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="ca" dir="ltr"> <head> <meta charset="UTF-8"> <title>Esfera - Viquipèdia, l'enciclopèdia lliure</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(/(?:^|; )cawikimwclientpreferences=([^;]+)/);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":["","gener","febrer","març","abril","maig","juny","juliol","agost","setembre","octubre","novembre","desembre"],"wgRequestId":"9d5ad00b-ab25-4f96-b8e9-78acc113a68c","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Esfera","wgTitle":"Esfera","wgCurRevisionId":34004524,"wgRevisionId":34004524,"wgArticleId":7167,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles amb enllaços externs no actius","Articles sense referències","Pàgines amb enllaç commonscat des de Wikidata","Control d'autoritats","Esferes"],"wgPageViewLanguage":"ca","wgPageContentLanguage":"ca","wgPageContentModel":"wikitext","wgRelevantPageName":"Esfera","wgRelevantArticleId":7167,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true, "wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"ca","pageLanguageDir":"ltr","pageVariantFallbacks":"ca"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":20000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q12507","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready", "user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","ext.3d.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","wikibase.client.data-bridge.externalModifiers":"ready","ext.wikimediaBadges":"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.UkensKonkurranse","ext.gadget.refToolbar","ext.gadget.charinsert","ext.gadget.AltresViccionari","ext.gadget.purgetab","ext.gadget.DocTabs","ext.gadget.switcher","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","wikibase.client.data-bridge.init","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","oojs-ui.styles.icons-media","oojs-ui-core.icons","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=ca&modules=ext.3d.styles%7Cext.cite.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.data-bridge.externalModifiers%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=ca&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=ca&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/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/1200px-Sphere_wireframe_10deg_6r.svg.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1200"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/800px-Sphere_wireframe_10deg_6r.svg.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="800"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/640px-Sphere_wireframe_10deg_6r.svg.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="640"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Esfera - Viquipèdia, l'enciclopèdia lliure"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//ca.m.wikipedia.org/wiki/Esfera"> <link rel="alternate" type="application/x-wiki" title="Modifica" href="/w/index.php?title=Esfera&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="Viquipèdia (ca)"> <link rel="EditURI" type="application/rsd+xml" href="//ca.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://ca.wikipedia.org/wiki/Esfera"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.ca"> <link rel="alternate" type="application/atom+xml" title="Canal de sindicació Atom Viquipèdia" href="/w/index.php?title=Especial:Canvis_recents&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-Esfera rootpage-Esfera skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Vés al contingut</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="Lloc"> <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="Menú 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">Menú 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">Menú principal</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">amaga</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navegació </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Portada" title="Visiteu la pàgina principal [z]" accesskey="z"><span>Portada</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Especial:Article_aleatori" title="Carrega una pàgina a l’atzar [x]" accesskey="x"><span>Article a l'atzar</span></a></li><li id="n-Articles-de-qualitat" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Articles_de_qualitat"><span>Articles de qualitat</span></a></li> </ul> </div> </div> <div id="p-Comunitat" class="vector-menu mw-portlet mw-portlet-Comunitat" > <div class="vector-menu-heading"> Comunitat </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-portal" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Portal" title="Sobre el projecte, què podeu fer, on trobareu les coses"><span>Portal viquipedista</span></a></li><li id="n-Agenda-d'actes" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Trobades"><span>Agenda d'actes</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Especial:Canvis_recents" title="Una llista dels canvis recents al wiki [r]" accesskey="r"><span>Canvis recents</span></a></li><li id="n-La-taverna" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:La_taverna"><span>La taverna</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Contacte"><span>Contacte</span></a></li><li id="n-Xat" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Canals_IRC"><span>Xat</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Viquip%C3%A8dia:Ajuda" title="El lloc per a saber més coses"><span>Ajuda</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Portada" 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="Viquipèdia" src="/static/images/mobile/copyright/wikipedia-wordmark-ca.svg" style="width: 7.5em; height: 1.4375em;"> <img class="mw-logo-tagline" alt="l'Enciclopèdia Lliure" src="/static/images/mobile/copyright/wikipedia-tagline-ca.svg" width="120" height="14" style="width: 7.5em; height: 0.875em;"> </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:Cerca" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Cerca a la Viquipèdia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Cerca</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="Cerca a Viquipèdia" aria-label="Cerca a Viquipèdia" autocapitalize="sentences" title="Cerca a la Viquipèdia [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:Cerca"> </div> <button class="cdx-button cdx-search-input__end-button">Cerca</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Eines personals"> <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="Aparença"> <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="Aparença" > <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">Aparença</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ca.wikipedia.org&uselang=ca" class=""><span>Donatius</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:Crea_compte&returnto=Esfera" title="Us animem a crear un compte i iniciar una sessió, encara que no és obligatori" class=""><span>Crea un compte</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:Registre_i_entrada&returnto=Esfera" title="Us animem a registrar-vos, però no és obligatori [o]" accesskey="o" class=""><span>Inicia la sessió</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="Més opcions" > <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="Eines personals" > <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">Eines personals</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Menú d'usuari" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ca.wikipedia.org&uselang=ca"><span>Donatius</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Crea_compte&returnto=Esfera" title="Us animem a crear un compte i iniciar una sessió, encara que no és obligatori"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Crea un compte</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Registre_i_entrada&returnto=Esfera" title="Us animem a registrar-vos, però no és obligatori [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Inicia la sessió</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"> Pàgines per a editors no registrats <a href="/wiki/Ajuda:Introducci%C3%B3" aria-label="Vegeu més informació sobre l'edició"><span>més informació</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:Contribucions_pr%C3%B2pies" title="Una llista de les modificacions fetes des d'aquesta adreça IP [y]" accesskey="y"><span>Contribucions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:Discussi%C3%B3_personal" title="Discussió sobre les edicions per aquesta adreça ip. [n]" accesskey="n"><span>Discussió per aquest IP</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Lloc"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contingut" 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">Contingut</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">amaga</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">Inici</div> </a> </li> <li id="toc-Equació" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Equació"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Equació</span> </div> </a> <ul id="toc-Equació-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Superfície_i_volum" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Superfície_i_volum"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Superfície i volum</span> </div> </a> <ul id="toc-Superfície_i_volum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zona_i_segment_esfèrics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Zona_i_segment_esfèrics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Zona i segment esfèrics</span> </div> </a> <ul id="toc-Zona_i_segment_esfèrics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fus_i_tascó_esfèrics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fus_i_tascó_esfèrics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Fus i tascó esfèrics</span> </div> </a> <ul id="toc-Fus_i_tascó_esfèrics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Triangle_esfèric" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Triangle_esfèric"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Triangle esfèric</span> </div> </a> <ul id="toc-Triangle_esfèric-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sector_esfèric" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sector_esfèric"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Sector esfèric</span> </div> </a> <ul id="toc-Sector_esfèric-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Moments_d'inèrcia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Moments_d'inèrcia"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Moments d'inèrcia</span> </div> </a> <ul id="toc-Moments_d'inèrcia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Obres_amb_contingut_sobre_l'esfera" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Obres_amb_contingut_sobre_l'esfera"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Obres amb contingut sobre l'esfera</span> </div> </a> <ul id="toc-Obres_amb_contingut_sobre_l'esfera-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referències" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referències"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Referències</span> </div> </a> <ul id="toc-Referències-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Enllaços_externs" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Enllaços_externs"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Enllaços externs</span> </div> </a> <ul id="toc-Enllaços_externs-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="Contingut" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Commuta la taula de continguts." > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Commuta la taula de continguts.