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href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_gl.wikipedia.org&uselang=gl" class=""><span>Doazóns</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:Crear_unha_conta&returnto=Esfera" title="É recomendable que cree unha conta e acceda ao sistema, se ben non é obrigatorio" class=""><span>Crear unha conta</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Especial:Iniciar_sesi%C3%B3n&returnto=Esfera" title="É recomendable que se rexistre, se ben non é obrigatorio [o]" accesskey="o" class=""><span>Acceder ao sistema</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right 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mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_gl.wikipedia.org&uselang=gl"><span>Doazóns</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Crear_unha_conta&returnto=Esfera" title="É recomendable que cree unha conta e acceda ao sistema, se ben non é obrigatorio"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Crear unha conta</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Especial:Iniciar_sesi%C3%B3n&returnto=Esfera" title="É recomendable que se rexistre, se ben non é obrigatorio [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Acceder ao sistema</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"> Páxinas para os editores sen a sesión iniciada <a href="/wiki/Axuda:Introduci%C3%B3n" aria-label="Máis información sobre a edición"><span>máis información</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:As_mi%C3%B1as_contribuci%C3%B3ns" title="Unha lista das modificacións feitas desde este enderezo IP [y]" accesskey="y"><span>Contribucións</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Especial:A_mi%C3%B1a_conversa" title="Conversa acerca de edicións feitas desde este enderezo IP [n]" accesskey="n"><span>Conversa</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="Sitio"> <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="Contidos" 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">Contidos</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mover á barra lateral</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">agochar</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">Inicio</div> </a> </li> <li id="toc-Terminoloxía_básica" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Terminoloxía_básica"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Terminoloxía básica</span> </div> </a> <ul id="toc-Terminoloxía_básica-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ecuacións" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ecuacións"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Ecuacións</span> </div> </a> <button aria-controls="toc-Ecuacións-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Mostrar ou agochar a subsección "Ecuacións"</span> </button> <ul id="toc-Ecuacións-sublist" class="vector-toc-list"> <li id="toc-Paramétricas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Paramétricas"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Paramétricas</span> </div> </a> <ul id="toc-Paramétricas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fórmulas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fórmulas"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Fórmulas</span> </div> </a> <ul id="toc-Fórmulas-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Rexións" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rexións"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Rexións</span> </div> </a> <ul id="toc-Rexións-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notas" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notas"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notas</span> </div> </a> <ul id="toc-Notas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Véxase_tamén" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Véxase_tamén"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Véxase tamén</span> </div> </a> <button aria-controls="toc-Véxase_tamén-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Mostrar ou agochar a subsección "Véxase tamén"</span> </button> <ul id="toc-Véxase_tamén-sublist" class="vector-toc-list"> <li id="toc-Outros_artigos" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Outros_artigos"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Outros artigos</span> </div> </a> <ul id="toc-Outros_artigos-sublist" class="vector-toc-list"> </ul> </li> </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="Contidos" 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="Mostrar ou agochar a táboa de contidos" > <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">Mostrar ou agochar a táboa de contidos</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="Ir a un artigo noutra lingua. Dispoñible en 106 linguas" > <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 linguas</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 – amhárico" lang="am" hreflang="am" data-title="ሉል" data-language-autonym="አማርኛ" data-language-local-name="amhárico" 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 – árabe" lang="ar" hreflang="ar" data-title="كرة" data-language-autonym="العربية" data-language-local-name="árabe" 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 – asturiano" lang="ast" hreflang="ast" data-title="Esfera" data-language-autonym="Asturianu" data-language-local-name="asturiano" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Sfera" title="Sfera – acerbaixano" lang="az" hreflang="az" data-title="Sfera" data-language-autonym="Azərbaycanca" data-language-local-name="acerbaixano" 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 – baxkir" lang="ba" hreflang="ba" data-title="Сфера" data-language-autonym="Башҡортса" data-language-local-name="baxkir" 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 – belaruso" lang="be" hreflang="be" data-title="Сфера" data-language-autonym="Беларуская" data-language-local-name="belaruso" 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 – búlgaro" lang="bg" hreflang="bg" data-title="Сфера" data-language-autonym="Български" data-language-local-name="búlgaro" 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 – bosníaco" lang="bs" hreflang="bs" data-title="Sfera" data-language-autonym="Bosanski" data-language-local-name="bosníaco" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Esfera" title="Esfera – catalán" lang="ca" hreflang="ca" data-title="Esfera" data-language-autonym="Català" data-language-local-name="catalán" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-chr mw-list-item"><a href="https://chr.wikipedia.org/wiki/%E1%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 – kurdo central" lang="ckb" hreflang="ckb" data-title="گۆ" data-language-autonym="کوردی" data-language-local-name="kurdo 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) – checo" lang="cs" hreflang="cs" data-title="Sféra (matematika)" data-language-autonym="Čeština" data-language-local-name="checo" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0" title="Сфера – chuvaxo" lang="cv" hreflang="cv" data-title="Сфера" data-language-autonym="Чӑвашла" data-language-local-name="chuvaxo" 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 – galés" lang="cy" hreflang="cy" data-title="Sffêr" data-language-autonym="Cymraeg" data-language-local-name="galés" 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 – dinamarqués" lang="da" hreflang="da" data-title="Kugle" data-language-autonym="Dansk" data-language-local-name="dinamarqués" 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 – alemán" lang="de" hreflang="de" data-title="Kugel" data-language-autonym="Deutsch" data-language-local-name="alemán" 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 – grego" lang="el" hreflang="el" data-title="Σφαίρα" data-language-autonym="Ελληνικά" data-language-local-name="grego" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Sphere" title="Sphere – inglés" lang="en" hreflang="en" data-title="Sphere" data-language-autonym="English" data-language-local-name="inglés" 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 – español" lang="es" hreflang="es" data-title="Esfera" data-language-autonym="Español" data-language-local-name="español" 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 – estoniano" lang="et" hreflang="et" data-title="Sfäär" data-language-autonym="Eesti" data-language-local-name="estoniano" 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 – éuscaro" lang="eu" hreflang="eu" data-title="Esfera" data-language-autonym="Euskara" data-language-local-name="éuscaro" 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) – finés" lang="fi" hreflang="fi" data-title="Pallo (geometria)" data-language-autonym="Suomi" data-language-local-name="finés" 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) – fixiano" lang="fj" hreflang="fj" data-title="Vuravura (Geometry)" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fixiano" 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 – francés" lang="fr" hreflang="fr" data-title="Sphère" data-language-autonym="Français" data-language-local-name="francés" 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 – frisón setentrional" lang="frr" hreflang="frr" data-title="Kuugel" data-language-autonym="Nordfriisk" data-language-local-name="frisón setentrional" 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 – irlandés" lang="ga" hreflang="ga" data-title="Sféar" data-language-autonym="Gaeilge" data-language-local-name="irlandés" 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 – Gan" lang="gan" hreflang="gan" data-title="球面" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/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 – gaélico escocés" lang="gd" hreflang="gd" data-title="Cruinne" data-language-autonym="Gàidhlig" data-language-local-name="gaélico escocés" class="interlanguage-link-target"><span>Gàidhlig</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 – guxarati" lang="gu" hreflang="gu" data-title="ગોળો" data-language-autonym="ગુજરાતી" data-language-local-name="guxarati" 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) – hebreo" lang="he" hreflang="he" data-title="ספירה (גאומטריה)" data-language-autonym="עברית" data-language-local-name="hebreo" 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 – croata" lang="hr" hreflang="hr" data-title="Sfera" data-language-autonym="Hrvatski" data-language-local-name="croata" 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 – crioulo haitiano" lang="ht" hreflang="ht" data-title="Esfè" data-language-autonym="Kreyòl ayisyen" data-language-local-name="crioulo haitiano" 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 – húngaro" lang="hu" hreflang="hu" data-title="Gömb" data-language-autonym="Magyar" data-language-local-name="húngaro" 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) – indonesio" lang="id" hreflang="id" data-title="Bola (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesio" 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 – islandés" lang="is" hreflang="is" data-title="Kúla" data-language-autonym="Íslenska" data-language-local-name="islandés" 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 – italiano" lang="it" hreflang="it" data-title="Sfera" data-language-autonym="Italiano" data-language-local-name="italiano" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%90%83%E9%9D%A2" title="球面 – xaponés" lang="ja" hreflang="ja" data-title="球面" data-language-autonym="日本語" data-language-local-name="xaponés" 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 – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Sfier" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-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 – xeorxiano" lang="ka" hreflang="ka" data-title="სფერო" data-language-autonym="ქართული" data-language-local-name="xeorxiano" 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 – cabila" lang="kab" hreflang="kab" data-title="Tasegla" data-language-autonym="Taqbaylit" data-language-local-name="cabila" 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 – kazako" lang="kk" hreflang="kk" data-title="Сфера" data-language-autonym="Қазақша" data-language-local-name="kazako" 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 – kannará" lang="kn" hreflang="kn" data-title="ಗೋಳ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannará" 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) – coreano" lang="ko" hreflang="ko" data-title="구 (기하학)" data-language-autonym="한국어" data-language-local-name="coreano" 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 – latín" lang="la" hreflang="la" data-title="Sphaera" data-language-autonym="Latina" data-language-local-name="latín" 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 – lituano" lang="lt" hreflang="lt" data-title="Sfera" data-language-autonym="Lietuvių" data-language-local-name="lituano" 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 – letón" lang="lv" hreflang="lv" data-title="Sfēra" data-language-autonym="Latviešu" data-language-local-name="letón" 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 – moksha" lang="mdf" hreflang="mdf" data-title="Сферась" data-language-autonym="Мокшень" data-language-local-name="moksha" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Bola_(je%C3%B4metria)" title="Bola (jeômetria) – malgaxe" lang="mg" hreflang="mg" data-title="Bola (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="malgaxe" 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 – macedonio" lang="mk" hreflang="mk" data-title="Сфера" data-language-autonym="Македонски" data-language-local-name="macedonio" 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 – malabar" lang="ml" hreflang="ml" data-title="ഗോളം" data-language-autonym="മലയാളം" data-language-local-name="malabar" 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 – malaio" lang="ms" hreflang="ms" data-title="Sfera" data-language-autonym="Bahasa