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rel="dns-prefetch" href="auth.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Sffêr rootpage-Sffêr skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Neidio i'r cynnwys</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Safle"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" title="Prif ddewislen" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Prif ddewislen" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Prif ddewislen</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Prif ddewislen</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">symud i'r bar ochr</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">cuddio</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Llywio </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Hafan" title="Ymweld â'r Hafan [z]" accesskey="z"><span>Hafan</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wicipedia:Porth_y_Gymuned" title="Pethau i'w gwneud, adnoddau a thudalennau'r gymuned"><span>Porth y Gymuned</span></a></li><li id="n-cafe" class="mw-list-item"><a href="/wiki/Wicipedia:Y_Caffi"><span>Y Caffi</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Categori:Materion_cyfoes" title="Gwybodaeth yn gysylltiedig â materion cyfoes"><span>Materion cyfoes</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Arbennig:RecentChanges" title="Rhestr y newidiadau diweddar ar y wici. [r]" accesskey="r"><span>Newidiadau diweddar</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Arbennig:Random" title="Llwytho tudalen ar hap [x]" accesskey="x"><span>Erthygl ar hap</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Wicipedia:Cymorth" title="Tudalennau cymorth"><span>Cymorth</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Arbennig:SpecialPages"><span>Tudalennau arbennig</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Hafan" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wicipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-cy.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-cy.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Arbennig:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Chwilio Wicipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Chwilio</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Chwilio Wicipedia" aria-label="Chwilio Wicipedia" autocapitalize="sentences" title="Chwilio Wicipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Arbennig:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Chwilio</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Offer personol"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Gwedd"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Newidiwch ymddangosiad maint ffont, lled a lliw y dudalen" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Gwedd" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Gwedd</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=cy.wikipedia.org&uselang=cy" class=""><span>Rhoi</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=Arbennig:CreateAccount&returnto=Sff%C3%AAr" title="Rydym yn argymell eich bod yn creu cyfri ac yn menwgofnodi. Fodd bynnag, dydy hyn ddim yn orfodol" class=""><span>Creu cyfrif</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=Arbennig:UserLogin&returnto=Sff%C3%AAr" title="Fe'ch anogir i fewngofnodi, er nad oes rhaid gwneud. [o]" accesskey="o" class=""><span>Mewngofnodi</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Rhagor o opsiynau" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Offer personol" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Offer personol</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal" title="Dewislen defnyddiwr" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=cy.wikipedia.org&uselang=cy"><span>Rhoi</span></a></li><li id="pt-contribute" class="mw-list-item"><a href="/wiki/Arbennig:Contribute"><span class="vector-icon mw-ui-icon-edit mw-ui-icon-wikimedia-edit"></span> <span>Cyfrannu</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Arbennig:CreateAccount&returnto=Sff%C3%AAr" title="Rydym yn argymell eich bod yn creu cyfri ac yn menwgofnodi. Fodd bynnag, dydy hyn ddim yn orfodol"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Creu cyfrif</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Arbennig:UserLogin&returnto=Sff%C3%AAr" title="Fe'ch anogir i fewngofnodi, er nad oes rhaid gwneud. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Mewngofnodi</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"> Tudalennau ar gyfer golygyddion allgofnodedig <a href="/wiki/Cymorth:Cyflwyniad" aria-label="Dysgu mwy am olygu"><span>dysgu mwy</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Arbennig:MyTalk" title="Sgwrs ynglŷn â golygiadau o'r cyfeiriad IP hwn [n]" accesskey="n"><span>Sgwrs</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="Safle"> <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="Cynnwys" 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">Cynnwys</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">symud i'r bar ochr</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">cuddio</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">Y dechrau</div> </a> </li> <li id="toc-Hafaliadau_yn_y_gofod_tri_dimensiwn" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Hafaliadau_yn_y_gofod_tri_dimensiwn"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Hafaliadau yn y gofod tri dimensiwn</span> </div> </a> <ul id="toc-Hafaliadau_yn_y_gofod_tri_dimensiwn-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cyfaint_mewnol" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cyfaint_mewnol"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Cyfaint mewnol</span> </div> </a> <ul id="toc-Cyfaint_mewnol-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Arwynebedd" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Arwynebedd"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Arwynebedd</span> </div> </a> <ul id="toc-Arwynebedd-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cyfeiriadau" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cyfeiriadau"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Cyfeiriadau</span> </div> </a> <ul id="toc-Cyfeiriadau-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Cynnwys" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Tabl Cynnwys" > <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="Toglo'r tabl cynnwys" > <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">Toglo'r tabl cynnwys</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">Sffêr</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="Ewch i erthygl mewn iaith arall. Ar gael mewn 106 iaith" > <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 iaith</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 - Affricaneg" lang="af" hreflang="af" data-title="Sfeer" data-language-autonym="Afrikaans" data-language-local-name="Affricaneg" 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 - Amhareg" lang="am" hreflang="am" data-title="ሉል" data-language-autonym="አማርኛ" data-language-local-name="Amhareg" 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 - Arabeg" lang="ar" hreflang="ar" data-title="كرة" data-language-autonym="العربية" data-language-local-name="Arabeg" 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 - Arabeg Moroco" lang="ary" hreflang="ary" data-title="كورة" data-language-autonym="الدارجة" data-language-local-name="Arabeg Moroco" 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 - Astwrianeg" lang="ast" hreflang="ast" data-title="Esfera" data-language-autonym="Asturianu" data-language-local-name="Astwrianeg" 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 - Aserbaijaneg" lang="az" hreflang="az" data-title="Sfera" data-language-autonym="Azərbaycanca" data-language-local-name="Aserbaijaneg" 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 - Bashcorteg" lang="ba" hreflang="ba" data-title="Сфера" data-language-autonym="Башҡортса" data-language-local-name="Bashcorteg" 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 - Belarwseg" lang="be" hreflang="be" data-title="Сфера" data-language-autonym="Беларуская" data-language-local-name="Belarwseg" 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 - Bwlgareg" lang="bg" hreflang="bg" data-title="Сфера" data-language-autonym="Български" data-language-local-name="Bwlgareg" 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 - Bengaleg" lang="bn" hreflang="bn" data-title="গোলক" data-language-autonym="বাংলা" data-language-local-name="Bengaleg" 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 - Bosnieg" lang="bs" hreflang="bs" data-title="Sfera" data-language-autonym="Bosanski" data-language-local-name="Bosnieg" 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 - Catalaneg" lang="ca" hreflang="ca" data-title="Esfera" data-language-autonym="Català" data-language-local-name="Catalaneg" 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 - Tsierocî" lang="chr" hreflang="chr" data-title="ᎦᏐᏆᎸ" data-language-autonym="ᏣᎳᎩ" data-language-local-name="Tsierocî" 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 - Cwrdeg Sorani" lang="ckb" hreflang="ckb" data-title="گۆ" data-language-autonym="کوردی" data-language-local-name="Cwrdeg Sorani" 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) - Tsieceg" lang="cs" hreflang="cs" data-title="Sféra (matematika)" data-language-autonym="Čeština" data-language-local-name="Tsieceg" 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 - Tshwfasheg" lang="cv" hreflang="cv" data-title="Сфера" data-language-autonym="Чӑвашла" data-language-local-name="Tshwfasheg" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Kugle" title="Kugle - Daneg" lang="da" hreflang="da" data-title="Kugle" data-language-autonym="Dansk" data-language-local-name="Daneg" 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 - Almaeneg" lang="de" hreflang="de" data-title="Kugel" data-language-autonym="Deutsch" data-language-local-name="Almaeneg" 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 - Groeg" lang="el" hreflang="el" data-title="Σφαίρα" data-language-autonym="Ελληνικά" data-language-local-name="Groeg" 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 - Saesneg" lang="en" hreflang="en" data-title="Sphere" data-language-autonym="English" data-language-local-name="Saesneg" 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 - Sbaeneg" lang="es" hreflang="es" data-title="Esfera" data-language-autonym="Español" data-language-local-name="Sbaeneg" 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 - Estoneg" lang="et" hreflang="et" data-title="Sfäär" data-language-autonym="Eesti" data-language-local-name="Estoneg" 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 - Basgeg" lang="eu" hreflang="eu" data-title="Esfera" data-language-autonym="Euskara" data-language-local-name="Basgeg" 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) - Perseg" lang="fa" hreflang="fa" data-title="کره (هندسه)" data-language-autonym="فارسی" data-language-local-name="Perseg" 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) - Ffinneg" lang="fi" hreflang="fi" data-title="Pallo (geometria)" data-language-autonym="Suomi" data-language-local-name="Ffinneg" 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_(jiometri)" title="Vuravura (jiometri) - Ffijïeg" lang="fj" hreflang="fj" data-title="Vuravura (jiometri)" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Ffijïeg" 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 - Ffrangeg" lang="fr" hreflang="fr" data-title="Sphère" data-language-autonym="Français" data-language-local-name="Ffrangeg" 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 - Ffriseg Gogleddol" lang="frr" hreflang="frr" data-title="Kuugel" data-language-autonym="Nordfriisk" data-language-local-name="Ffriseg Gogleddol" 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 - Gwyddeleg" lang="ga" hreflang="ga" data-title="Sféar" data-language-autonym="Gaeilge" data-language-local-name="Gwyddeleg" 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 - Gaeleg yr Alban" lang="gd" hreflang="gd" data-title="Cruinne" data-language-autonym="Gàidhlig" data-language-local-name="Gaeleg yr Alban" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Esfera" title="Esfera - Galisieg" lang="gl" hreflang="gl" data-title="Esfera" data-language-autonym="Galego" data-language-local-name="Galisieg" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%97%E0%AB%8B%E0%AA%B3%E0%AB%8B" title="ગોળો - Gwjarati" lang="gu" hreflang="gu" data-title="ગોળો" data-language-autonym="ગુજરાતી" data-language-local-name="Gwjarati" 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) - Hebraeg" lang="he" hreflang="he" data-title="ספירה (גאומטריה)" data-language-autonym="עברית" data-language-local-name="Hebraeg" 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 - Croateg" lang="hr" hreflang="hr" data-title="Sfera" data-language-autonym="Hrvatski" data-language-local-name="Croateg" 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 - Creol Haiti" lang="ht" hreflang="ht" data-title="Esfè" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Creol Haiti" 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 - Hwngareg" lang="hu" hreflang="hu" data-title="Gömb" data-language-autonym="Magyar" data-language-local-name="Hwngareg" 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) - Indoneseg" lang="id" hreflang="id" data-title="Bola (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indoneseg" 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 - Islandeg" lang="is" hreflang="is" data-title="Kúla" data-language-autonym="Íslenska" data-language-local-name="Islandeg" 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 - Eidaleg" lang="it" hreflang="it" data-title="Sfera" data-language-autonym="Italiano" data-language-local-name="Eidaleg" 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 - Japaneeg" lang="ja" hreflang="ja" data-title="球面" data-language-autonym="日本語" data-language-local-name="Japaneeg" 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 - Georgeg" lang="ka" hreflang="ka" data-title="სფერო" data-language-autonym="ქართული" data-language-local-name="Georgeg" 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 - Cabileg" lang="kab" hreflang="kab" data-title="Tasegla" data-language-autonym="Taqbaylit" data-language-local-name="Cabileg" 