</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Esfera</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Vés a un article en una altra llengua. Disponible en 106 llengües" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-106" 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">106 llengües</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Sfeer" title="Sfeer - afrikaans" lang="af" hreflang="af" data-title="Sfeer" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%89%E1%88%8D" title="ሉል - amhàric" lang="am" hreflang="am" data-title="ሉል" data-language-autonym="አማርኛ" data-language-local-name="amhàric" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%83%D8%B1%D8%A9" title="كرة - àrab" lang="ar" hreflang="ar" data-title="كرة" data-language-autonym="العربية" data-language-local-name="àrab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%83%D9%88%D8%B1%D8%A9" title="كورة - Moroccan Arabic" lang="ary" hreflang="ary" data-title="كورة" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Esfera" title="Esfera - asturià" lang="ast" hreflang="ast" data-title="Esfera" data-language-autonym="Asturianu" data-language-local-name="asturià" 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/Sfera" title="Sfera - azerbaidjanès" lang="az" hreflang="az" data-title="Sfera" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaidjanès" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%A9%D9%88%D8%B1%D9%87_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="کوره (هندسه) - South Azerbaijani" lang="azb" hreflang="azb" data-title="کوره (هندسه)" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - baixkir" lang="ba" hreflang="ba" data-title="Сфера" data-language-autonym="Башҡортса" data-language-local-name="baixkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - belarús" lang="be" hreflang="be" data-title="Сфера" data-language-autonym="Беларуская" data-language-local-name="belarús" 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%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - búlgar" lang="bg" hreflang="bg" data-title="Сфера" data-language-autonym="Български" data-language-local-name="búlgar" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%97%E0%A5%8B%E0%A4%B2%E0%A4%BE" title="गोला - Bhojpuri" lang="bh" hreflang="bh" data-title="गोला" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A7%8B%E0%A6%B2%E0%A6%95" title="গোলক - bengalí" lang="bn" hreflang="bn" data-title="গোলক" data-language-autonym="বাংলা" data-language-local-name="bengalí" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Sfera" title="Sfera - bosnià" lang="bs" hreflang="bs" data-title="Sfera" data-language-autonym="Bosanski" data-language-local-name="bosnià" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-chr mw-list-item"><a href="https://chr.wikipedia.org/wiki/%E1%8E%A6%E1%8F%90%E1%8F%86%E1%8E%B8" title="ᎦᏐᏆᎸ - cherokee" lang="chr" hreflang="chr" data-title="ᎦᏐᏆᎸ" data-language-autonym="ᏣᎳᎩ" data-language-local-name="cherokee" class="interlanguage-link-target"><span>ᏣᎳᎩ</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%AF%DB%86" title="گۆ - kurd central" lang="ckb" hreflang="ckb" data-title="گۆ" data-language-autonym="کوردی" data-language-local-name="kurd central" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Sf%C3%A9ra_(matematika)" title="Sféra (matematika) - txec" lang="cs" hreflang="cs" data-title="Sféra (matematika)" data-language-autonym="Čeština" data-language-local-name="txec" 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%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - txuvaix" lang="cv" hreflang="cv" data-title="Сфера" data-language-autonym="Чӑвашла" data-language-local-name="txuvaix" 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/Sff%C3%AAr" title="Sffêr - gal·lès" lang="cy" hreflang="cy" data-title="Sffêr" data-language-autonym="Cymraeg" data-language-local-name="gal·lès" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kugle" title="Kugle - danès" lang="da" hreflang="da" data-title="Kugle" data-language-autonym="Dansk" data-language-local-name="danès" 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/Kugel" title="Kugel - alemany" lang="de" hreflang="de" data-title="Kugel" data-language-autonym="Deutsch" data-language-local-name="alemany" 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%A3%CF%86%CE%B1%CE%AF%CF%81%CE%B1" title="Σφαίρα - grec" lang="el" hreflang="el" data-title="Σφαίρα" data-language-autonym="Ελληνικά" data-language-local-name="grec" 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/Sphere" title="Sphere - anglès" lang="en" hreflang="en" data-title="Sphere" data-language-autonym="English" data-language-local-name="anglès" 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/Sfero" title="Sfero - esperanto" lang="eo" hreflang="eo" data-title="Sfero" 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/Esfera" title="Esfera - espanyol" lang="es" hreflang="es" data-title="Esfera" data-language-autonym="Español" data-language-local-name="espanyol" 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/Sf%C3%A4%C3%A4r" title="Sfäär - estonià" lang="et" hreflang="et" data-title="Sfäär" data-language-autonym="Eesti" data-language-local-name="estonià" 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/Esfera" title="Esfera - basc" lang="eu" hreflang="eu" data-title="Esfera" data-language-autonym="Euskara" data-language-local-name="basc" 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/%DA%A9%D8%B1%D9%87_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="کره (هندسه) - persa" lang="fa" hreflang="fa" data-title="کره (هندسه)" 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/Pallo_(geometria)" title="Pallo (geometria) - finès" lang="fi" hreflang="fi" data-title="Pallo (geometria)" data-language-autonym="Suomi" data-language-local-name="finès" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Vuravura_(Geometry)" title="Vuravura (Geometry) - fijià" lang="fj" hreflang="fj" data-title="Vuravura (Geometry)" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fijià" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Sph%C3%A8re" title="Sphère - francès" lang="fr" hreflang="fr" data-title="Sphère" data-language-autonym="Français" data-language-local-name="francès" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Kuugel" title="Kuugel - frisó septentrional" lang="frr" hreflang="frr" data-title="Kuugel" data-language-autonym="Nordfriisk" data-language-local-name="frisó septentrional" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Sf%C3%A9ar" title="Sféar - irlandès" lang="ga" hreflang="ga" data-title="Sféar" data-language-autonym="Gaeilge" data-language-local-name="irlandès" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E7%90%83%E9%9D%A2" title="球面 - xinès gan" lang="gan" hreflang="gan" data-title="球面" data-language-autonym="贛語" data-language-local-name="xinès gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Sf%C3%A8r" title="Sfèr - Guianan Creole" lang="gcr" hreflang="gcr" data-title="Sfèr" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Cruinne" title="Cruinne - gaèlic escocès" lang="gd" hreflang="gd" data-title="Cruinne" data-language-autonym="Gàidhlig" data-language-local-name="gaèlic escocès" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Esfera" title="Esfera - gallec" lang="gl" hreflang="gl" data-title="Esfera" data-language-autonym="Galego" data-language-local-name="gallec" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%97%E0%AB%8B%E0%AA%B3%E0%AB%8B" title="ગોળો - gujarati" lang="gu" hreflang="gu" data-title="ગોળો" data-language-autonym="ગુજરાતી" data-language-local-name="gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A1%D7%A4%D7%99%D7%A8%D7%94_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="ספירה (גאומטריה) - hebreu" lang="he" hreflang="he" data-title="ספירה (גאומטריה)" data-language-autonym="עברית" data-language-local-name="hebreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A5%8B%E0%A4%B2%E0%A4%BE" title="गोला - hindi" lang="hi" hreflang="hi" data-title="गोला" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Sfera" title="Sfera - croat" lang="hr" hreflang="hr" data-title="Sfera" data-language-autonym="Hrvatski" data-language-local-name="croat" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Esf%C3%A8" title="Esfè - crioll d’Haití" lang="ht" hreflang="ht" data-title="Esfè" data-language-autonym="Kreyòl ayisyen" data-language-local-name="crioll d’Haití" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/G%C3%B6mb" title="Gömb - hongarès" lang="hu" hreflang="hu" data-title="Gömb" data-language-autonym="Magyar" data-language-local-name="hongarès" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Sphera" title="Sphera - interlingua" lang="ia" hreflang="ia" data-title="Sphera" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Bola_(geometri)" title="Bola (geometri) - indonesi" lang="id" hreflang="id" data-title="Bola (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesi" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Sfero" title="Sfero - ido" lang="io" hreflang="io" data-title="Sfero" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/K%C3%BAla" title="Kúla - islandès" lang="is" hreflang="is" data-title="Kúla" data-language-autonym="Íslenska" data-language-local-name="islandès" 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/Sfera" title="Sfera - italià" lang="it" hreflang="it" data-title="Sfera" data-language-autonym="Italiano" data-language-local-name="italià" 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/%E7%90%83%E9%9D%A2" title="球面 - japonès" lang="ja" hreflang="ja" data-title="球面" data-language-autonym="日本語" data-language-local-name="japonès" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Sfier" title="Sfier - crioll anglès de Jamaica" lang="jam" hreflang="jam" data-title="Sfier" data-language-autonym="Patois" data-language-local-name="crioll anglès de Jamaica" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%A4%E1%83%94%E1%83%A0%E1%83%9D" title="სფერო - georgià" lang="ka" hreflang="ka" data-title="სფერო" data-language-autonym="ქართული" data-language-local-name="georgià" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tasegla" title="Tasegla - cabilenc" lang="kab" hreflang="kab" data-title="Tasegla" data-language-autonym="Taqbaylit" data-language-local-name="cabilenc" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - kazakh" lang="kk" hreflang="kk" data-title="Сфера" data-language-autonym="Қазақша" data-language-local-name="kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%97%E0%B3%8B%E0%B2%B3" title="ಗೋಳ - kannada" lang="kn" hreflang="kn" data-title="ಗೋಳ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B5%AC_(%EA%B8%B0%ED%95%98%ED%95%99)" title="구 (기하학) - coreà" lang="ko" hreflang="ko" data-title="구 (기하학)" data-language-autonym="한국어" data-language-local-name="coreà" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Sphaera" title="Sphaera - llatí" lang="la" hreflang="la" data-title="Sphaera" data-language-autonym="Latina" data-language-local-name="llatí" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Sfera" title="Sfera - lituà" lang="lt" hreflang="lt" data-title="Sfera" data-language-autonym="Lietuvių" data-language-local-name="lituà" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Sf%C4%93ra" title="Sfēra - letó" lang="lv" hreflang="lv" data-title="Sfēra" data-language-autonym="Latviešu" data-language-local-name="letó" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0%D1%81%D1%8C" title="Сферась - mordovià moksa" lang="mdf" hreflang="mdf" data-title="Сферась" data-language-autonym="Мокшень" data-language-local-name="mordovià moksa" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Bola_(je%C3%B4metria)" title="Bola (jeômetria) - malgaix" lang="mg" hreflang="mg" data-title="Bola (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="malgaix" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - macedoni" lang="mk" hreflang="mk" data-title="Сфера" data-language-autonym="Македонски" data-language-local-name="macedoni" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B5%8B%E0%B4%B3%E0%B4%82" title="ഗോളം - malaiàlam" lang="ml" hreflang="ml" data-title="ഗോളം" data-language-autonym="മലയാളം" data-language-local-name="malaiàlam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%91%D3%A9%D0%BC%D0%B1%D3%A9%D0%BB%D3%A9%D0%B3" title="Бөмбөлөг - mongol" lang="mn" hreflang="mn" data-title="Бөмбөлөг" data-language-autonym="Монгол" data-language-local-name="mongol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sfera" title="Sfera - malai" lang="ms" hreflang="ms" data-title="Sfera" data-language-autonym="Bahasa Melayu" data-language-local-name="malai" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%85%E1%80%80%E1%80%BA%E1%80%9C%E1%80%AF%E1%80%B6%E1%80%B8" title="စက်လုံး - birmà" lang="my" hreflang="my" data-title="စက်လုံး" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmà" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Sfeer_(wiskunde)" title="Sfeer (wiskunde) - neerlandès" lang="nl" hreflang="nl" data-title="Sfeer (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="neerlandès" 