Melayu" data-language-local-name="malaio" 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 – birmano" lang="my" hreflang="my" data-title="စက်လုံး" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmano" 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) – neerlandés" lang="nl" hreflang="nl" data-title="Sfeer (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="neerlandés" 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 – noruegués nynorsk" lang="nn" hreflang="nn" data-title="Kule" data-language-autonym="Norsk nynorsk" data-language-local-name="noruegués 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 – noruegués bokmål" lang="nb" hreflang="nb" data-title="Kule" data-language-autonym="Norsk bokmål" data-language-local-name="noruegués 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 – occitano" lang="oc" hreflang="oc" data-title="Esfèra" data-language-autonym="Occitan" data-language-local-name="occitano" 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 – panxabí" lang="pa" hreflang="pa" data-title="ਗੋਲ਼ਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panxabí" 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 – polaco" lang="pl" hreflang="pl" data-title="Sfera" data-language-autonym="Polski" data-language-local-name="polaco" 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 – Piedmontese" lang="pms" hreflang="pms" data-title="Sfera" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" 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 – portugués" lang="pt" hreflang="pt" data-title="Esfera" data-language-autonym="Português" data-language-local-name="portugués" 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 – quechua" lang="qu" hreflang="qu" data-title="Lunq'u" data-language-autonym="Runa Simi" data-language-local-name="quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Sfer%C4%83" title="Sferă – romanés" lang="ro" hreflang="ro" data-title="Sferă" data-language-autonym="Română" data-language-local-name="romanés" 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 – ruso" lang="ru" hreflang="ru" data-title="Сфера" data-language-autonym="Русский" data-language-local-name="ruso" 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 – iacuto" lang="sah" hreflang="sah" data-title="Сфера" data-language-autonym="Саха тыла" data-language-local-name="iacuto" 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 – siciliano" lang="scn" hreflang="scn" data-title="Sfera" data-language-autonym="Sicilianu" data-language-local-name="siciliano" 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 – serbocroata" lang="sh" hreflang="sh" data-title="Sfera" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbocroata" 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 – cingalés" lang="si" hreflang="si" data-title="ගෝලය" data-language-autonym="සිංහල" data-language-local-name="cingalés" 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) – eslovaco" lang="sk" hreflang="sk" data-title="Guľa (matematika)" data-language-autonym="Slovenčina" data-language-local-name="eslovaco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Sfera" title="Sfera – esloveno" lang="sl" hreflang="sl" data-title="Sfera" data-language-autonym="Slovenščina" data-language-local-name="esloveno" 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 – somalí" lang="so" hreflang="so" data-title="Kubad" data-language-autonym="Soomaaliga" data-language-local-name="somalí" 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 – albanés" lang="sq" hreflang="sq" data-title="Sfera" data-language-autonym="Shqip" data-language-local-name="albanés" 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 – serbio" lang="sr" hreflang="sr" data-title="Сфера" data-language-autonym="Српски / srpski" data-language-local-name="serbio" 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 – sundanés" lang="su" hreflang="su" data-title="Buleudan" data-language-autonym="Sunda" data-language-local-name="sundanés" 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 – sueco" lang="sv" hreflang="sv" data-title="Sfär" data-language-autonym="Svenska" data-language-local-name="sueco" 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 – támil" lang="ta" hreflang="ta" data-title="கோளம்" data-language-autonym="தமிழ்" data-language-local-name="támil" 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 – tailandés" lang="th" hreflang="th" data-title="ทรงกลม" data-language-autonym="ไทย" data-language-local-name="tailandés" 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 – tagalo" lang="tl" hreflang="tl" data-title="Espera" data-language-autonym="Tagalog" data-language-local-name="tagalo" 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 – turco" lang="tr" hreflang="tr" data-title="Küre" data-language-autonym="Türkçe" data-language-local-name="turco" 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 – tártaro" lang="tt" hreflang="tt" data-title="Сфера" data-language-autonym="Татарча / tatarça" data-language-local-name="tártaro" 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 – ucraíno" lang="uk" hreflang="uk" data-title="Сфера" data-language-autonym="Українська" data-language-local-name="ucraíno" 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 – uzbeko" lang="uz" hreflang="uz" data-title="Sfera" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeko" 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-waray" lang="war" hreflang="war" data-title="Espira" data-language-autonym="Winaray" data-language-local-name="waray-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 – chinés wu" lang="wuu" hreflang="wuu" data-title="球面" data-language-autonym="吴语" data-language-local-name="chinés 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 – chinés" lang="zh" hreflang="zh" data-title="球面" data-language-autonym="中文" data-language-local-name="chinés" 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 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="球" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Ki%C3%BB-b%C4%ABn" title="Kiû-bīn – Minnan" lang="nan" hreflang="nan" data-title="Kiû-bīn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 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alt="1000 12/16" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Hezkuntza_Programa_12-16_ikonoa.png/19px-Hezkuntza_Programa_12-16_ikonoa.png" decoding="async" width="19" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Hezkuntza_Programa_12-16_ikonoa.png/28px-Hezkuntza_Programa_12-16_ikonoa.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Hezkuntza_Programa_12-16_ikonoa.png/38px-Hezkuntza_Programa_12-16_ikonoa.png 2x" data-file-width="747" data-file-height="794" /></a></span></div></div> </div> <div id="siteSub" class="noprint">Na Galipedia, a Wikipedia en galego.</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="gl" dir="ltr"><p class="mw-empty-elt"> </p> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/Ficheiro:Sphere-wireframe.