguais, o elipsoide é um <a href="/wiki/Esferoide" title="Esferoide">esferoide</a>; se os três forem iguais, trata-se de uma <a href="/wiki/Esfera_(geometria)" class="mw-redirect" title="Esfera (geometria)">esfera</a>. </p><p>Supondo a ≥ b ≥ c, então: </p> <ul><li>a ≠ b ≠ c : o elipsoide é <b>escaleno</b></li> <li>c = 0 : o elipsoide é <b>plano</b> (duas elipses em simetria)</li> <li>b = c : esferoide em forma de charuto</li> <li>a = b : esferoide em forma de comprimido</li> <li>a = b = c : esfera</li></ul> <p><br /> Os esferoides resultam da rotação de uma <a href="/wiki/Elipse" title="Elipse">elipse</a> em torno de um dos seus eixos. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Volume">Volume</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elipsoide&veaction=edit&section=1" title="Editar secção: Volume" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elipsoide&action=edit&section=1" title="Editar código-fonte da secção: Volume"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>O <a href="/wiki/Volume" title="Volume">volume</a> de um elipsoide é dado por:<sup id="cite_ref-nist_1-0" class="reference"><a href="#cite_note-nist-1"><span>[</span>1<span>]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {4}{3}}\pi abc}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> <mi>π</mi> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {4}{3}}\pi abc}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6bab0d7b6f5d52c794e589223f04011463277e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.565ex; height:5.176ex;" alt="{\displaystyle {\frac {4}{3}}\pi abc}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Área_da_superfície"><span id=".C3.81rea_da_superf.C3.ADcie"></span>Área da superfície</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elipsoide&veaction=edit&section=2" title="Editar secção: Área da superfície" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elipsoide&action=edit&section=2" title="Editar código-fonte da secção: Área da superfície"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/%C3%81rea" title="Área">área</a> da superfície tem uma fórmula mais complexa, dada por: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\pi \left(c^{2}+{\frac {bc^{2}}{\sqrt {a^{2}-c^{2}}}}F(\theta ,m)+b{\sqrt {a^{2}-c^{2}}}E(\theta ,m)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>b</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mi>F</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mi>E</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi \left(c^{2}+{\frac {bc^{2}}{\sqrt {a^{2}-c^{2}}}}F(\theta ,m)+b{\sqrt {a^{2}-c^{2}}}E(\theta ,m)\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d29d2d06a3b9c0e2457396401beae9fa0d610567" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:50.622ex; height:7.509ex;" alt="{\displaystyle 2\pi \left(c^{2}+{\frac {bc^{2}}{\sqrt {a^{2}-c^{2}}}}F(\theta ,m)+b{\sqrt {a^{2}-c^{2}}}E(\theta ,m)\right)}"></span></dd></dl> <p>em que </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2})}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2})}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fd3daf2901d888630395e76a6476c11d74ba76a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:17.022ex; height:6.676ex;" alt="{\displaystyle m={\frac {a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2})}}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta =\arcsin {\left(e\right)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mi>arcsin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =\arcsin {\left(e\right)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3afb0146f8d76777f0a78a92678b89082fa7214" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.431ex; height:2.843ex;" alt="{\displaystyle \theta =\arcsin {\left(e\right)}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e={\sqrt {1-{\frac {c^{2}}{a^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e={\sqrt {1-{\frac {c^{2}}{a^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/395f1ed832bb9f70df4721193be39a960b17e0a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:13.629ex; height:7.509ex;" alt="{\displaystyle e={\sqrt {1-{\frac {c^{2}}{a^{2}}}}}}"></span></dd></dl> <p>e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(\theta ,m)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(\theta ,m)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b72b6d6f6598b49eab5bdf7c8668a079af280401" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.715ex; height:2.843ex;" alt="{\displaystyle F(\theta ,m)}"></span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E(\theta ,m)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E(\theta ,m)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bd6ebb4c1a7a17f539c6c239c415b044c7ba676" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.75ex; height:2.843ex;" alt="{\displaystyle E(\theta ,m)}"></span> são os integrais elípticos incompletos do segundo e terceiro tipos. </p><p>Fórmulas aproximadas: </p> <dl><dd>Elipsoide plano: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle =2\pi \left(ab\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mi>b</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =2\pi \left(ab\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d85e01ad132ba7278e9cceda8500bb7bdfe65fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.372ex; height:2.843ex;" alt="{\displaystyle =2\pi \left(ab\right)}"></span></dd></dl> <dl><dd>Se <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b=c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b=c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b133a00dc90e54130a96482c99750f845feb955e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.103ex; height:2.176ex;" alt="{\displaystyle b=c}"></span>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \approx 2\pi \left(c^{2}+ac{\frac {\arcsin {\left(e\right)}}{e}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≈</mo> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>a</mi> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>arcsin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mi>e</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \approx 2\pi \left(c^{2}+ac{\frac {\arcsin {\left(e\right)}}{e}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4697ab592e444d7fe6f7a69e385802b160a68aa1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.972ex; height:6.343ex;" alt="{\displaystyle \approx 2\pi \left(c^{2}+ac{\frac {\arcsin {\left(e\right)}}{e}}\right)}"></span></dd></dl> <dl><dd>Se <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a=b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a=b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1956b03d1314c7071ac1f45ed7b1e29422dcfcc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.326ex; height:2.176ex;" alt="{\displaystyle a=b}"></span>: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \approx 2\pi \left(a^{2}+c^{2}{\frac {\operatorname {arctanh} {\left(e\right)}}{e}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≈</mo> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>arctanh</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mi>e</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \approx 2\pi \left(a^{2}+c^{2}{\frac {\operatorname {arctanh} {\left(e\right)}}{e}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/636f1d2cf574637db14468bfa78165e0980b7ca5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.816ex; height:6.343ex;" alt="{\displaystyle \approx 2\pi \left(a^{2}+c^{2}{\frac {\operatorname {arctanh} {\left(e\right)}}{e}}\right)}"></span></dd></dl> <dl><dd>Se o elipsoide é escaleno: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \approx 4\pi \left({\frac {a^{p}b^{p}+a^{p}c^{p}+b^{p}c^{p}}{3}}\right)^{1/p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≈</mo> <mn>4</mn> <mi>π</mi> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>p</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \approx 4\pi \left({\frac {a^{p}b^{p}+a^{p}c^{p}+b^{p}c^{p}}{3}}\right)^{1/p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/854bbeb50f27e9bf78e96b8e8d28740239a2a03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.412ex; height:6.676ex;" alt="{\displaystyle \approx 4\pi \left({\frac {a^{p}b^{p}+a^{p}c^{p}+b^{p}c^{p}}{3}}\right)^{1/p}}"></span></dd></dl> <p>onde p ≈ 1,6075 resulta num erro relativo máximo de cerca de 1 061% (fórmula de Knud Thomsen); um valor de p = 8/5 = 1,6 resulta bem para praticamente todos os elipsoides esferoides, com erro relativo máximo de 1 178% (fórmula de David W. Cantrell). </p> <div class="mw-heading mw-heading2"><h2 id="Transformações_lineares"><span id="Transforma.C3.A7.C3.B5es_lineares"></span>Transformações lineares</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elipsoide&veaction=edit&section=3" title="Editar secção: Transformações lineares" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elipsoide&action=edit&section=3" title="Editar código-fonte da secção: Transformações lineares"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ao aplicar uma <a href="/wiki/Transforma%C3%A7%C3%A3o_linear" title="Transformação linear">transformação linear</a> invertível a uma esfera, obtém-se um elipsoide </p><p>A intersecção de um elipsoide com um <a href="/wiki/Plano_(matem%C3%A1tica)" class="mw-redirect" title="Plano (matemática)">plano</a> é um <a href="/wiki/Conjunto_vazio" title="Conjunto vazio">conjunto vazio</a>, um <a href="/wiki/Ponto_(matem%C3%A1tica)" title="Ponto (matemática)">ponto</a> ou uma elipse. </p> <div class="mw-heading mw-heading2"><h2 id="Aplicação_em_cartografia"><span id="Aplica.C3.A7.C3.A3o_em_cartografia"></span>Aplicação em cartografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elipsoide&veaction=edit&section=4" title="Editar secção: Aplicação em cartografia" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elipsoide&action=edit&section=4" title="Editar código-fonte da secção: Aplicação em cartografia"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nas ciências cartográficas, os elipsoides são utilizados como aproximação da forma irregular da <a href="/wiki/Terra" title="Terra">Terra</a>, já que representam o achatamento nos polos, ao contrário das <a href="/wiki/Esfera_(geometria)" class="mw-redirect" title="Esfera (geometria)">esferas</a>. As <a href="/wiki/Projec%C3%A7%C3%A3o_cartogr%C3%A1fica" class="mw-redirect" title="Projecção cartográfica">projecções cartográficas</a> têm como domínio coordenadas elipsoidais. </p> <div class="mw-heading mw-heading2"><h2 id="Ver_também"><span id="Ver_tamb.C3.A9m"></span>Ver também</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elipsoide&veaction=edit&section=5" title="Editar secção: Ver também" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elipsoide&action=edit&section=5" title="Editar código-fonte da secção: Ver também"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Elipse" title="Elipse">Elipse</a></li> <li><a href="/wiki/Paraboloide" title="Paraboloide">Paraboloide</a></li> <li><a href="/wiki/Hiperboloide" title="Hiperboloide">Hiperboloide</a></li> <li><a href="/wiki/Elipsoide_de_refer%C3%AAncia" title="Elipsoide de referência">Elipsoide de