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/Kule" title="Kule - noruec nynorsk" lang="nn" hreflang="nn" data-title="Kule" data-language-autonym="Norsk nynorsk" data-language-local-name="noruec 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/Kule" title="Kule - noruec bokmål" lang="nb" hreflang="nb" data-title="Kule" data-language-autonym="Norsk bokmål" data-language-local-name="noruec bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Esf%C3%A8ra" title="Esfèra - occità" lang="oc" hreflang="oc" data-title="Esfèra" data-language-autonym="Occitan" data-language-local-name="occità" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Duqunqula" title="Duqunqula - oromo" lang="om" hreflang="om" data-title="Duqunqula" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%97%E0%A9%8B%E0%A8%B2%E0%A8%BC%E0%A8%BE" title="ਗੋਲ਼ਾ - panjabi" lang="pa" hreflang="pa" data-title="ਗੋਲ਼ਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sfera" title="Sfera - polonès" lang="pl" hreflang="pl" data-title="Sfera" data-language-autonym="Polski" data-language-local-name="polonès" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Sfera" title="Sfera - piemontès" lang="pms" hreflang="pms" data-title="Sfera" data-language-autonym="Piemontèis" data-language-local-name="piemontès" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Esfera" title="Esfera - portuguès" lang="pt" hreflang="pt" data-title="Esfera" data-language-autonym="Português" data-language-local-name="portuguès" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Lunq%27u" title="Lunq'u - quítxua" lang="qu" hreflang="qu" data-title="Lunq'u" data-language-autonym="Runa Simi" data-language-local-name="quítxua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Sfer%C4%83" title="Sferă - romanès" lang="ro" hreflang="ro" data-title="Sferă" data-language-autonym="Română" data-language-local-name="romanès" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rsk mw-list-item"><a href="https://rsk.wikipedia.org/wiki/%D0%9B%D0%B0%D0%B1%D0%B4%D0%B0_(%D2%91%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Лабда (ґеометрия) - Pannonian Rusyn" lang="rsk" hreflang="rsk" data-title="Лабда (ґеометрия)" data-language-autonym="Руски" data-language-local-name="Pannonian Rusyn" class="interlanguage-link-target"><span>Руски</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - rus" lang="ru" hreflang="ru" data-title="Сфера" data-language-autonym="Русский" data-language-local-name="rus" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - iacut" lang="sah" hreflang="sah" data-title="Сфера" data-language-autonym="Саха тыла" data-language-local-name="iacut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Sfera" title="Sfera - sicilià" lang="scn" hreflang="scn" data-title="Sfera" data-language-autonym="Sicilianu" data-language-local-name="sicilià" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Sfera" title="Sfera - serbocroat" lang="sh" hreflang="sh" data-title="Sfera" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroat" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9C%E0%B7%9D%E0%B6%BD%E0%B6%BA" title="ගෝලය - singalès" lang="si" hreflang="si" data-title="ගෝලය" data-language-autonym="සිංහල" data-language-local-name="singalès" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Sphere" title="Sphere - Simple English" lang="en-simple" hreflang="en-simple" data-title="Sphere" 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/Gu%C4%BEa_(matematika)" title="Guľa (matematika) - eslovac" lang="sk" hreflang="sk" data-title="Guľa (matematika)" data-language-autonym="Slovenčina" data-language-local-name="eslovac" 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/Sfera" title="Sfera - eslovè" lang="sl" hreflang="sl" data-title="Sfera" data-language-autonym="Slovenščina" data-language-local-name="eslovè" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Mburungwa" title="Mburungwa - shona" lang="sn" hreflang="sn" data-title="Mburungwa" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Kubad" title="Kubad - somali" lang="so" hreflang="so" data-title="Kubad" data-language-autonym="Soomaaliga" data-language-local-name="somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Sfera" title="Sfera - albanès" lang="sq" hreflang="sq" data-title="Sfera" data-language-autonym="Shqip" data-language-local-name="albanès" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - serbi" lang="sr" hreflang="sr" data-title="Сфера" data-language-autonym="Српски / srpski" data-language-local-name="serbi" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Buleudan" title="Buleudan - sondanès" lang="su" hreflang="su" data-title="Buleudan" data-language-autonym="Sunda" data-language-local-name="sondanès" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Sf%C3%A4r" title="Sfär - suec" lang="sv" hreflang="sv" data-title="Sfär" data-language-autonym="Svenska" data-language-local-name="suec" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Tufe" title="Tufe - suahili" lang="sw" hreflang="sw" data-title="Tufe" data-language-autonym="Kiswahili" data-language-local-name="suahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%8B%E0%AE%B3%E0%AE%AE%E0%AF%8D" title="கோளம் - tàmil" lang="ta" hreflang="ta" data-title="கோளம்" data-language-autonym="தமிழ்" data-language-local-name="tàmil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%97%E0%B1%8B%E0%B0%B3%E0%B0%82" title="గోళం - telugu" lang="te" hreflang="te" data-title="గోళం" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%A1" title="ทรงกลม - tai" lang="th" hreflang="th" data-title="ทรงกลม" data-language-autonym="ไทย" data-language-local-name="tai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Espera" title="Espera - tagal" lang="tl" hreflang="tl" data-title="Espera" data-language-autonym="Tagalog" data-language-local-name="tagal" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/K%C3%BCre" title="Küre - turc" lang="tr" hreflang="tr" data-title="Küre" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - tàtar" lang="tt" hreflang="tt" data-title="Сфера" data-language-autonym="Татарча / tatarça" data-language-local-name="tàtar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера - ucraïnès" lang="uk" hreflang="uk" data-title="Сфера" data-language-autonym="Українська" data-language-local-name="ucraïnès" 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/Sfera" title="Sfera - uzbek" lang="uz" hreflang="uz" data-title="Sfera" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/M%E1%BA%B7t_c%E1%BA%A7u" title="Mặt cầu - vietnamita" lang="vi" hreflang="vi" data-title="Mặt cầu" 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-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Espira" title="Espira - waray" lang="war" hreflang="war" data-title="Espira" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%90%83%E9%9D%A2" title="球面 - xinès wu" lang="wuu" hreflang="wuu" data-title="球面" data-language-autonym="吴语" data-language-local-name="xinès wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%90%83%E9%9D%A2" title="球面 - xinès" lang="zh" hreflang="zh" data-title="球面" data-language-autonym="中文" data-language-local-name="xinès" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%90%83" title="球 - xinès clàssic" lang="lzh" hreflang="lzh" data-title="球" data-language-autonym="文言" data-language-local-name="xinès clàssic" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ki%C3%BB-b%C4%ABn" title="Kiû-bīn - xinès min del sud" lang="nan" hreflang="nan" data-title="Kiû-bīn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="xinès min del sud" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%90%83%E9%AB%94" title="球體 - cantonès" lang="yue" hreflang="yue" data-title="球體" data-language-autonym="粵語" data-language-local-name="cantonès" 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/Q12507#sitelinks-wikipedia" title="Modifica enllaços interlingües" class="wbc-editpage">Modifica els enllaços</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="Espais de noms"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Esfera" title="Vegeu el contingut de la pàgina [c]" accesskey="c"><span>Pàgina</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Discussi%C3%B3:Esfera" rel="discussion" title="Discussió sobre el contingut d'aquesta pàgina [t]" accesskey="t"><span>Discussió</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Canvia la variant de llengua" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">català</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="Vistes"> <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/Esfera"><span>Mostra</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Esfera&action=edit" title="Modifica el codi font d'aquesta pàgina [e]" accesskey="e"><span>Modifica</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Esfera&action=history" title="Versions antigues d'aquesta pàgina [h]" accesskey="h"><span>Mostra l'historial</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Eines de la pàgina"> <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="Eines" > <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">Eines</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">Eines</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">amaga</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Més opcions" > <div class="vector-menu-heading"> Accions </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/Esfera"><span>Mostra</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Esfera&action=edit" title="Modifica el codi font d'aquesta pàgina [e]" accesskey="e"><span>Modifica</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Esfera&action=history"><span>Mostra l'historial</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Especial:Enlla%C3%A7os/Esfera" title="Una llista de totes les pàgines wiki que enllacen amb aquesta [j]" accesskey="j"><span>Què hi enllaça</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Especial:Seguiment/Esfera" rel="nofollow" title="Canvis recents a pàgines enllaçades des d'aquesta pàgina [k]" accesskey="k"><span>Canvis relacionats</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Especial:P%C3%A0gines_especials" title="Llista totes les pàgines especials [q]" accesskey="q"><span>Pàgines especials</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Esfera&oldid=34004524" title="Enllaç permanent a aquesta revisió de la pàgina"><span>Enllaç permanent</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Esfera&action=info" title="Més informació sobre aquesta pàgina"><span>Informació de la pàgina</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Especial:Citau&page=Esfera&id=34004524&wpFormIdentifier=titleform" title="Informació sobre com citar aquesta pàgina"><span>Citau aquest article</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Especial:UrlShortener&url=https%3A%2F%2Fca.wikipedia.org%2Fwiki%2FEsfera"><span>Obtén una URL abreujada</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Especial:QrCode&url=https%3A%2F%2Fca.wikipedia.org%2Fwiki%2FEsfera"><span>Descarrega el codi 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"> Imprimeix/exporta </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:Llibre&bookcmd=book_creator&referer=Esfera"><span>Crea un llibre</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Especial:DownloadAsPdf&page=Esfera&action=show-download-screen"><span>Baixa com a PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Esfera&printable=yes" title="Versió per a impressió d'aquesta pàgina [p]" accesskey="p"><span>Versió per a impressora</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"> En altres projectes </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/Sphere" hreflang="en"><span>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/Q12507" title="Enllaç a l'element del repositori de dades connectat [g]" accesskey="g"><span>Element a 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="Eines de la pàgina"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aparença"> <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">Aparença</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mou a la barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">amaga</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">De la Viquipèdia, l'enciclopèdia lliure</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="ca" dir="ltr"><table class="plainlinks ambox ambox-content" style="" data-severity="2"> <tbody><tr> <td class="mbox-image" style="width: 52px;"> <span typeof="mw:File"><a href="/wiki/Fitxer:Crystal128-pipe.