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/38/Sphere-wireframe.png/240px-Sphere-wireframe.png" decoding="async" width="240" height="240" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/3/38/Sphere-wireframe.png 1.5x" data-file-width="293" data-file-height="293" /></a><figcaption></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><span class="mw-3d-wrapper" data-label="3D"><a href="/wiki/Ficheiro:Esfera_3D.stl" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Esfera_3D.stl/220px-Esfera_3D.stl.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Esfera_3D.stl/330px-Esfera_3D.stl.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Esfera_3D.stl/440px-Esfera_3D.stl.png 2x" data-file-width="5120" data-file-height="2880" /></a></span><figcaption>Esfera 3D</figcaption></figure> <p>A <b>esfera</b> é o <a href="/wiki/Lugar_xeom%C3%A9trico" title="Lugar xeométrico">lugar xeométrico</a> dos puntos do espazo que teñen unha <a href="/wiki/Distancia" title="Distancia">distancia</a> constante respecto a outro chamado <a href="/wiki/Centro_(xeometr%C3%ADa)" title="Centro (xeometría)">centro</a>. Non debe confundirse o valor areal da súa superficie co volumétrico do espazo que pecha. Os dous están en función desa distancia constante chamada <a href="/wiki/Raio_(xeometr%C3%ADa)" title="Raio (xeometría)">raio</a> (R), pero a medida deste último ten o valor de: </p> <center><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}}\pi 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> <mi>π</mi> <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}}\pi R^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60d7dfd33621bd3f323449550e5808662468ad8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:11.035ex; height:5.176ex;" alt="{\displaystyle V={\frac {4}{3}}\pi R^{3}}"></span></center> <p>mentres que o valor da súa superficie é: </p> <center><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"> <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/d7b628bfaae1f0ec7467319f52c490a94a3a73bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.91ex; height:2.676ex;" alt="{\displaystyle S=4\pi R^{2}}"></span></center> <p>Podería definirse tamén a <b>esfera</b> coma un <a href="/wiki/Poliedro" title="Poliedro">poliedro</a> de infinitas caras. A importancia desta figura na xeometría levou á creación do sistema de <a href="/wiki/Coordenadas_polares" title="Coordenadas polares">coordenadas polares</a> en oposición ás tradicionais <a href="/wiki/Sistema_de_coordenadas_cartesianas" title="Sistema de coordenadas cartesianas">coordenadas cartesianas</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Terminoloxía_básica"><span id="Terminolox.C3.ADa_b.C3.A1sica"></span>Terminoloxía básica</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&veaction=edit&section=1" title="Editar a sección: «Terminoloxía básica»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Esfera&action=edit&section=1" title="Editar o código fonte da sección: Terminoloxía básica"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Ficheiro:Sphere_and_Ball.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Sphere_and_Ball.png/240px-Sphere_and_Ball.png" decoding="async" width="240" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Sphere_and_Ball.png/360px-Sphere_and_Ball.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Sphere_and_Ball.png/480px-Sphere_and_Ball.png 2x" data-file-width="1548" data-file-height="1536" /></a><figcaption>Dous raios ortogonais dunha esfera</figcaption></figure> <p>Como se mencionou anteriormente <span class="texhtml"><i>r</i></span> ou <span class="texhtml"><i>R</i></span> é o raio da esfera; calquera liña dende o centro ata un punto da esfera tamén se chama raio. "Raio" úsase en dous sentidos: como segmento de liña e tamén como lonxitude.<sup id="cite_ref-EB_1-0" class="reference"><a href="#cite_note-EB-1"><span>[</span>1<span>]</span></a></sup> </p><p>Se un raio se estende polo centro ata o lado oposto da esfera, crea un <a href="/wiki/Di%C3%A1metro" title="Diámetro">diámetro</a>. Do mesmo xeito que o raio, a lonxitude dun diámetro tamén se denomina diámetro e denótase <span class="texhtml"><i>d</i></span>. Os diámetros son os segmentos de liña máis longos que se poden trazar entre dous puntos da esfera: a súa lonxitude é o duplo do raio, <span class="texhtml"><i>d</i> = 2<i>r</i></span>. Dous puntos da esfera conectados por un diámetro son <a href="/w/index.php?title=Puntos_ant%C3%ADpodas&action=edit&redlink=1" class="new" title="Puntos antípodas (a páxina aínda non existe)">puntos antípodas</a> un do outro.<sup id="cite_ref-EB_1-1" class="reference"><a href="#cite_note-EB-1"><span>[</span>1<span>]</span></a></sup> </p><p>Unha <a href="/w/index.php?title=Esfera_unitaria&action=edit&redlink=1" class="new" title="Esfera unitaria (a páxina aínda non existe)">esfera unitaria</a> é unha esfera cun raio unitario (<span class="texhtml"><i>r</i> = 1</span>). Por comodidade, a miúdo considérase que as esferas teñen o seu centro na orixe do <a href="/wiki/Sistema_de_coordenadas" title="Sistema de coordenadas">sistema de coordenadas</a>, e as esferas deste artigo teñen o seu centro na orixe a non ser que se mencione outro centro. </p><p><span id="hemisferio"></span> Unha <i><a href="/w/index.php?title=Gran_circunferencia&action=edit&redlink=1" class="new" title="Gran circunferencia (a páxina aínda non existe)">gran circunferencia</a></i> na esfera ten o mesmo centro e raio que a esfera, e divídeo en dous <b>hemisferios</b> iguais. </p><p>Aínda que a <a href="/wiki/Terra" title="Terra">figura da Terra</a> non é perfectamente esférica, os termos tomados da xeografía son convenientes para aplicar á esfera. Unha liña particular que pasa polo seu centro define un <i><a href="/w/index.php?title=Eixe_de_simetr%C3%ADa&action=edit&redlink=1" class="new" title="Eixe de simetría (a páxina aínda non existe)">eixo</a></i> (como no <a href="/w/index.php?title=Eixo_de_rotaci%C3%B3n&action=edit&redlink=1" class="new" title="Eixo de rotación (a páxina aínda non existe)">eixo de rotación</a> da Terra). A intersección esfera-eixo define dous <i>polos</i> antípodas (<i>polo norte</i> e <i>polo sur</i>). O gran círculo equidistante aos polos chámase <i><a href="/wiki/Ecuador" title="Ecuador">ecuador</a></i>. Os grandes círculos que pasan polos polos chámanse liñas de <a href="/wiki/Lonxitude" title="Lonxitude">lonxitude</a> ou <a href="/wiki/Meridiano" title="Meridiano"><i>meridianos</i></a>. Os círculos pequenos da esfera que son paralelos ao ecuador son <a href="/wiki/Latitude" title="Latitude">círculos de latitude</a> (ou <i>paralelos</i>). </p><p>Os matemáticos consideran que unha esfera é unha <a href="/w/index.php?title=Superficie_pechada&action=edit&redlink=1" class="new" title="Superficie pechada (a páxina aínda non existe)">superficie pechada</a> <a href="/w/index.php?title=Incrustaci%C3%B3n&action=edit&redlink=1" class="new" title="Incrustación (a páxina aínda non