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 - Casacheg" lang="kk" hreflang="kk" data-title="Сфера" data-language-autonym="Қазақша" data-language-local-name="Casacheg" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%97%E0%B3%8B%E0%B2%B3" title="ಗೋಳ - Kannada" lang="kn" hreflang="kn" data-title="ಗೋಳ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B5%AC_(%EA%B8%B0%ED%95%98%ED%95%99)" title="구 (기하학) - Coreeg" lang="ko" hreflang="ko" data-title="구 (기하학)" data-language-autonym="한국어" data-language-local-name="Coreeg" 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 - Lladin" lang="la" hreflang="la" data-title="Sphaera" data-language-autonym="Latina" data-language-local-name="Lladin" 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 - Lithwaneg" lang="lt" hreflang="lt" data-title="Sfera" data-language-autonym="Lietuvių" data-language-local-name="Lithwaneg" 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 - Latfieg" lang="lv" hreflang="lv" data-title="Sfēra" data-language-autonym="Latviešu" data-language-local-name="Latfieg" 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 - Mocsia" lang="mdf" hreflang="mdf" data-title="Сферась" data-language-autonym="Мокшень" data-language-local-name="Mocsia" 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) - Malagaseg" lang="mg" hreflang="mg" data-title="Bola (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="Malagaseg" 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 - Macedoneg" lang="mk" hreflang="mk" data-title="Сфера" data-language-autonym="Македонски" data-language-local-name="Macedoneg" 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 - Malayalam" lang="ml" hreflang="ml" data-title="ഗോളം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%91%D3%A9%D0%BC%D0%B1%D3%A9%D0%BB%D3%A9%D0%B3" title="Бөмбөлөг - Mongoleg" lang="mn" hreflang="mn" data-title="Бөмбөлөг" data-language-autonym="Монгол" data-language-local-name="Mongoleg" 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 - Maleieg" lang="ms" hreflang="ms" data-title="Sfera" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleieg" 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 - Byrmaneg" lang="my" hreflang="my" data-title="စက်လုံး" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Byrmaneg" 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) - Iseldireg" lang="nl" hreflang="nl" data-title="Sfeer (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="Iseldireg" 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 - Norwyeg Nynorsk" lang="nn" hreflang="nn" data-title="Kule" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwyeg 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 - Norwyeg Bokmål" lang="nb" hreflang="nb" data-title="Kule" data-language-autonym="Norsk bokmål" data-language-local-name="Norwyeg 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 - Ocsitaneg" lang="oc" hreflang="oc" data-title="Esfèra" data-language-autonym="Occitan" data-language-local-name="Ocsitaneg" 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 - Pwnjabeg" lang="pa" hreflang="pa" data-title="ਗੋਲ਼ਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Pwnjabeg" 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 - Pwyleg" lang="pl" hreflang="pl" data-title="Sfera" data-language-autonym="Polski" data-language-local-name="Pwyleg" 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 - Piedmonteg" lang="pms" hreflang="pms" data-title="Sfera" data-language-autonym="Piemontèis" data-language-local-name="Piedmonteg" 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 - Portiwgaleg" lang="pt" hreflang="pt" data-title="Esfera" data-language-autonym="Português" data-language-local-name="Portiwgaleg" 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 - Rwmaneg" lang="ro" hreflang="ro" data-title="Sferă" data-language-autonym="Română" data-language-local-name="Rwmaneg" 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 - Rwseg" lang="ru" hreflang="ru" data-title="Сфера" data-language-autonym="Русский" data-language-local-name="Rwseg" 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 - Sakha" lang="sah" hreflang="sah" data-title="Сфера" data-language-autonym="Саха тыла" data-language-local-name="Sakha" 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 - Sisileg" lang="scn" hreflang="scn" data-title="Sfera" data-language-autonym="Sicilianu" data-language-local-name="Sisileg" 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 - Serbo-Croateg" lang="sh" hreflang="sh" data-title="Sfera" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croateg" 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 - Sinhaleg" lang="si" hreflang="si" data-title="ගෝලය" data-language-autonym="සිංහල" data-language-local-name="Sinhaleg" 