referência</a></li> <li><a href="/wiki/Geoide" title="Geoide">Geoide</a></li> <li><a href="/wiki/Lugar_geom%C3%A9trico" title="Lugar geométrico">Lugar geométrico</a></li></ul> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h2> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-nist-1"><span class="mw-cite-backlink"><a href="#cite_ref-nist_1-0">↑</a></span> <span class="reference-text"> F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, (editores), 2010, <a rel="nofollow" class="external text" href="http://dlmf.nist.gov/19.33">NIST Handbook of Mathematical Functions</a> (Cambridge University Press)</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Ligações_externas"><span id="Liga.C3.A7.C3.B5es_externas"></span>Ligações externas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Elipsoide&veaction=edit&section=6" title="Editar secção: Ligações externas" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Elipsoide&action=edit&section=6" title="Editar código-fonte da secção: Ligações externas"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070927031757/http://www.professores.uff.br/hjbortol/arquivo/2007.1/qs/quadric-surfaces_br.html">Applet Interativo 3D em Java do elipsoide</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Obtida de "<a dir="ltr" href="https://pt.wikipedia.org/w/index.php?title=Elipsoide&oldid=68369566">https://pt.wikipedia.org/w/index.php?title=Elipsoide&oldid=68369566</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Especial:Categorias" title="Especial:Categorias">Categorias</a>: <ul><li><a href="/wiki/Categoria:Qu%C3%A1dricas" title="Categoria:Quádricas">Quádricas</a></li><li><a href="/wiki/Categoria:Cartografia" title="Categoria:Cartografia">Cartografia</a></li><li><a href="/wiki/Categoria:Geod%C3%A9sia" title="Categoria:Geodésia">Geodésia</a></li><li><a href="/wiki/Categoria:S%C3%B3lidos_geom%C3%A9tricos" title="Categoria:Sólidos geométricos">Sólidos geométricos</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categorias ocultas: <ul><li><a href="/wiki/Categoria:!Artigos_que_carecem_de_notas_de_rodap%C3%A9_desde_outubro_de_2012" title="Categoria:!Artigos que carecem de notas de rodapé desde outubro de 2012">!Artigos que carecem de notas de rodapé desde outubro de 2012</a></li><li><a href="/wiki/Categoria:!Artigos_que_carecem_de_notas_de_rodap%C3%A9_sem_indica%C3%A7%C3%A3o_de_tema" title="Categoria:!Artigos que carecem de notas de rodapé sem indicação de tema">!Artigos que carecem de notas de rodapé sem indicação de tema</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"> Esta página foi editada pela última vez às 00h16min de 2 de agosto de 2024.</li> <li id="footer-info-copyright">Este texto é disponibilizado nos termos da licença <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.pt">Atribuição-CompartilhaIgual 4.0 Internacional (CC BY-SA 4.0) da Creative Commons</a>; pode estar sujeito a condições adicionais. Para mais detalhes, consulte as <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">condições de utilização</a>.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy/pt-br">Política de privacidade</a></li> <li id="footer-places-about"><a href="/wiki/Wikip%C3%A9dia:Sobre">Sobre a Wikipédia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikip%C3%A9dia:Aviso_geral">Avisos gerais</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Código de conduta</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Programadores</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/pt.wikipedia.org">Estatísticas</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Declaração sobre ''cookies''</a></li> <li id="footer-places-mobileview"><a href="//pt.m.wikipedia.org/w/index.php?title=Elipsoide&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Versão móvel</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-f69cdc8f6-2kd4h","wgBackendResponseTime":158,"wgPageParseReport":{"limitreport":{"cputime":"0.186","walltime":"0.510","ppvisitednodes":{"value":286,"limit":1000000},"postexpandincludesize":{"value":8530,"limit":2097152},"templateargumentsize":{"value":48,"limit":2097152},"expansiondepth":{"value":11,"limit":100},"expensivefunctioncount":{"value":2,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":10349,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 261.274 1 -total"," 95.30% 249.007 1 Predefinição:Mais_fontes"," 48.74% 127.342 1 Predefinição:Ambox"," 3.25% 8.483 1 Predefinição:Argvar"," 2.48% 6.487 1 Predefinição:Encontre_fontes"," 2.23% 5.830 1 Predefinição:Referências"," 1.25% 3.263 4 Predefinição:*"," 1.00% 2.605 1 Predefinição:AO-pAO"," 0.68% 1.770 1 Predefinição:Esconder_link_para_editar_seção"]},"scribunto":{"limitreport-timeusage":{"value":"0.107","limit":"10.000"},"limitreport-memusage":{"value":955426,"limit":52428800}},"cachereport":{"origin":"mw-api-int.codfw.main-5cfcf7bc8d-wqlr8","timestamp":"20241121131711","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Elipsoide","url":"https:\/\/pt.wikipedia.org\/wiki\/Elipsoide","sameAs":"http:\/\/www.wikidata.org\/entity\/Q190046","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q190046","author":{"@type":"Organization","name":"Contribuidores dos projetos da Wikimedia"},"publisher":{"@type":"Organization","name":"Funda\u00e7\u00e3o Wikimedia, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2004-11-28T15:57:14Z","dateModified":"2024-08-02T00:16:12Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/9\/95\/Ellipsoid_3d.jpg","headline":"superf\u00edcie qu\u00e1drica fechada que \u00e9 o an\u00e1logo tridimensional de uma elipse"}</script> </body> </html>