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Crystal128-pipe.svg/25px-Crystal128-pipe.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Crystal128-pipe.svg/38px-Crystal128-pipe.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Crystal128-pipe.svg/50px-Crystal128-pipe.svg.png 2x" data-file-width="192" data-file-height="192" /></a></span></td> <td class="mbox-text" style=""> <div class="mbox-text-span">Aquest article o secció no <a href="/wiki/Viquip%C3%A8dia:Citau_les_fonts" title="Viquipèdia:Citau les fonts">cita les fonts</a> o necessita més referències per a la seva <a href="/wiki/VP:VER" class="mw-redirect" title="VP:VER">verificabilitat</a>.</div> </td> </tr> </tbody></table> <table class="infobox" style="font-size:90%;width:25em"><caption style="font-weight:bold;background:#b0d1ad"><span style="float:left;"><span typeof="mw:File"><span title="Infotaula de polítop"><img alt="Infotaula de polítop" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Pyramid_icon.svg/22px-Pyramid_icon.svg.png" decoding="async" width="22" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Pyramid_icon.svg/33px-Pyramid_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Pyramid_icon.svg/44px-Pyramid_icon.svg.png 2x" data-file-width="303" data-file-height="258" /></span></span></span>Esfera</caption><tbody><tr><td colspan="2" class="infobox-full-data infobox-data" style="text-align:center"><span typeof="mw:File"><a href="/w/index.php?title=Fitxer:Sphere_wireframe_10deg_6r.svg&lang=ca" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/langca-300px-Sphere_wireframe_10deg_6r.svg.png" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/langca-450px-Sphere_wireframe_10deg_6r.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/langca-600px-Sphere_wireframe_10deg_6r.svg.png 2x" data-file-width="800" data-file-height="800" /></a></span></td></tr><tr><td colspan="2" class="infobox-full-data infobox-data" style="text-align:center"><span typeof="mw:File"><span class="mw-3d-wrapper" data-label="3D"><a href="/wiki/Fitxer:Kugel_high_poly_20230214.stl" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Kugel_high_poly_20230214.stl/300px-Kugel_high_poly_20230214.stl.png" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Kugel_high_poly_20230214.stl/450px-Kugel_high_poly_20230214.stl.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Kugel_high_poly_20230214.stl/600px-Kugel_high_poly_20230214.stl.png 2x" data-file-width="5120" data-file-height="2880" /></a></span></span><div style="font-size:90%;">Model 3D</div></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left;background:#eeeeee">Tipus</th><td class="infobox-data"><a href="/wiki/Esferoide" title="Esferoide">esferoide</a>, <a href="/wiki/Lloc_geom%C3%A8tric" title="Lloc geomètric">lloc geomètric</a>, <a href="https://www.wikidata.org/wiki/Special:EntityPage/Q30092280" class="extiw" title="d:Special:EntityPage/Q30092280">superfície quàdrica no degenerada</a>, <a href="/wiki/Frontera_(topologia)" title="Frontera (topologia)">frontera</a>, <a href="https://www.wikidata.org/wiki/Special:EntityPage/Q4751134" class="extiw" title="d:Special:EntityPage/Q4751134">varietat analítica</a>, <a href="https://www.wikidata.org/wiki/Special:EntityPage/Q22808481" class="extiw" title="d:Special:EntityPage/Q22808481">hiperesfera</a>, <a href="/wiki/N-esfera" title="N-esfera">N-esfera</a>, <a href="/wiki/Superf%C3%ADcie_(matem%C3%A0tiques)" title="Superfície (matemàtiques)">superfície</a> i <a href="/wiki/Primitiu_geom%C3%A8tric" title="Primitiu geomètric">primitiu geomètric</a> <span class="penicon"><span class="mw-valign-baseline" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q12507?uselang=ca#P279" title="Modifica el valor a Wikidata"><img alt="Modifica el valor a Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/10px-Arbcom_ru_editing.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/15px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/20px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left;background:#eeeeee"><a href="/wiki/Caracter%C3%ADstica_d%27Euler" title="Característica d'Euler">Característica</a></th><td class="infobox-data">2 <span class="penicon"><span class="mw-valign-baseline" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q12507?uselang=ca#P6438" title="Modifica el valor a Wikidata"><img alt="Modifica el valor a Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/10px-Arbcom_ru_editing.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/15px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/20px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span></td></tr><tr><th colspan="2" class="infobox-header" style="text-align:center;background:#b0d1ad">Sèrie</th></tr><tr><td colspan="2" class="infobox-full-data infobox-data" style="text-align:center"><div style="float: left;">← <a href="/wiki/Circumfer%C3%A8ncia" title="Circumferència">circumferència</a> <span class="penicon"><span class="mw-valign-baseline" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q12507?uselang=ca#P155" title="Modifica el valor a Wikidata"><img alt="Modifica el valor a Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/10px-Arbcom_ru_editing.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/15px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/20px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span> </div><div style="float: right;"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q2274197" class="extiw" title="d:Special:EntityPage/Q2274197">3-esfera</a> i <a href="/wiki/Tor_(geometria)" title="Tor (geometria)">tor</a> <span class="penicon"><span class="mw-valign-baseline" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q12507?uselang=ca#P156" title="Modifica el valor a Wikidata"><img alt="Modifica el valor a Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/10px-Arbcom_ru_editing.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/15px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/20px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span> →</div></td></tr><tr><th colspan="2" class="infobox-header" style="text-align:center;background:#b0d1ad">Més informació</th></tr><tr><th scope="row" class="infobox-label" style="text-align:left;background:#eeeeee"><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></th><td class="infobox-data"><a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Sphere.html">Sphere</a> <span class="penicon"><span class="mw-valign-baseline" typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q12507?uselang=ca#P2812" title="Modifica el valor a Wikidata"><img alt="Modifica el valor a Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/10px-Arbcom_ru_editing.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/15px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/20px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></span></td></tr></tbody></table> <p>En <a href="/wiki/Geometria" title="Geometria">geometria</a>, una <b>esfera</b> és la <a href="/wiki/Superf%C3%ADcie" class="mw-redirect" title="Superfície">superfície</a> formada per tots els punts que es troben a una mateixa <a href="/wiki/Dist%C3%A0ncia" title="Distància">distància</a> (anomenada <i><a href="/wiki/Radi_(geometria)" title="Radi (geometria)">radi</a></i>) d'un <a href="/wiki/Punt_(geometria)" title="Punt (geometria)">punt</a> donat (anomenat <i><a href="/wiki/Centre_(geometria)" title="Centre (geometria)">centre</a></i>) de l'<a href="/wiki/Espai" title="Espai">espai</a>.<sup id="cite_ref-Llengua_catalana_o267_1-0" class="reference"><a href="#cite_note-Llengua_catalana_o267-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> El segment que uneix un punt de l'esfera amb el seu centre també rep el nom de <i>radi</i>. Una recta que passa pel centre de l'esfera la talla en dos punts; el segment que determinen s'anomena <a href="/wiki/Di%C3%A0metre" title="Diàmetre">diàmetre</a>. Tots els diàmetres tenen la mateixa longitud, també anomenada <i>diàmetre</i>. El diàmetre val el doble que el radi, i és la màxima distància entre dos punts de l'esfera. </p><p>En llenguatge comú també s'anomena <i>esfera</i> la regió <a href="/wiki/S%C3%B2lid" title="Sòlid">sòlida</a> limitada per una superfície esfèrica, tot i que el terme matemàtic per designar aquesta regió és <i><a href="/wiki/Bola_(matem%C3%A0tiques)" title="Bola (matemàtiques)">bola</a></i>. El nom de l'esfera prové del terme grec σφαῖρα, <i>sfaîra</i>, «bola».<sup id="cite_ref-Search_Online_Etymology_Dictionary_v450_2-0" class="reference"><a href="#cite_note-Search_Online_Etymology_Dictionary_v450-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Equació"><span id="Equaci.C3.B3"></span>Equació</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=1" title="Modifica la secció: Equació"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En un sistema de coordenades ortogonal i unitari, l'equació de l'esfera unitària centrada a l'origen de coordenades és <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}+y^{2}+z^{2}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}+z^{2}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5b5c3e3525a1604f9425edb80835d236fe7af82" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.685ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}+z^{2}=1}"></span>. </p><p>L'equació anterior s'obté considerant que un punt <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x,y,z)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x,y,z)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22a8c93372e8f8b6e24d523bd5545aed3430baf4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.45ex; height:2.843ex;" alt="{\displaystyle (x,y,z)}"></span> és de l'esfera unitat si té mòdul unitari, és a dir, si <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 {\sqrt {x^{2}+y^{2}+z^{2}}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {x^{2}+y^{2}+z^{2}}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe72c00b6b7cc8856f135d7ade869ab573e152c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:19.009ex; height:4.843ex;" alt="{\displaystyle {\sqrt {x^{2}+y^{2}+z^{2}}}=1}"></span>, i elevant al quadrat a ambdós costats. </p><p>Més generalment l'esfera de radi <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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> i centre <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_{0},y_{0},z_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{0},y_{0},z_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39177ddeeb9f9a393b664e522bc8e3bf0face153" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.59ex; height:2.843ex;" alt="{\displaystyle (x_{0},y_{0},z_{0})}"></span> té per equació <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-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <mi>z</mi> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d00dce5d0686fd9f1bd5b0f60583a94e41afd764" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.28ex; height:3.176ex;" alt="{\displaystyle (x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=r^{2}}"></span>. Anàlogament al cas anterior, aquesta equació s'obté de considerar que un punt és de l'esfera si la distància euclidiana entre el centre i el punt és exactament <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>. </p><p>El pla tangent al punt <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x',y',z')}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x',y',z')}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458e2bfb57b764bc4352ab1a83d0351b39cc1967" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.512ex; height:3.009ex;" alt="{\displaystyle (x',y',z')}"></span> té com a vector normal un múltiple del radi, com per exemple <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'-x_{0},y'-y_{0},z'-z_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x'-x_{0},y'-y_{0},z'-z_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f7a6feacc50eb16cbccc36bea52595b40092946" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.746ex; height:3.009ex;" alt="{\displaystyle (x'-x_{0},y'-y_{0},z'-z_{0})}"></span>, i imposant que el pla passa per <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x',y',z')}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x',y',z')}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458e2bfb57b764bc4352ab1a83d0351b39cc1967" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.512ex; height:3.009ex;" alt="{\displaystyle (x',y',z')}"></span> s'obté l'equació del pla tangent: <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'-x_{0})(x'-x)+(y'-y_{0})(y'-y)+(z'-z_{0})(z'-z)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>y</mi> <mo>′</mo> </msup> <mo>−</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mo stretchy="false">(</mo> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <msup> <mi>z</mi> <mo>′</mo> </msup> <mo>−</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x'-x_{0})(x'-x)+(y'-y_{0})(y'-y)+(z'-z_{0})(z'-z)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b536c2926b80a8b75a933da98db4e59bab016043" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:59.395ex; height:3.009ex;" alt="{\displaystyle (x'-x_{0})(x'-x)+(y'-y_{0})(y'-y)+(z'-z_{0})(z'-z)=0}"></span>. </p><p>La parametrització clàssica de l'esfera de radi <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 r>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23cbbcd53bd13620bc53490e3eec42790850b452" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.31ex; height:2.176ex;" alt="{\displaystyle r>0}"></span> i centre <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_{0},y_{0},z_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{0},y_{0},z_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39177ddeeb9f9a393b664e522bc8e3bf0face153" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.59ex; height:2.843ex;" alt="{\displaystyle (x_{0},y_{0},z_{0})}"></span> és <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}x=&x_{0}+r\cos \theta \cos \varphi \\y=&y_{0}+r\cos \theta \sin \varphi \quad \quad \quad \theta \in [0,\pi ]),\ \varphi \in [0,2\pi )\\z=&z_{0}+r\sin \theta \\\end{aligned}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>x</mi> <mo>=</mo> </mtd> <mtd> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>r</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> <mo>=</mo> </mtd> <mtd> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>r</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> <mspace width="1em" /> <mspace width="1em" /> <mspace width="1em" /> <mi>θ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>π</mi> <mo stretchy="false">]</mo> <mo stretchy="false">)</mo> <mo>,</mo> <mtext> </mtext> <mi>φ</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> <mo>=</mo> </mtd> <mtd> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>r</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> </mtd> </mtr> </mtable> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x=&x_{0}+r\cos \theta \cos \varphi \\y=&y_{0}+r\cos \theta \sin \varphi \quad \quad \quad \theta \in [0,\pi ]),\ \varphi \in [0,2\pi )\\z=&z_{0}+r\sin \theta \\\end{aligned}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6165df4eab58374ab0eb8715b11530c636ef3140" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:50.233ex; height:9.176ex;" alt="{\displaystyle {\begin{aligned}x=&x_{0}+r\cos \theta \cos \varphi \\y=&y_{0}+r\cos \theta \sin \varphi \quad \quad \quad \theta \in [0,\pi ]),\ \varphi \in [0,2\pi )\\z=&z_{0}+r\sin \theta \\\end{aligned}}.}"></span>Observem que si fixem la variable <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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> de la parametrització i fem variar <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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span>, obtenim una parametrització dels paral·lels de l'esfera. Anàlogament, fixant <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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> i fent variar <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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span>, obtenim una parametrització dels meridians de l'esfera. </p> <div class="mw-heading mw-heading2"><h2 id="Superfície_i_volum"><span id="Superf.C3.ADcie_i_volum"></span>Superfície i volum</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=2" title="Modifica la secció: Superfície i volum"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La superfície d'una esfera de radi <i>r</i> és:  <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 \!S=4\pi r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="negativethinmathspace" /> <mi>S</mi> <mo>=</mo> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \!S=4\pi r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/984e24db4ff75f7c44d192efc928756137c21194" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-left: -0.387ex; width:9.195ex; height:2.676ex;" alt="{\displaystyle \!S=4\pi r^{2}}"></span> </p><p>El volum d'una esfera de radi <i>r</i> és:  <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 V={\frac {4}{3}}\cdot \pi \cdot r^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> <mo>⋅</mo> <mi>π</mi> <mo>⋅</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {4}{3}}\cdot \pi \cdot r^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5fda2693fe3a85c9bc7147e3bd30f010879acce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.677ex; height:5.176ex;" alt="{\displaystyle V={\frac {4}{3}}\cdot \pi \cdot r^{3}}"></span> </p><p>Si es considera la superfície i el volum com funcions S(r) i V(r) del radi, llavors es nota que la superfície és la <a href="/wiki/Derivada" title="Derivada">funció derivada</a> del volum. Aquest fet no és casualitat, ja que es pot descompondre el volum en capes de gruix arbitràriament petit <b>dr</b> (diferencial de r), i els volums d'aquestes capes s'aproximen a <b>S(r)·dr</b> quan <b>dr</b> tendeix a 0. Sumant els volums infinitesimals de totes aquestes capes (en quantitat infinita) quan el radi <i>r</i> varia de zero a <i>R</i> dona per definició la integral següent: <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 V(R)=\int _{0}^{R}S(r)dr}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> </msubsup> <mi>S</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(R)=\int _{0}^{R}S(r)dr}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e8f3398bcbbe9c7750fa1a3a388cd4b8f3f95a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.412ex; height:6.176ex;" alt="{\displaystyle V(R)=\int _{0}^{R}S(r)dr}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Zona_i_segment_esfèrics"><span id="Zona_i_segment_esf.C3.A8rics"></span>Zona i segment esfèrics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=3" title="Modifica la secció: Zona i segment esfèrics"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Una <b>zona esfèrica</b> és la part de la superfície esfèrica delimitada per dos plans paral·lels que tallen l'esfera, formant dos cercles anomenats <i>bases</i>. L'àrea de la zona esfèrica, d'una esfera de radi <i>r</i>, delimitada per dues bases separades per una altura <i>h</i> és: </p> <pre>A = 2 · π · r · h </pre> <p>Un <b>segment esfèric</b> és el sòlid delimitat per una zona esfèrica i els dos plans paral·lels que el delimiten. El volum del segment esfèric, d'una esfera de radi <i>r</i>, delimitat per dues bases, de radis <i>a</i> i <i>b</i> respectivament, separades per una altura <i>h</i> és: </p> <pre>V = 1/6 · π · h · (h² + 3·a² + 3·b²) </pre> <p>Com a cas especial de zona esfèrica, un <b><a href="/wiki/Casquet_esf%C3%A8ric" title="Casquet esfèric">casquet esfèric</a></b> és una zona esfèrica delimitada per un sol pla que talla l'esfera (un dels dos plans anteriors seria tangent, o amb una base de radi 0). En aquest cas, l'àrea del casquet es calcula com per a un segment de dos bases, i el volum del casquet seria simplement: </p> <pre>V = 1/6 · π · h · (h² + 3·a²) </pre> <p>Un <b><a href="/wiki/Hemisferi" title="Hemisferi">hemisferi</a></b> és un casquet esfèric delimitat per un sol pla que passa per un <a href="/wiki/Cercle_m%C3%A0xim" title="Cercle màxim">cercle màxim</a> de l'esfera. </p> <div class="mw-heading mw-heading2"><h2 id="Fus_i_tascó_esfèrics"><span id="Fus_i_tasc.C3.B3_esf.C3.A8rics"></span>Fus i tascó esfèrics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=4" title="Modifica la secció: Fus i tascó esfèrics"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Un <b>fus esfèric</b> o <b>lúnula</b> és una de les dues parts (oposades i simètriques) de la superfície esfèrica delimitada per dos cercles màxims que es tallen. L'àrea d'un fus esfèric, d'una esfera de radi <i>r</i>, amb una longitud angular de <i>θ</i> (l'angle de tall dels cercles màxims, en <a href="/wiki/Radian" title="Radian">radians</a>) és: </p> <pre>A = 2 · r² · θ </pre> <p>Un <b>tascó esfèric</b> o <b>cuny</b> és el sòlid delimitat per un fus esfèric, i els dos plans que el delimiten, que es tallen a l'eix de l'esfera. El volum d'un cuny esfèric, d'una esfera de radi <i>r</i>, amb una longitud angular de <i>θ</i> (en radians) és: </p> <pre>V = 2/3 · r<sup>3</sup> · θ </pre> <div class="mw-heading mw-heading2"><h2 id="Triangle_esfèric"><span id="Triangle_esf.C3.A8ric"></span>Triangle esfèric</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=5" title="Modifica la secció: Triangle esfèric"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Un <b>triangle esfèric</b> és una part de la superfície esfèrica delimitada per tres cercles màxims que es tallen. L'àrea d'un triangle esfèric, d'una esfera de radi <i>r</i>, amb angles <i>L</i>, <i>M</i> i <i>N</i> (mesurats en <a href="/wiki/Radian" title="Radian">radians</a>) és: </p> <pre>A = r² · (L + M + N - π) </pre> <p>La magnitud <i>(L + M + N - pi)</i> s'anomena <i>excés esfèric</i>, i és l'excés sobre pi de la suma dels tres angles del triangle esfèric (els tres angles d'un triangle sobre el pla euclidià sumen sempre <i>pi</i>; en canvi, els tres angles d'un triangle esfèric sumen sempre més gran que <i>pi</i>). </p> <div class="mw-heading mw-heading2"><h2 id="Sector_esfèric"><span id="Sector_esf.C3.A8ric"></span>Sector esfèric</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=6" title="Modifica la secció: Sector esfèric"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Un <b>sector esfèric</b> és el sòlid limitat per una <a href="/wiki/Con" title="Con">superfície cònica</a> que té el <a href="/wiki/V%C3%A8rtex_(geometria)" title="Vèrtex (geometria)">vèrtex</a> en el centre d'una esfera, i la superfície de l'esfera. Si <i>S</i> és l'<a href="/wiki/%C3%80rea" title="Àrea">àrea</a> de la part d'esfera que el limita i <i>r</i> n'és el radi, el volum del sector val <i>rS</i>/3. </p> <div class="mw-heading mw-heading2"><h2 id="Moments_d'inèrcia"><span id="Moments_d.27in.C3.A8rcia"></span>Moments d'inèrcia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=7" title="Modifica la secció: Moments d'inèrcia"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Esfera buida de radi «r» i massa «m». <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 I={\frac {2}{3}}mr^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mi>m</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I={\frac {2}{3}}mr^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d9ee49edba0394b8d74fe2a174bb1e505f633a9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:10.799ex; height:5.176ex;" alt="{\displaystyle I={\frac {2}{3}}mr^{2}\,\!}"></span>  <sup id="cite_ref-Universit&eacute_1_2018_k155_3-0" class="reference"><a href="#cite_note-Universit&eacute_1_2018_k155-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li>Esfera sòlida. <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 I={\frac {2}{5}}mr^{2}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>5</mn> </mfrac> </mrow> <mi>m</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I={\frac {2}{5}}mr^{2}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ed3b74af5b1ee0ef5173ed2fcfb17e28071fe235" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:10.799ex; height:5.176ex;" alt="{\displaystyle I={\frac {2}{5}}mr^{2}\,\!}"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Obres_amb_contingut_sobre_l'esfera"><span id="Obres_amb_contingut_sobre_l.27esfera"></span>Obres amb contingut sobre l'esfera</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=8" title="Modifica la secció: Obres amb contingut sobre l'esfera"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:IBM_Selectric_Globe_Wiki.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/IBM_Selectric_Globe_Wiki.jpg/220px-IBM_Selectric_Globe_Wiki.jpg" decoding="async" width="220" height="153" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/IBM_Selectric_Globe_Wiki.jpg/330px-IBM_Selectric_Globe_Wiki.