existe)">incrustada</a> no <a href="/wiki/Espazo_euclidiano" title="Espazo euclidiano">espazo euclidiano</a> tridimensional. Estabelecen unha distinción entre unha <i>esfera</i> e unha <i><a href="/wiki/B%C3%B3la_(matem%C3%A1ticas)" title="Bóla (matemáticas)">bóla</a></i>, que é unha <a href="/wiki/Variedade_(xeometr%C3%ADa)" title="Variedade (xeometría)">variedade con límite</a> tridimensional que inclúe o volume que contén a esfera. Unha <i>bóla aberta</i> exclúe a esfera en si, mentres que unha <i>bóla pechada</i> inclúe a esfera: unha bóla pechada é a unión da bóla aberta e a esfera, e unha esfera é o <a href="/w/index.php?title=L%C3%ADmite_(topolox%C3%ADa)&action=edit&redlink=1" class="new" title="Límite (topoloxía) (a páxina aínda non existe)"> límite</a> dunha bóla (pechada ou aberta). A distinción entre <i>bóla</i> e <i>esfera</i> non sempre se mantivo e, sobre todo, as referencias matemáticas máis antigas falan dunha esfera como un sólido. A distinción entre "<a href="/wiki/C%C3%ADrculo" title="Círculo">círculo</a>" e "<a href="/w/index.php?title=Disco_(matem%C3%A1ticas)&action=edit&redlink=1" class="new" title="Disco (matemáticas) (a páxina aínda non existe)">disco</a>" no <a href="/wiki/Plano_(xeometr%C3%ADa)" title="Plano (xeometría)">plano</a> é semellante. </p><p>As pequenas esferas ou bólas chámanse ás veces esférulas. </p> <div class="mw-heading mw-heading2"><h2 id="Ecuacións"><span id="Ecuaci.C3.B3ns"></span>Ecuacións</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&veaction=edit&section=2" title="Editar a sección: «Ecuacións»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Esfera&action=edit&section=2" title="Editar o código fonte da sección: Ecuacións"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En <a href="/wiki/Xeometr%C3%ADa_anal%C3%ADtica" title="Xeometría analítica">xeometría analítica</a>, unha esfera co centro <span class="texhtml">(<i>x</i><sub>0</sub>, <i>y</i><sub>0</sub>, <i>z</i><sub>0</sub>)</span> e o raio <span class="texhtml mvar" style="font-style:italic;">r</span> é o <a href="/wiki/Lugar_xeom%C3%A9trico" title="Lugar xeométrico">lugar xeométrico</a> de todos os puntos <span class="texhtml">(<i>x</i>, <i>y</i>, <i>z</i>)</span> tal que </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (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> <mo>.</mo> </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/a476c6003522e221e5620b363ad446c25c0044b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.927ex; height:3.176ex;" alt="{\displaystyle (x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=r^{2}.}"></span></dd></dl> <p>Dado que se pode expresar como un polinomio cadrático, unha esfera é unha <a href="/w/index.php?title=Superficie_cadr%C3%A1tica&action=edit&redlink=1" class="new" title="Superficie cadrática (a páxina aínda non existe)">superficie cadrática</a>, un tipo de <a href="/w/index.php?title=Superficie_alx%C3%A9brica&action=edit&redlink=1" class="new" title="Superficie alxébrica (a páxina aínda non existe)">superficie alxébrica</a>.<sup id="cite_ref-EB_1-2" class="reference"><a href="#cite_note-EB-1"><span>[</span>1<span>]</span></a></sup> </p><p>Sexan <span class="texhtml mvar" style="font-style:italic;">a, b, c, d, e</span> números reais con <span class="texhtml"><i>a</i> ≠ 0</span> e facemos </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{0}={\frac {-b}{a}},\quad y_{0}={\frac {-c}{a}},\quad z_{0}={\frac {-d}{a}},\quad \rho ={\frac {b^{2}+c^{2}+d^{2}-ae}{a^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>b</mi> </mrow> <mi>a</mi> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>c</mi> </mrow> <mi>a</mi> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>d</mi> </mrow> <mi>a</mi> </mfrac> </mrow> <mo>,</mo> <mspace width="1em" /> <mi>ρ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>a</mi> <mi>e</mi> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{0}={\frac {-b}{a}},\quad y_{0}={\frac {-c}{a}},\quad z_{0}={\frac {-d}{a}},\quad \rho ={\frac {b^{2}+c^{2}+d^{2}-ae}{a^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/836ec8f22b47f49bcc6dd7dfdf439aa1229fa65b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:60.234ex; height:6.009ex;" alt="{\displaystyle x_{0}={\frac {-b}{a}},\quad y_{0}={\frac {-c}{a}},\quad z_{0}={\frac {-d}{a}},\quad \rho ={\frac {b^{2}+c^{2}+d^{2}-ae}{a^{2}}}.}"></span></dd></dl> <p>Así a ecuación </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x,y,z)=a(x^{2}+y^{2}+z^{2})+2(bx+cy+dz)+e=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mo stretchy="false">(</mo> <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 stretchy="false">)</mo> <mo>+</mo> <mn>2</mn> <mo stretchy="false">(</mo> <mi>b</mi> <mi>x</mi> <mo>+</mo> <mi>c</mi> <mi>y</mi> <mo>+</mo> <mi>d</mi> <mi>z</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>e</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x,y,z)=a(x^{2}+y^{2}+z^{2})+2(bx+cy+dz)+e=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8a133703df70ba0dab184e3fcf4be2cd38c74eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:53.762ex; height:3.176ex;" alt="{\displaystyle f(x,y,z)=a(x^{2}+y^{2}+z^{2})+2(bx+cy+dz)+e=0}"></span></dd></dl> <p>non ten puntos reais como solucións se <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho <0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho <0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/befc67bb24ee0793a950953cd8b7464bdde924e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.463ex; height:2.676ex;" alt="{\displaystyle \rho <0}"></span> e chámase a ecuación dunha <b>esfera imaxinaria</b>. Se <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho =0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho =0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ba6310b27df5f9c9b0b1732e08cce27b99d68cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.463ex; height:2.676ex;" alt="{\displaystyle \rho =0}"></span>, a única solución de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x,y,z)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x,y,z)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d9dc9c0f7052aaefb6f7194bb0d9e419086a4bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.99ex; height:2.843ex;" alt="{\displaystyle f(x,y,z)=0}"></span> é o punto <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 P_{0}=(x_{0},y_{0},z_{0})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <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 P_{0}=(x_{0},y_{0},z_{0})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2728b2a274122fbaf50539fa2dd9c885afca413" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.235ex; height:2.843ex;" alt="{\displaystyle P_{0}=(x_{0},y_{0},z_{0})}"></span> e dise que a ecuación é a ecuación dunha <b>esfera puntual</b>. Finalmente, no caso <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 \rho >0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho >0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/11bd697f113e3e1bd7c76f2f441fd102eca99cab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.463ex; height:2.676ex;" alt="{\displaystyle \rho >0}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x,y,z)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x,y,z)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d9dc9c0f7052aaefb6f7194bb0d9e419086a4bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.99ex; height:2.843ex;" alt="{\displaystyle f(x,y,z)=0}"></span> é unha ecuación dunha esfera cuxo centro é <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 P_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/671bd891701e0d6cfa6da0114a5dd64233b58709" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.547ex; height:2.509ex;" alt="{\displaystyle P_{0}}"></span> e cuxo raio é <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 {\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>ρ</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {\rho }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aae01a7de75247c1dabce17e09101772823066e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:3.138ex; height:3.009ex;" alt="{\displaystyle {\sqrt {\rho }}}"></span>.<sup id="cite_ref-Albert54_2-0" class="reference"><a href="#cite_note-Albert54-2"><span>[</span>2<span>]</span></a></sup> </p><p>Se <span class="texhtml mvar" style="font-style:italic;">a</span> na ecuación anterior é cero, entón <span class="texhtml"><i>f</i>(<i>x</i>, <i>y</i>, <i>z</i>) = 0</span> é a ecuación dun plano. Así, pódese pensar que un plano é unha esfera de raio infinito cuxo centro é un <a href="/w/index.php?title=Punto_no_infinito&action=edit&redlink=1" class="new" title="Punto no infinito (a páxina aínda non existe)">punto no infinito</a>.<sup id="cite_ref-Woods266_3-0" class="reference"><a href="#cite_note-Woods266-3"><span>[</span>3<span>]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Paramétricas"><span id="Param.C3.A9tricas"></span>Paramétricas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&veaction=edit&section=3" title="Editar a sección: «Paramétricas»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Esfera&action=edit&section=3" title="Editar o código fonte da sección: Paramétricas"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Unha <a href="/w/index.php?title=Ecuaci%C3%B3n_param%C3%A9trica&action=edit&redlink=1" class="new" title="Ecuación paramétrica (a páxina aínda non existe)">ecuación paramétrica</a> para a esfera con raio <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> e centro <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> pódese parametrizar usando <a href="/wiki/Funci%C3%B3n_trigonom%C3%A9trica" title="Función trigonométrica">función trigonométricas</a>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \\z&=z_{0}+r\cos \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> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>r</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mspace width="thickmathspace" /> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>r</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mspace width="thickmathspace" /> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> </mtd> </mtr> <mtr> <mtd> <mi>z</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>r</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace" /> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \\z&=z_{0}+r\cos \theta \,\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6eff6f3bffe842c32b34301992d7f2f765469e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:22.223ex; height:8.843ex;" alt="{\displaystyle {\begin{aligned}x&=x_{0}+r\sin \theta \;\cos \varphi \\y&=y_{0}+r\sin \theta \;\sin \varphi \\z&=z_{0}+r\cos \theta \,\end{aligned}}}"></span><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span>[</span>4<span>]</span></a></sup></dd></dl> <p>Os símbolos usados aquí son os mesmos que os usados nas <a href="/w/index.php?title=Coordenadas_esf%C3%A9ricas&action=edit&redlink=1" class="new" title="Coordenadas esféricas (a páxina aínda non existe)">coordenadas esféricas</a>. Así, <span class="texhtml mvar" style="font-style:italic;">r</span> é constante, mentres que <span class="texhtml mvar" style="font-style:italic;">θ</span> varía de 0 a <span class="texhtml mvar" style="font-style:italic;">π</span> e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \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> varía de 0 a 2<span class="texhtml mvar" style="font-style:italic;">π</span>. </p> <div class="mw-heading mw-heading3"><h3 id="Fórmulas"><span id="F.C3.B3rmulas"></span>Fórmulas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&veaction=edit&section=4" title="Editar a sección: «Fórmulas»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Esfera&action=edit&section=4" title="Editar o código fonte da sección: Fórmulas"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/%C3%81rea" title="Área">área</a> dunha esfera de raio <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> é: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=4\pi r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</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 A=4\pi r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca925588619ce34da35b2c2ffb5b267e313d50ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.439ex; height:2.676ex;" alt="{\displaystyle A=4\pi r^{2}}"></span>.</dd></dl> <p>O <a href="/wiki/Volume" class="mw-disambig" title="Volume">volume da bóla</a> que contén é: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V={\frac {4\pi r^{3}}{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <mn>3</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V={\frac {4\pi r^{3}}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7648e6255fc0b126d6614cd8a56f4d02f4997bed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.319ex; height:5.676ex;" alt="{\displaystyle V={\frac {4\pi r^{3}}{3}}}"></span>.</dd></dl> <p>A súa “compacidade”, é dicir, a súa proporción área-volume, é polo tanto: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C={\frac {A}{V}}={\frac {3}{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mi>V</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mi>r</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C={\frac {A}{V}}={\frac {3}{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09a4b732cf9022c0d7bc00a4f0acf39cae5cbd5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.585ex; height:5.509ex;" alt="{\displaystyle C={\frac {A}{V}}={\frac {3}{r}}}"></span>.