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) - Slofaceg" lang="sk" hreflang="sk" data-title="Guľa (matematika)" data-language-autonym="Slovenčina" data-language-local-name="Slofaceg" 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 - Slofeneg" lang="sl" hreflang="sl" data-title="Sfera" data-language-autonym="Slovenščina" data-language-local-name="Slofeneg" 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 - Somaleg" lang="so" hreflang="so" data-title="Kubad" data-language-autonym="Soomaaliga" data-language-local-name="Somaleg" 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 - Albaneg" lang="sq" hreflang="sq" data-title="Sfera" data-language-autonym="Shqip" data-language-local-name="Albaneg" 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 - Serbeg" lang="sr" hreflang="sr" data-title="Сфера" data-language-autonym="Српски / srpski" data-language-local-name="Serbeg" 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 - Swndaneg" lang="su" hreflang="su" data-title="Buleudan" data-language-autonym="Sunda" data-language-local-name="Swndaneg" 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 - Swedeg" lang="sv" hreflang="sv" data-title="Sfär" data-language-autonym="Svenska" data-language-local-name="Swedeg" 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 - Swahili" lang="sw" hreflang="sw" data-title="Tufe" data-language-autonym="Kiswahili" data-language-local-name="Swahili" 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 - Tamileg" lang="ta" hreflang="ta" data-title="கோளம்" data-language-autonym="தமிழ்" data-language-local-name="Tamileg" 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 - Thai" lang="th" hreflang="th" data-title="ทรงกลม" data-language-autonym="ไทย" data-language-local-name="Thai" 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 - Tagalog" lang="tl" hreflang="tl" data-title="Espera" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/K%C3%BCre" title="Küre - Tyrceg" lang="tr" hreflang="tr" data-title="Küre" data-language-autonym="Türkçe" data-language-local-name="Tyrceg" 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 - Tatareg" lang="tt" hreflang="tt" data-title="Сфера" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatareg" 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 - Wcreineg" lang="uk" hreflang="uk" data-title="Сфера" data-language-autonym="Українська" data-language-local-name="Wcreineg" 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 - Wsbeceg" lang="uz" hreflang="uz" data-title="Sfera" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Wsbeceg" 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 - Fietnameg" lang="vi" hreflang="vi" data-title="Mặt cầu" data-language-autonym="Tiếng Việt" data-language-local-name="Fietnameg" 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 - Winarayeg" lang="war" hreflang="war" data-title="Espira" data-language-autonym="Winaray" data-language-local-name="Winarayeg" 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 - Wu Tsieineaidd" lang="wuu" hreflang="wuu" data-title="球面" data-language-autonym="吴语" data-language-local-name="Wu Tsieineaidd" 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 - Tsieinëeg" lang="zh" hreflang="zh" data-title="球面" data-language-autonym="中文" data-language-local-name="Tsieinëeg" 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 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%90%83%E9%AB%94" title="球體 - 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class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Offer tudalen"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Gwedd"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Gwedd</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">symud i'r bar ochr</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">cuddio</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Oddi ar Wicipedia</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="cy" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Delwedd:Sphere_wireframe_10deg_6r.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/220px-Sphere_wireframe_10deg_6r.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/330px-Sphere_wireframe_10deg_6r.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Sphere_wireframe_10deg_6r.svg/440px-Sphere_wireframe_10deg_6r.svg.png 2x" data-file-width="800" data-file-height="800" /></a><figcaption>Diagram <a href="/wiki/Dau_ddimensiwn" class="mw-redirect" title="Dau ddimensiwn">dau ddimensiwn</a> o sffêr.</figcaption></figure> <p>Mae <b>sffêr</b> (enw gwrywaidd; o'r Groeg σφαῖρα - sphaira, "pelen") yn wrthrych geometrig perffaith mewn <a href="/wiki/Gofod_tri_dimensiwn" title="Gofod tri dimensiwn">gofod tri dimensiwn</a>; dyma wyneb pêl cwbwl gron sy'n cyfateb yn nhermau <a href="/wiki/Dau_ddimensiwn" class="mw-redirect" title="Dau ddimensiwn">dau ddimensiwn</a> i gylch.