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/IBM_Selectric_Globe_Wiki.jpg/440px-IBM_Selectric_Globe_Wiki.jpg 2x" data-file-width="1243" data-file-height="865" /></a><figcaption>Boles de tipus IBM, cadascuna amb el seu <a href="/w/index.php?title=Joc_de_car%C3%A0cters&action=edit&redlink=1" class="new" title="Joc de caràcters (encara no existeix)">joc de caràcters</a>.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Campbell-Stokes_recorder.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Campbell-Stokes_recorder.jpg/220px-Campbell-Stokes_recorder.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Campbell-Stokes_recorder.jpg/330px-Campbell-Stokes_recorder.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Campbell-Stokes_recorder.jpg/440px-Campbell-Stokes_recorder.jpg 2x" data-file-width="1500" data-file-height="1125" /></a><figcaption>Heliògraf Campbell–Stokes usat en una regió tropical.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fitxer:Ball_joint_cross_section_(from_English_Wikipedia_to_be_used_in_other_languages).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Ball_joint_cross_section_%28from_English_Wikipedia_to_be_used_in_other_languages%29.jpg/220px-Ball_joint_cross_section_%28from_English_Wikipedia_to_be_used_in_other_languages%29.jpg" decoding="async" width="220" height="162" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c3/Ball_joint_cross_section_%28from_English_Wikipedia_to_be_used_in_other_languages%29.jpg/330px-Ball_joint_cross_section_%28from_English_Wikipedia_to_be_used_in_other_languages%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/c3/Ball_joint_cross_section_%28from_English_Wikipedia_to_be_used_in_other_languages%29.jpg 2x" data-file-width="343" data-file-height="253" /></a><figcaption>Ròtula típica mostrant el seu interior</figcaption></figure> <p>Les propietats de la superfície esfèrica i de la bola han estat objecte de diversos estudis teòrics i de nombroses aplicacions pràctiques. Vegeu una relació aleatòria (necessàriament incompleta) a continuació. </p> <ul><li>c220aC. <a href="/wiki/Arquimedes" title="Arquimedes">Arquimedes</a>. <i>De l'esfera i el cilindre</i>.<sup id="cite_ref-Biblioteca_Provinciale_1844_p._144_4-0" class="reference"><a href="#cite_note-Biblioteca_Provinciale_1844_p._144-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Masià_2010_p._5-0" class="reference"><a href="#cite_note-Masià_2010_p.-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>c1320. <b>De Sphaera mundi</b> (<i>De l'esfera del món</i>, també anomenat <i>Tractatus de Sphaera</i> o simplement <i>De Sphaera</i>)<sup id="cite_ref-Sacrobosco.)1501_6-0" class="reference"><a href="#cite_note-Sacrobosco.)1501-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> és una obra medieval escrita per <a href="/wiki/Johannes_de_Sacrobosco" title="Johannes de Sacrobosco">Johannes de Sacrobosco</a> cap a l'any <a href="/wiki/1230" title="1230">1230</a> que introdueix els elements bàsics de l'<a href="/wiki/Astronomia" title="Astronomia">astronomia</a>. Inspirat en gran manera en l'<i><a href="/wiki/Almagest" title="Almagest">Almagest</a> </i> de <a href="/wiki/Claudi_Ptolemeu" title="Claudi Ptolemeu">Claudi Ptolemeu</a> i afegint idees de l'astronomia àrab, va ser una de les obres sobre astronomia més influents a Europa abans de <a href="/wiki/Nicolau_Cop%C3%A8rnic" title="Nicolau Copèrnic">Nicolau Copèrnic</a>. La primera edició va aparèixer el <a href="/wiki/1472" title="1472">1472</a> en <a href="/wiki/Ferrara" title="Ferrara">Ferrara</a>,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> i es van fer nombroses edicions i traduccions en els dos segles següents.</li></ul> <ul><li>1490. El primer globus terraqüi, anomenat «Globus Terraqüi de Nürnberg», va ser fabricat durant els anys <a href="/wiki/1490" title="1490">1490</a> i <a href="/wiki/1492" title="1492">1492</a> pel cartògraf alemany <a href="/wiki/Martin_Behaim" title="Martin Behaim">Martin Behaim</a>.<sup id="cite_ref-Bruce_2021_p._23_8-0" class="reference"><a href="#cite_note-Bruce_2021_p._23-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>c.1500. Rodament de boles de Leonardo da Vinci.<sup id="cite_ref-Conley_1998_p._287_9-0" class="reference"><a href="#cite_note-Conley_1998_p._287-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>c1502. Jaume Ferrer de Blanes.<sup id="cite_ref-Calvo_1869_p._77_10-0" class="reference"><a href="#cite_note-Calvo_1869_p._77-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li></ul> <div style="clear:{{#switch:left|center=both|#default=left;"> <table style="margin:auto; width:auto; border-collapse:collapse; border-style:none;"> <tbody><tr> <td width="20" valign="top" style="font-size:35px; padding:0 10px; text-align:left; font-family:'Times New Roman', serif; font-weight:bold; color:silver;">« </td> <td valign="middle" align="left" style="">...Y porque la carta de navegar no sierve del todo, ni abasta en la demostración mathemática de la regla susodicha, es menester una <b>forma mundi en figura spérica</b> y en dos emisperios, conpartida por sus líneas y grados, y el situ272 de la tierra, islas y mar; cada cosa puesta en su lugar. La qual figura mundi, yo dexo junto con estos capítulos de mi intensión y parescer porque más claramente sea vista la verdad. Y digo que, por entender la regla y plática susodicha, és menester que sea cosmógrapho, arismético y marinero, o saber su arte. Y quien estas tres sciencias juntas no havrá, es inpossible la pueda entender; ni tanpoco por otra forma ni regla, si pericia de las dichas tres sciencias no terná ... </td> <td width="20" valign="bottom" style="font-size:35px; padding:0 10px 10px; text-align:right; font-family:'Times New Roman', serif; font-weight:bold; color:silver;">» </td></tr> <tr> <td colspan="3" style="text-align:right; font-size:smaller;">— Jaume Ferrer de Blanes. Lo vot y parer de mossèn Jaume Ferrer acerca la capitulació feta entre los molt Cathòlichs Reys y lo rey de Portugal, en què se demostra quant ere lo auctor gran cosmògraph y mirablament pràtich en la mar. </td></tr></tbody></table></div> <ul><li>1611. Explicació de l'arc de sant Martí (a partir de les esferes d'aigua de la pluja). <ul><li>Aquest fenomen òptic cridà l'atenció dels humans des de l'antiguitat, que van donar-li les més diverses interpretacions. No és, però, fins al <a href="/wiki/1611" title="1611">1611</a> que es formula la teoria elemental (<a href="/w/index.php?title=Antonius_Demini&action=edit&redlink=1" class="new" title="Antonius Demini (encara no existeix)">Antonius Demini</a>), la qual serví de base a <a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">René Descartes</a> per a les seves conclusions. <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> aportaria les seves troballes sobre la descomposició en colors de la llum blanca del <a href="/wiki/Sol" title="Sol">Sol</a> que atribuí a <a href="/wiki/Marc_Antoni_de_Dominis" title="Marc Antoni de Dominis">Marc Antoni de Dominis</a> en la seva obra <i>Tractatus de radiis visus et lucis in vitris, perspectivis et iride</i> (1611).<sup id="cite_ref-CE_11-0" class="reference"><a href="#cite_note-CE-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Thomas_Young" title="Thomas Young">Thomas Young</a> en formulà ja la teoria completa.<sup id="cite_ref-Zajonc_1996_p._173_12-0" class="reference"><a href="#cite_note-Zajonc_1996_p._173-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li></ul></li></ul> <ul><li>c1620. <a href="/wiki/Antonie_van_Leeuwenhoek" title="Antonie van Leeuwenhoek">Antonie van Leeuwenhoek</a>. Microscopis simples. Alguns amb lents esfèriques.<sup id="cite_ref-Bradbury_2014_p._73_13-0" class="reference"><a href="#cite_note-Bradbury_2014_p._73-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>1853. Heliògraf Campbell–Stokes. Basat en una esfera de vidre.<sup id="cite_ref-Editors_of_the_Observatory_1897_p._284_14-0" class="reference"><a href="#cite_note-Editors_of_the_Observatory_1897_p._284-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Agrawal_Tiwari_2011_p._15_15-0" class="reference"><a href="#cite_note-Agrawal_Tiwari_2011_p._15-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>1876. El billar es basa en boles de gran precisió.<i>Nouveau traité complet du jeu de billard</i>.<sup id="cite_ref-Mangin_Caillet_1876_p._16-0" class="reference"><a href="#cite_note-Mangin_Caillet_1876_p.-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>1892. <i>A Treatise on the Mathematical Theory of Elasticity</i>. <ul><li>Vibracions i modes de vibració d'una superfície esfèrica.<sup id="cite_ref-Love_1892_p._311_17-0" class="reference"><a href="#cite_note-Love_1892_p._311-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li></ul></li></ul> <ul><li>1910. <i>El hogar</i>.<sup id="cite_ref-El_hogar_1910_p._129_18-0" class="reference"><a href="#cite_note-El_hogar_1910_p._129-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> <ul><li><i>La reina Maud endevinadora</i> (emprant una esfera de vidre).</li> <li>Lobsang Rampa.<sup id="cite_ref-Tuesday_Lobsang_Rampa_l366_19-0" class="reference"><a href="#cite_note-Tuesday_Lobsang_Rampa_l366-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li></ul></li></ul> <ul><li>1931. <a href="/wiki/Bol%C3%ADgraf" title="Bolígraf">Bolígraf</a>.<sup id="cite_ref-Walker_2019_p._21_20-0" class="reference"><a href="#cite_note-Walker_2019_p._21-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>1936. Junta Rzeppa. Amb sis boles.<sup id="cite_ref-Arafa_2020_p._157_21-0" class="reference"><a href="#cite_note-Arafa_2020_p._157-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>1961. Màquina d'escriure IBM Selectric. Anomenada "de bola".<sup id="cite_ref-Bywater_2019_p._8_22-0" class="reference"><a href="#cite_note-Bywater_2019_p._8-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>2004. Miralls esfèrics.<sup id="cite_ref-Majou_Borel_Mensch_2004_p._44_23-0" class="reference"><a href="#cite_note-Majou_Borel_Mensch_2004_p._44-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>2013. Ictineu 3.<sup id="cite_ref-ICTINEU_Submarins_v456_24-0" class="reference"><a href="#cite_note-ICTINEU_Submarins_v456-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>2017. Space360 Spherical Projection Theater.<sup id="cite_ref-Front_Pictures_2021_r006_25-0" class="reference"><a href="#cite_note-Front_Pictures_2021_r006-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup></li></ul> <ul><li>2023. <i>Sphere at The Venetian Resort</i> a Las Vegas.<sup id="cite_ref-Engadget_2023_a113_26-0" class="reference"><a href="#cite_note-Engadget_2023_a113-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referències"><span id="Refer.C3.A8ncies"></span>Referències</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=9" title="Modifica la secció: Referències"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist {{#if: | references-column-count references-column-count-{{{col}}}" style="list-style-type: decimal;"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Llengua_catalana_o267-1"><span class="mw-cite-backlink"><a href="#cite_ref-Llengua_catalana_o267_1-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="https://aplicacions.llengua.gencat.cat/llc/AppJava/index.html?action=Principal&method=detall&input_cercar=esfera&numPagina=1&database=DIEC&idFont=41253&idHit=41253&tipusFont=%3CI%3EDiccionari+de+la+llengua+catalana%3C%2FI%3E+de+l%27Institut+d%27Estudis+Catalans+%282a+edici%F3%29&numeroResultat=1&databases_avansada=&categories_avansada=&clickLink=detall&títol=esfera++&tematica=%28Totes%29&tipusCerca=cerca.tot">Optimot. Consultes lingüístiques</a>». [Consulta: 22 juliol 2023].</span><sup class="noprint Inline-Template"><span title=" since de juny 2024" style="white-space: nowrap;"><i>[<a href="/wiki/Viquip%C3%A8dia:Enlla%C3%A7os_externs#Manteniment_d'enllaços_externs" title="Viquipèdia:Enllaços externs">Enllaç no actiu</a>]</i></span></sup></span> </li> <li id="cite_note-Search_Online_Etymology_Dictionary_v450-2"><span class="mw-cite-backlink"><a href="#cite_ref-Search_Online_Etymology_Dictionary_v450_2-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="https://www.etymonline.com/search?q=sphere&ref=searchbar_searchhint">sphere</a>». [Consulta: 23 juliol 2023].