</dd></dl> <p>O <a href="/wiki/Momento_de_inercia" title="Momento de inercia">momento de inercia</a> dunha <b>bóla</b> homoxénea de raio <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>, densidade <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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> e masa <i>M</i>, con respecto a un eixo que pasa polo seu centro é: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I={\frac {2Mr^{2}}{5}}={\frac {8\pi \rho r^{5}}{15}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>M</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>5</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mi>π</mi> <mi>ρ</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mrow> <mn>15</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I={\frac {2Mr^{2}}{5}}={\frac {8\pi \rho r^{5}}{15}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c0e961c57cd6ea17e941f8263a1b40afdace986" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.548ex; height:5.676ex;" alt="{\displaystyle I={\frac {2Mr^{2}}{5}}={\frac {8\pi \rho r^{5}}{15}}}"></span>.</dd></dl> <p>O momento de inercia dunha <b>esfera</b> homoxénea de raio <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> e masa <i>M</i>, en relación a un eixe que pasa polo seu centro é: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I={\frac {2Mr^{2}}{3}}={\frac {8\pi \rho r^{5}}{9}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>M</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>3</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mi>π</mi> <mi>ρ</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mrow> <mn>9</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I={\frac {2Mr^{2}}{3}}={\frac {8\pi \rho r^{5}}{9}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8ea152aeb62635c0cd2a6a77b67b46ba6eadf4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.548ex; height:5.676ex;" alt="{\displaystyle I={\frac {2Mr^{2}}{3}}={\frac {8\pi \rho r^{5}}{9}}}"></span>.</dd></dl> <p>O elemento de área da esfera de raio <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> en coordenadas latitude-lonxitude (<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 \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span>-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \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>) é <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 \mathrm {d} \sigma =r^{2}\cos \lambda \,\mathrm {d} \lambda \,d\varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>σ</mi> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>cos</mi> <mo>⁡</mo> <mi>λ</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>λ</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} \sigma =r^{2}\cos \lambda \,\mathrm {d} \lambda \,d\varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4963c631449a3e4f99bbf20fa66aa02b06a86cbe" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.222ex; height:3.176ex;" alt="{\displaystyle \mathrm {d} \sigma =r^{2}\cos \lambda \,\mathrm {d} \lambda \,d\varphi }"></span>. Deducimos disto que a área dunha porción limitada por dous semicírculos que unen os polos e forman un ángulo <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> expresado en <a href="/wiki/Radi%C3%A1n" title="Radián">radiáns</a>) é <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\alpha \,r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>α</mi> <mspace width="thinmathspace" /> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\alpha \,r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c14cb1aecbdef096a6ff80d52474e6082438007" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.14ex; height:2.676ex;" alt="{\displaystyle 2\alpha \,r^{2}}"></span>. </p><p>Isto tamén permite calcular a área dunha <b><a href="/w/index.php?title=Zona_esf%C3%A9rica&action=edit&redlink=1" class="new" title="Zona esférica (a páxina aínda non existe)">zona esférica</a></b>, é dicir, unha porción dunha esfera limitada por dous planos paralelos que cortan a esfera (ou son tanxentes). Atopamos <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\pi rh}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi rh}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f07078e1d90c08fc9da0783148430ba17472d282" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.882ex; height:2.176ex;" alt="{\displaystyle 2\pi rh}"></span> onde <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 h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span> designa a distancia dos dous planos: a área é a mesma que a dun cilindro circular da mesma altura tanxente á esfera (cilindro circunscrito). Este notable resultado é demostrado por <a href="/wiki/Arqu%C3%ADmedes" title="Arquímedes">Arquímedes</a> no seu tratado <i><a href="/w/index.php?title=Sobre_a_esfera_e_o_cilindro&action=edit&redlink=1" class="new" title="Sobre a esfera e o cilindro (a páxina aínda non existe)">Sobre a esfera e o cilindro</a></i><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span>[</span>5<span>]</span></a></sup>. Segundo <a href="/wiki/Cicer%C3%B3n" title="Cicerón">Cicerón</a>, Arquímedes pediría que se gravaran na súa tumba unha esfera e o seu cilindro circunscrito, en lembranza deste resultado<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span>[</span>6<span>]</span></a></sup>. </p><p>O <a href="/wiki/Cilindro" title="Cilindro">cilindro</a> circunscrito por unha esfera dada ten un volume igual a 1.5 veces o volume da esfera. </p><p>A esfera ten a menor área entre as superficies que encerran un determinado volume e encerra o maior volume entre as superficies dunha determinada área. É a resposta á pregunta da <a href="/w/index.php?title=Isoperimetr%C3%ADa&action=edit&redlink=1" class="new" title="Isoperimetría (a páxina aínda non existe)">isoperimetría</a> para o espazo euclidiano de dimensión 3. Por este motivo, a esfera aparece na natureza, por exemplo as burbullas e as pingas de auga (en ausencia de <a href="/wiki/Gravidade" title="Gravidade">gravidade</a>) son esferas, porque a <a href="/wiki/Tensi%C3%B3n_superficial" title="Tensión superficial">tensión superficial</a> intenta minimizar a área. </p> <div class="mw-heading mw-heading2"><h2 id="Rexións"><span id="Rexi.C3.B3ns"></span>Rexións</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&veaction=edit&section=5" title="Editar a sección: «Rexións»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Esfera&action=edit&section=5" title="Editar o código fonte da sección: Rexións"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="detail principal"> <dl><dd><span><span><i>Véxase tamén</i><i>:</i> <a href="/wiki/B%C3%B3la_(matem%C3%A1ticas)#Rexións" title="Bóla (matemáticas)">Bóla (matemáticas)#Rexións</a>.</span></span></dd></dl></div> <figure class="mw-halign-right" typeof="mw:File"><a href="/wiki/Ficheiro:Esfera_celeste.jpg" class="mw-file-description" title="Esfera celeste"><img alt="Esfera celeste" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Esfera_celeste.jpg/300px-Esfera_celeste.jpg" decoding="async" width="300" height="321" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Esfera_celeste.jpg/450px-Esfera_celeste.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Esfera_celeste.jpg/600px-Esfera_celeste.jpg 2x" data-file-width="1245" data-file-height="1333" /></a><figcaption>Esfera celeste</figcaption></figure> <p>Pódense definir unha serie de rexións especiais para unha bóla: </p> <ul><li><i><a href="/w/index.php?title=Casquete_esf%C3%A9rico&action=edit&redlink=1" class="new" title="Casquete esférico (a páxina aínda non existe)">casquete</a></i>, limitado por un plano.