</span></span> </li> <li id="cite_note-Universit&eacute_1_2018_k155-3"><span class="mw-cite-backlink"><a href="#cite_ref-Universit&eacute_1_2018_k155_3-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal" id="CITEREFUniversit&eacute12018"><span style="font-variant: small-caps;">Universit&eacute</span>, Hassina ZEGHLACHE -; <span style="font-variant: small-caps;">1</span>, de Lille. «<a rel="nofollow" class="external text" href="http://res-nlp.univ-lemans.fr/NLP_C_M02_G01/co/grain12.html">Éléments de mécanique du solideMoments d'inertie d'une sphère.</a>» (en francès), 28-06-2018. [Consulta: 22 juliol 2023].</span></span> </li> <li id="cite_note-Biblioteca_Provinciale_1844_p._144-4"><span class="mw-cite-backlink"><a href="#cite_ref-Biblioteca_Provinciale_1844_p._144_4-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal">Biblioteca Provinciale. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=2p-ZMA_ygDIC&pg=PA144"><i>Oeuvres d'Archimède, traduites littéralement, avec un commentaire par F. Peyrard,...: Tome 1</i></a> (en francès).  Bachelier, 1844, p. 144 [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Oeuvres+d%27Archim%C3%A8de%2C+traduites+litt%C3%A9ralement%2C+avec+un+commentaire+par+F.+Peyrard%2C...%3A+Tome+1&rft.au=Biblioteca+Provinciale&rft.date=1844&rft.pub=Bachelier&rft.pages=144&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3D2p-ZMA_ygDIC%26pg%3DPA144"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Masià_2010_p.-5"><span class="mw-cite-backlink"><a href="#cite_ref-Masià_2010_p._5-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFMasià2010"><span style="font-variant: small-caps;">Masià</span>, R. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=PJTXwnS8jaMC"><i>Sobre l'esfera i el cilindre</i></a>.  Fundació Bernat Metge, 2010. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-84-9859-154-5" title="Especial:Fonts bibliogràfiques/978-84-9859-154-5">ISBN 978-84-9859-154-5</a></span> [Consulta: 21 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sobre+l%27esfera+i+el+cilindre&rft.aulast=Masi%C3%A0&rft.aufirst=R.&rft.date=2010&rft.pub=Fundaci%C3%B3+Bernat+Metge&rft.isbn=978-84-9859-154-5&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DPJTXwnS8jaMC"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Sacrobosco.)1501-6"><span class="mw-cite-backlink"><a href="#cite_ref-Sacrobosco.)1501_6-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal">Johannes (de Sacrobosco.). <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=K_RPAAAAcAAJ&pg=PA32-IA1"><i>Sphaera mundi</i></a>, 1501, p. 32–.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sphaera+mundi&rft.au=Johannes+%28de+Sacrobosco.%29&rft.date=1501&rft.pages=32%E2%80%93&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DK_RPAAAAcAAJ%26pg%3DPA32-IA1"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFThorntonTully1971"><span style="font-variant: small-caps;">Thornton</span>, John Leonard; <span style="font-variant: small-caps;">Tully</span>, R. I. J.. <a rel="nofollow" class="external text" href="http://books.google.cat/books?id=HQUFAQAAIAAJ&q=De+sphaera+mundi+ferrara+1472&dq=De+sphaera+mundi+ferrara+1472&hl=ca&sa=X&ei=HcLaUN-bL63P0AXyx4HQDg&ved=0CDkQ6AEwAQ"><i>Scientific books, libraries and collectors: a study of bibliography and the book trade in relation to science</i></a> (en anglès).  Library Association, 1971, p.40.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Scientific+books%2C+libraries+and+collectors%3A+a+study+of+bibliography+and+the+book+trade+in+relation+to+science&rft.aulast=Thornton&rft.aufirst=John+Leonard&rft.date=1971&rft.pub=Library+Association&rft.pages=p.40&rft_id=http%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DHQUFAQAAIAAJ%26q%3DDe%2Bsphaera%2Bmundi%2Bferrara%2B1472%26dq%3DDe%2Bsphaera%2Bmundi%2Bferrara%2B1472%26hl%3Dca%26sa%3DX%26ei%3DHcLaUN-bL63P0AXyx4HQDg%26ved%3D0CDkQ6AEwAQ"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Bruce_2021_p._23-8"><span class="mw-cite-backlink"><a href="#cite_ref-Bruce_2021_p._23_8-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFBruce2021"><span style="font-variant: small-caps;">Bruce</span>, B.C.. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=WkUpEAAAQBAJ&pg=PR23"><i>Thinking with Maps: Understanding the World Through Spatialization</i></a>.  Rowman & Littlefield Publishers, 2021, p. 23. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-1-4758-5930-0" title="Especial:Fonts bibliogràfiques/978-1-4758-5930-0">ISBN 978-1-4758-5930-0</a></span> [Consulta: 23 agost 2021].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Thinking+with+Maps%3A+Understanding+the+World+Through+Spatialization&rft.aulast=Bruce&rft.aufirst=B.C.&rft.date=2021&rft.pub=Rowman+%26+Littlefield+Publishers&rft.pages=23&rft.isbn=978-1-4758-5930-0&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DWkUpEAAAQBAJ%26pg%3DPR23"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Conley_1998_p._287-9"><span class="mw-cite-backlink"><a href="#cite_ref-Conley_1998_p._287_9-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFConley1998"><span style="font-variant: small-caps;">Conley</span>, P.L.. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=9e4Omibz3L4C&pg=PA287"><i>Space Vehicle Mechanisms: Elements of Successful Design</i></a>.  Wiley, 1998, p. 287. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-0-471-12141-1" title="Especial:Fonts bibliogràfiques/978-0-471-12141-1">ISBN 978-0-471-12141-1</a></span> [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Space+Vehicle+Mechanisms%3A+Elements+of+Successful+Design&rft.aulast=Conley&rft.aufirst=P.L.&rft.date=1998&rft.pub=Wiley&rft.pages=287&rft.isbn=978-0-471-12141-1&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3D9e4Omibz3L4C%26pg%3DPA287"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Calvo_1869_p._77-10"><span class="mw-cite-backlink"><a href="#cite_ref-Calvo_1869_p._77_10-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFCalvo1869"><span style="font-variant: small-caps;">Calvo</span>, C. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=a340AQAAMAAJ&pg=PA77"><i>Coleccion histórica completa de los tratdos, convenciones, capitulaciones, armistricios, y otros actos diplomáticos de todos los estados: de la America Latina comprendidos entre el golfo de Méjico y el cabo de Hornos, desde el año de 1493 hasta nuestros dias</i></a> (en castellà).  A. Durand, 1869, p. 77 [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Coleccion+hist%C3%B3rica+completa+de+los+tratdos%2C+convenciones%2C+capitulaciones%2C+armistricios%2C+y+otros+actos+diplom%C3%A1ticos+de+todos+los+estados%3A+de+la+America+Latina+comprendidos+entre+el+golfo+de+M%C3%A9jico+y+el+cabo+de+Hornos%2C+desde+el+a%C3%B1o+de+1493+hasta+nuestros+dias&rft.aulast=Calvo&rft.aufirst=C.&rft.date=1869&rft.pub=A.+Durand&rft.pages=77&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3Da340AQAAMAAJ%26pg%3DPA77"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-CE-11"><span class="mw-cite-backlink"><a href="#cite_ref-CE_11-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFMyers1909"><span style="font-variant: small-caps;">Myers</span>, E. «<a rel="nofollow" class="external text" href="http://www.newadvent.org/cathen/05113b.htm">Marco Antonio de Dominis</a>». A: <i>The Catholic Encyclopedia</i> (en anglès).  <a href="/wiki/Nova_York" title="Nova York">Nova York</a>: Robert Appleton Company, 1909.</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Catholic+Encyclopedia&rft.atitle=Marco+Antonio+de+Dominis&rft.aulast=Myers&rft.aufirst=E&rft.date=1909&rft.pub=Robert+Appleton+Company&rft.place=%5B%5BNova+York%5D%5D"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Zajonc_1996_p._173-12"><span class="mw-cite-backlink"><a href="#cite_ref-Zajonc_1996_p._173_12-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFZajonc1996"><span style="font-variant: small-caps;">Zajonc</span>, A. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=lWUylHJVrscC&pg=PA173"><i>Atrapando la Luz: Historia de la Luz y de la Mente</i></a> (en castellà).  Andrés Bello, 1996, p. 173. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-956-13-1270-8" title="Especial:Fonts bibliogràfiques/978-956-13-1270-8">ISBN 978-956-13-1270-8</a></span> [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atrapando+la+Luz%3A+Historia+de+la+Luz+y+de+la+Mente&rft.aulast=Zajonc&rft.aufirst=A.&rft.date=1996&rft.pub=Andr%C3%A9s+Bello&rft.pages=173&rft.isbn=978-956-13-1270-8&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DlWUylHJVrscC%26pg%3DPA173"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Bradbury_2014_p._73-13"><span class="mw-cite-backlink"><a href="#cite_ref-Bradbury_2014_p._73_13-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFBradbury2014"><span style="font-variant: small-caps;">Bradbury</span>, S. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=1bGRBQAAQBAJ&pg=PA73"><i>The Evolution of the Microscope</i></a>.  Elsevier Science, 2014, p. 73. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-1-4831-6432-8" title="Especial:Fonts bibliogràfiques/978-1-4831-6432-8">ISBN 978-1-4831-6432-8</a></span> [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Evolution+of+the+Microscope&rft.aulast=Bradbury&rft.aufirst=S.&rft.date=2014&rft.pub=Elsevier+Science&rft.pages=73&rft.isbn=978-1-4831-6432-8&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3D1bGRBQAAQBAJ%26pg%3DPA73"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Editors_of_the_Observatory_1897_p._284-14"><span class="mw-cite-backlink"><a href="#cite_ref-Editors_of_the_Observatory_1897_p._284_14-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=HgE4AAAAMAAJ&pg=PA284"><i>The Observatory</i></a>.  Editors of the Observatory, 1897, p. 284 [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Observatory&rft.date=1897&rft.pub=Editors+of+the+Observatory&rft.pages=284&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DHgE4AAAAMAAJ%26pg%3DPA284"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Agrawal_Tiwari_2011_p._15-15"><span class="mw-cite-backlink"><a href="#cite_ref-Agrawal_Tiwari_2011_p._15_15-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFAgrawalTiwari2011"><span style="font-variant: small-caps;">Agrawal</span>, B.; <span style="font-variant: small-caps;">Tiwari</span>, G.N.. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=SNNpN6jBBkQC&pg=PA15"><i>Building Integrated Photovoltaic Thermal Systems: For Sustainable Developments</i></a>.  Royal Society of Chemistry, 2011, p. 15. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-1-84973-090-7" title="Especial:Fonts bibliogràfiques/978-1-84973-090-7">ISBN 978-1-84973-090-7</a></span> [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Building+Integrated+Photovoltaic+Thermal+Systems%3A+For+Sustainable+Developments&rft.aulast=Agrawal&rft.aufirst=B.&rft.date=2011&rft.pub=Royal+Society+of+Chemistry&rft.pages=15&rft.isbn=978-1-84973-090-7&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DSNNpN6jBBkQC%26pg%3DPA15"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Mangin_Caillet_1876_p.-16"><span class="mw-cite-backlink"><a href="#cite_ref-Mangin_Caillet_1876_p._16-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFManginCaillet1876"><span style="font-variant: small-caps;">Mangin</span>, E.; <span style="font-variant: small-caps;">Caillet</span>, J. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=NeH9dMr0C9EC"><i>Nouveau traité complet du jeu de billard. ... Préface par M. J. C. [i.e. J. Caillet.</i></a>] (en francès), 1876 [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nouveau+trait%C3%A9+complet+du+jeu+de+billard.+...+Pr%C3%A9face+par+M.+J.+C.+%5Bi.e.+J.+Caillet.%5D&rft.aulast=Mangin&rft.aufirst=E.&rft.date=1876&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DNeH9dMr0C9EC"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Love_1892_p._311-17"><span class="mw-cite-backlink"><a href="#cite_ref-Love_1892_p._311_17-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFLove1892"><span style="font-variant: small-caps;">Love</span>, A.E.H.. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=-GkSAAAAIAAJ&pg=PA311"><i>A Treatise on the Mathematical Theory of Elasticity</i></a>.  At the University Press, 1892, p. 311 [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Treatise+on+the+Mathematical+Theory+of+Elasticity&rft.aulast=Love&rft.aufirst=A.E.H.&rft.date=1892&rft.pub=At+the+University+Press&rft.pages=311&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3D-GkSAAAAIAAJ%26pg%3DPA311"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-El_hogar_1910_p._129-18"><span class="mw-cite-backlink"><a href="#cite_ref-El_hogar_1910_p._129_18-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal"> <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=GkUxAQAAMAAJ&pg=PP129"><i>El hogar</i></a> (en castellà), 1910, p. 129 [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=El+hogar&rft.date=1910&rft.pages=129&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DGkUxAQAAMAAJ%26pg%3DPP129"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Tuesday_Lobsang_Rampa_l366-19"><span class="mw-cite-backlink"><a href="#cite_ref-Tuesday_Lobsang_Rampa_l366_19-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="https://www.lobsangrampa.org/scrying.html">Scrying</a>». [Consulta: 22 juliol 2023].</span></span> </li> <li id="cite_note-Walker_2019_p._21-20"><span class="mw-cite-backlink"><a href="#cite_ref-Walker_2019_p._21_20-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFWalker2019"><span style="font-variant: small-caps;">Walker</span>, K. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=3MiNDwAAQBAJ&pg=PT21"><i>STEAM guía los inventos: STEAM guides in Inventions</i></a> (en castellà).  Rourke Educational Media, 2019, p. 21. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-1-7316-2035-4" title="Especial:Fonts bibliogràfiques/978-1-7316-2035-4">ISBN 978-1-7316-2035-4</a></span> [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=STEAM+gu%C3%ADa+los+inventos%3A+STEAM+guides+in+Inventions&rft.aulast=Walker&rft.aufirst=K.&rft.date=2019&rft.pub=Rourke+Educational+Media&rft.pages=21&rft.isbn=978-1-7316-2035-4&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3D3MiNDwAAQBAJ%26pg%3DPT21"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Arafa_2020_p._157-21"><span class="mw-cite-backlink"><a href="#cite_ref-Arafa_2020_p._157_21-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFArafa2020"><span style="font-variant: small-caps;">Arafa</span>, H.A.. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=vZEAEAAAQBAJ&pg=PA157"><i>Design for Durability and Performance Density</i></a>.  Springer International Publishing, 2020, p. 157. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-3-030-56816-0" title="Especial:Fonts bibliogràfiques/978-3-030-56816-0">ISBN 978-3-030-56816-0</a></span> [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Design+for+Durability+and+Performance+Density&rft.aulast=Arafa&rft.aufirst=H.A.&rft.date=2020&rft.pub=Springer+International+Publishing&rft.pages=157&rft.isbn=978-3-030-56816-0&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DvZEAEAAAQBAJ%26pg%3DPA157"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Bywater_2019_p._8-22"><span class="mw-cite-backlink"><a href="#cite_ref-Bywater_2019_p._8_22-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFBywater2019"><span style="font-variant: small-caps;">Bywater</span>, E. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=hi9zDAAAQBAJ&pg=PT8"><i>Social Inertia & Keyboards</i></a>.  Lulu.com, 2019, p. 8. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-1-365-15273-3" title="Especial:Fonts bibliogràfiques/978-1-365-15273-3">ISBN 978-1-365-15273-3</a></span> [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Social+Inertia+%26+Keyboards&rft.aulast=Bywater&rft.aufirst=E.&rft.date=2019&rft.pub=Lulu.com&rft.pages=8&rft.isbn=978-1-365-15273-3&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3Dhi9zDAAAQBAJ%26pg%3DPT8"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-Majou_Borel_Mensch_2004_p._44-23"><span class="mw-cite-backlink"><a href="#cite_ref-Majou_Borel_Mensch_2004_p._44_23-0">↑</a></span> <span class="reference-text"><span class="citation book" style="font-style:normal" id="CITEREFMajouBorelMensch2004"><span style="font-variant: small-caps;">Majou</span>, J.; <span style="font-variant: small-caps;">Borel</span>, F.; <span style="font-variant: small-caps;">Mensch</span>, H. <a rel="nofollow" class="external text" href="https://books.google.cat/books?id=mZoeR4EMaDMC&pg=PA44"><i>Physique !: tout le programme PCSI, MPSI, PTSI</i></a> (en francès).  Bréal, 2004, p. 44. <span style="font-size:90%; white-space:nowrap;"><a href="/wiki/Especial:Fonts_bibliogr%C3%A0fiques/978-2-7495-0307-3" title="Especial:Fonts bibliogràfiques/978-2-7495-0307-3">ISBN 978-2-7495-0307-3</a></span> [Consulta: 22 juliol 2023].</span><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Physique+%21%3A+tout+le+programme+PCSI%2C+MPSI%2C+PTSI&rft.aulast=Majou&rft.aufirst=J.&rft.date=2004&rft.pub=Br%C3%A9al&rft.pages=44&rft.isbn=978-2-7495-0307-3&rft_id=https%3A%2F%2Fbooks.google.cat%2Fbooks%3Fid%3DmZoeR4EMaDMC%26pg%3DPA44"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-ICTINEU_Submarins_v456-24"><span class="mw-cite-backlink"><a href="#cite_ref-ICTINEU_Submarins_v456_24-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="http://www.ictineu.net/projectes/ictineu-3/">Submarí ICTINEU 3</a>». [Consulta: 22 juliol 2023].</span></span> </li> <li id="cite_note-Front_Pictures_2021_r006-25"><span class="mw-cite-backlink"><a href="#cite_ref-Front_Pictures_2021_r006_25-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="https://frontpictures.com/backstage/spherical-projection-theater-space360-making-of">Space360 Spherical Projection Theater Making-of</a>», 11-02-2021. [Consulta: 22 juliol 2023].</span></span> </li> <li id="cite_note-Engadget_2023_a113-26"><span class="mw-cite-backlink"><a href="#cite_ref-Engadget_2023_a113_26-0">↑</a></span> <span class="reference-text"><span class="citation" style="font-style:normal">«<a rel="nofollow" class="external text" href="https://www.engadget.com/the-venetian-resort-starts-testing-its-giant-led-video-sphere-153112387.html">Sphere testing its giant LED video dome in Las Vegas</a>», 04-07-2023. [Consulta: 22 juliol 2023].</span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Enllaços_externs"><span id="Enlla.C3.A7os_externs"></span>Enllaços externs</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&action=edit&section=10" title="Modifica la secció: Enllaços externs"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r33663753">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}.mw-parser-output .side-box-center{clear:both;margin:auto}}</style><div class="side-box metadata side-box-right plainlinks"> <div class="side-box-flex"> <div class="side-box-image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">A <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/P%C3%A0gina_principal?uselang=ca">Wikimedia Commons</a></span> hi ha contingut multimèdia relatiu a: <i><b><a href="https://commons.wikimedia.org/wiki/Category:Spheres" class="extiw" title="commons:Category:Spheres">Esfera</a></b></i></div></div> </div> <ul><li><a rel="nofollow" class="external text" href="http://www.xtec.cat/~ebraso/visual/geometria3d/escudella/escudella.html">Demostració de la fórmula del volum de l'esfera utilitzant el principi de Cavalieri</a></li></ul> <div role="navigation" class="navbox" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Control_d%27autoritats" title="Control d'autoritats">Registres d'autoritat</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/Biblioth%C3%A8que_nationale_de_France" class="mw-redirect" title="Bibliothèque nationale de France">BNF</a> <span class="uid"> (<a rel="nofollow" class="external text" href="http://catalogue.bnf.fr/ark:/12148/cb119812876">1</a>)</span></li> <li><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a> <span class="uid"> (<a rel="nofollow" class="external text" href="http://d-nb.info/gnd/4165914-4">1</a>)</span></li> <li><a href="/wiki/LCCN" class="mw-redirect" title="LCCN">LCCN</a> <span class="uid"> (<a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/subjects/sh85126590">1</a>)</span></li></ul> </div></td></tr></tbody></table></div> <p><span style="display: none;" class="interProject"><a href="https://ca.wiktionary.org/wiki/esfera" class="extiw" title="wikt:esfera">Viccionari</a></span> </p>    </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="">Obtingut de «<a dir="ltr" href="https://ca.wikipedia.org/w/index.php?title=Esfera&oldid=34004524">https://ca.wikipedia.org/w/index.php?title=Esfera&oldid=34004524</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">Categoria</a>: <ul><li><a href="/wiki/Categoria:Esferes" title="Categoria:Esferes">Esferes</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Categories ocultes: <ul><li><a href="/wiki/Categoria:Articles_amb_enlla%C3%A7os_externs_no_actius" title="Categoria:Articles amb enllaços externs no actius">Articles amb enllaços externs no actius</a></li><li><a href="/wiki/Categoria:Articles_sense_refer%C3%A8ncies" title="Categoria:Articles sense referències">Articles sense referències</a></li><li><a href="/wiki/Categoria:P%C3%A0gines_amb_enlla%C3%A7_commonscat_des_de_Wikidata" title="Categoria:Pàgines amb enllaç commonscat des de Wikidata">Pàgines amb enllaç commonscat des de Wikidata</a></li><li><a href="/wiki/Categoria:Control_d%27autoritats" title="Categoria:Control d'autoritats">Control d'autoritats</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"> La pàgina va ser modificada per darrera vegada el 24 set 2024 a les 09:39.</li> <li id="footer-info-copyright">El text està disponible sota la <a href="/wiki/Viquip%C3%A8dia:Text_de_la_llic%C3%A8ncia_de_Creative_Commons_Reconeixement-Compartir_Igual_4.0_No_adaptada" title="Viquipèdia:Text de la llicència de Creative Commons Reconeixement-Compartir Igual 4.0 No adaptada"> Llicència de Creative Commons Reconeixement i Compartir-Igual</a>; es poden aplicar termes addicionals. Vegeu les <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use/ca">Condicions d'ús</a>. Wikipedia® (Viquipèdia™) és una <a href="/wiki/Marca_comercial" title="Marca comercial">marca registrada</a> de <a rel="nofollow" class="external text" href="https://www.wikimediafoundation.org">Wikimedia Foundation, Inc</a>.<br /></li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Política de privadesa</a></li> <li id="footer-places-about"><a href="/wiki/Viquip%C3%A8dia:Quant_a_la_Viquip%C3%A8dia">Quant al projecte Viquipèdia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Viquip%C3%A8dia:Av%C3%ADs_d%27exempci%C3%B3_de_responsabilitat">Descàrrec de responsabilitat</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Codi de conducta</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Desenvolupadors</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/ca.wikipedia.org">Estadístiques</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Declaració de cookies</a></li> <li id="footer-places-mobileview"><a href="//ca.m.wikipedia.org/w/index.php?title=Esfera&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Versió per a mòbils</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-vbjf2","wgBackendResponseTime":188,"wgPageParseReport":{"limitreport":{"cputime":"0.385","walltime":"0.882","ppvisitednodes":{"value":8188,"limit":1000000},"postexpandincludesize":{"value":60791,"limit":2097152},"templateargumentsize":{"value":17425,"limit":2097152},"expansiondepth":{"value":12,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":32848,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 466.867 1 -total"," 46.17% 215.571 1 Plantilla:Infotaula_polítop"," 45.10% 210.554 1 Plantilla:Infotaula"," 34.45% 160.828 1 Plantilla:Referències"," 20.11% 93.885 19 Plantilla:Ref-llibre"," 8.94% 41.761 7 Plantilla:Ref-web"," 8.59% 40.102 1 Plantilla:Commonscat"," 6.91% 32.241 1 Plantilla:Sister"," 6.53% 30.498 1 Plantilla:Caixa_lateral"," 5.63% 26.287 23 Plantilla:Data_consulta"]},"scribunto":{"limitreport-timeusage":{"value":"0.119","limit":"10.000"},"limitreport-memusage":{"value":2898321,"limit":52428800}},"cachereport":{"origin":"mw-web.eqiad.main-7c55db6c78-r9mwj","timestamp":"20241026130613","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Esfera","url":"https:\/\/ca.wikipedia.org\/wiki\/Esfera","sameAs":"http:\/\/www.wikidata.org\/entity\/Q12507","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q12507","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2004-01-13T23:15:27Z","dateModified":"2024-09-24T08:39:26Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/7\/7e\/Sphere_wireframe_10deg_6r.svg","headline":"forma geom\u00e8trica"}</script> </body> </html>