</li> <li><i><a href="/w/index.php?title=Sector_esf%C3%A9rico&action=edit&redlink=1" class="new" title="Sector esférico (a páxina aínda non existe)">sector</a></i>, limitado por un límite cónico cun ápice no centro da esfera.</li> <li><i><a href="/w/index.php?title=Segmento_esf%C3%A9rico&action=edit&redlink=1" class="new" title="Segmento esférico (a páxina aínda non existe)">segmento</a></i>, limitado por un par de planos paralelos.</li> <li><i><a href="/w/index.php?title=Coroa_esf%C3%A9rica&action=edit&redlink=1" class="new" title="Coroa esférica (a páxina aínda non existe)">coroa</a></i>, limitado por dúas esferas concéntricas de diferentes raios.</li> <li><i><a href="/w/index.php?title=Cu%C3%B1a_esf%C3%A9rica&action=edit&redlink=1" class="new" title="Cuña esférica (a páxina aínda non existe)">cuña</a></i>, limitada por dous planos que pasan polo centro da esfera e pola superficie da esfera.</li> <li>Hemisferio</li> <li><a href="/w/index.php?title=L%C3%BAa_esf%C3%A9rica&action=edit&redlink=1" class="new" title="Lúa esférica (a páxina aínda non existe)">lúa esférica</a>, área nunha esfera delimitada por dous semicírculos grandes que se atopan en puntos antípodas.</li> <li><a href="/w/index.php?title=Trigonometr%C3%ADa_esf%C3%A9rica&action=edit&redlink=1" class="new" title="Trigonometría esférica (a páxina aínda non existe)">polígono esférico</a>, polígono na superficie da esfera</li></ul> <div class="mw-heading mw-heading2"><h2 id="Notas">Notas</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&veaction=edit&section=6" title="Editar a sección: «Notas»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Esfera&action=edit&section=6" title="Editar o código fonte da sección: Notas"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-EB-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-EB_1-0">1,0</a></sup> <sup><a href="#cite_ref-EB_1-1">1,1</a></sup> <sup><a href="#cite_ref-EB_1-2">1,2</a></sup></span> <span class="reference-text"><cite class="citation encyclopaedia"><a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm</a>, <a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Hugh</a>, ed. (1911). "<a href="https://gl.wikisource.org/wiki/en:1911_Encyclop%C3%A6dia_Britannica/Sphere" class="extiw" title="s:en:1911 Encyclopædia Britannica/Sphere">Sphere</a>". <i><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Encyclopædia Britannica</a></i> <b>25</b> (11ª ed.). <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a> <i>(en <a href="/wiki/Lingua_inglesa" title="Lingua inglesa">inglés</a>)</i>. pp. 647–648.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fgl.wikipedia.org%3AEsfera&rft.atitle=Sphere&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.date=1911&rft.edition=11%AA&rft.genre=bookitem&rft.pages=647-648&rft.pub=Cambridge+University+Press+%27%27%28en+ingl%C3%A9s%29%27%27&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> </span> </li> <li id="cite_note-Albert54-2"><span class="mw-cite-backlink"><a href="#cite_ref-Albert54_2-0">↑</a></span> <span class="reference-text"><a href="#CITEREFAlbert2016">Albert 2016</a>, p. 54</span> </li> <li id="cite_note-Woods266-3"><span class="mw-cite-backlink"><a href="#cite_ref-Woods266_3-0">↑</a></span> <span class="reference-text"><a href="#CITEREFWoods1961">Woods 1961</a>, p. 266.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><a href="#CITEREFKreyszig1972">Kreyszig (1972</a>, p. 342).</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Obra dixitalizada por Marc Szwajcer, <a rel="nofollow" class="external text" href="http://remacle.org/bloodwolf/erudits/">archimede/oeuvresintro.htm Obras de Arquímedes, traducidas literalmente, cun comentario, por F. Peyrard, profesor de Matemáticas e Astronomía en Lycée Bonaparte</a>.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text"> Ver por exemplo a <a href="/w/index.php?title=Enciclopedia_ou_Dictionnaire_raisonn%C3%A9_des_sciences,_des_arts_et_des_profesi%C3%B3ns_cient%C3%ADficas&action=edit&redlink=1" class="new" title="Enciclopedia ou Dictionnaire raisonné des sciences, des arts et des profesións científicas (a páxina aínda non existe)">Enciclopedia Diderot</a>, <a href="https://gl.wikisource.org/wiki/Page:Diderot_-_Encyclopedie_1ere_edition_tome_15.djvu/769" class="extiw" title="s:Page:Diderot - Encyclopedie 1ere edition tome 15.djvu/769">Artigo de Siracusa</a>, en <a href="/wiki/Wikisource" class="mw-redirect" title="Wikisource">Wikisource</a>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Véxase_tamén"><span id="V.C3.A9xase_tam.C3.A9n"></span>Véxase tamén</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&veaction=edit&section=7" title="Editar a sección: «Véxase tamén»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Esfera&action=edit&section=7" title="Editar o código fonte da sección: Véxase tamén"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <table role="presentation" class="mbox-small plainlinks sistersitebox" style="background-color:var(--background-color-neutral-subtle, #f8f9fa);border:1px solid var(--border-color-base, #a2a9b1);color:inherit"> <tbody><tr> <td class="mbox-image"><span class="noviewer" typeof="mw:File"><span><img 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></td> <td class="mbox-text plainlist"><a href="https://commons.wikimedia.org/wiki/Portada_galega" class="extiw" title="commons:Portada galega">Wikimedia Commons</a> ten máis contidos multimedia na categoría:  <i><b><a href="https://commons.wikimedia.org/wiki/Category:Spheres" class="extiw" title="commons:Category:Spheres">Esfera</a> <span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q12507" title="Modificar a ligazón no Wikidata"><img alt="Modificar a ligazón no Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/12px-Arbcom_ru_editing.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/18px-Arbcom_ru_editing.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Arbcom_ru_editing.svg/24px-Arbcom_ru_editing.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></b></i></td></tr> </tbody></table> <div class="mw-heading mw-heading3"><h3 id="Outros_artigos">Outros artigos</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Esfera&veaction=edit&section=8" title="Editar a sección: «Outros artigos»" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Esfera&action=edit&section=8" title="Editar o código fonte da sección: Outros artigos"><span>editar a fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/N%C3%BAmero_pi" title="Número pi">Número pi</a></li></ul> <div role="navigation" class="navbox" aria-labelledby="Control_de_autoridades" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Control_de_autoridades" scope="row" class="navbox-group" style="width:1%;width: 12%; 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