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Fel cylch mewn gofod dau ddimensiwn, diffinnir sffêr yn <a href="/wiki/Mathemateg" title="Mathemateg">fathemategol</a> fel y set o bwyntiau sydd i gyd ar yr un pellter <span class="texhtml"><i>r</i></span> o bwynt penodol, ond mewn man tri dimensiwn.<sup id="cite_ref-Albert54_2-0" class="reference"><a href="#cite_note-Albert54-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Y pellter <span class="texhtml"><i>r</i></span> yw radiws y bêl, sydd wedi'i ffurfio o bob pwynt gyda pellter llai na <span class="texhtml"><i>r</i></span> o'r pwynt a roddir, sef canolbwynt / canol y bêl fathemategol. Cyfeirir at y rhain hefyd fel "y radiws" a "chanol y cylch". Mae'r linell syth hiraf drwy'r bêl, sy'n cysylltu dwy bwynt y sffêr, yn mynd trwy'r canol gyda'i hyd, felly, ddwywaith y radiws; dyma "ddiamedr" y sffêr a'i bêl. </p><p>Ar y cae pêl-droed a mannau eraill y tu allan i fyd mathemateg, caiff y ddau air 'sffêr' a 'phêl eu cyfnewid a'u camddefnyddio'n aml. O fewn mathemateg, perchir y gwahaniaeth, lle mae sffêr yn arwyneb caeedig dau ddimensiwn, wedi'i fewnosod mewn gofod Ewclidaidd tri dimensiwn, ac ar y llaw arall, mae'r bêl yn siâp tri dimensiwn sy'n cynnwys y sffêr a phopeth y tu mewn i'r sffêr (pêl caeedig), neu, yn amlach, dim ond y pwyntiau y tu mewn, ond nid ar y sffêr (pêl agored). Nid yw'r gwahaniaeth hwn bob amser wedi'i gynnal, yn enwedig mae hen gyfeiriadau mathemategol lle ddisgrifir sffêr yn wrthrych solat. Mae hyn yn debyg i'r sefyllfa yn y <a href="/wiki/Pl%C3%A2n_geometraidd" title="Plân geometraidd">plân</a>, lle mae'r termau "cylch" a "disg" hefyd cael eu camddefnyddio. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Hafaliadau_yn_y_gofod_tri_dimensiwn">Hafaliadau yn y gofod tri dimensiwn</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sff%C3%AAr&veaction=edit&section=1" title="Golygu'r adran: Hafaliadau yn y gofod tri dimensiwn" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Sff%C3%AAr&action=edit&section=1" title="Edit section's source code: Hafaliadau yn y gofod tri dimensiwn"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Delwedd:Sphere_and_Ball.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Sphere_and_Ball.png/220px-Sphere_and_Ball.png" decoding="async" width="220" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Sphere_and_Ball.png/330px-Sphere_and_Ball.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Sphere_and_Ball.png/440px-Sphere_and_Ball.png 2x" data-file-width="1548" data-file-height="1536" /></a><figcaption>Dau radiws sffêr</figcaption></figure> <p>Mewn geometreg dadansoddol, mae sffêr sydd a'i ganol <span class="texhtml">(<i>x</i><sub>0</sub>, <i>y</i><sub>0</sub>, <i>z</i><sub>0</sub>)</span> a'i radiws <span class="texhtml mvar" style="font-style:italic;">r</span> yn locws i holl bwyntiau <span class="texhtml">(<i>x</i>, <i>y</i>, <i>z</i>)</span>, fel bod </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>Gadewch i <span class="texhtml mvar" style="font-style:italic;">a, b, c, d, e</span> fod yn <a href="/wiki/Rhifau_real" class="mw-redirect" title="Rhifau real">rhifau real</a>, gyda <span class="texhtml"><i>a</i> ≠ 0</span>, a rhowch </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"></mspace> <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"></mspace> <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"></mspace> <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>yna, nid oes gan yr hafaliad </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>unrhyw bwyntiau real fel datrysiadau os <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>, ac fe'i gelwir yn "sffêr dychmygol". </p><p>Os <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> yna'r unig ddatrysiad o <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> yw'r pwynt <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> a dywedir bod yr hafaliad yn "hafaliad y sffêr pwynt". Yn olaf, yn achos <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>, yna <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> yw hafaliad y sffêr sydd a'i ganol yn <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> a'i radiws yn <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_2-1" class="reference"><a href="#cite_note-Albert54-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Os yw <span class="texhtml mvar" style="font-style:italic;">a</span> yn yr hafaliad uchod yn <a href="/wiki/Sero" class="mw-redirect" title="Sero">sero</a>, yna <span class="texhtml"><i>f</i>(<i>x</i>, <i>y</i>, <i>z</i>) = 0</span> yw hafaliad y plân. Felly, gellir ystyried plân yn fath o sffêr gyda radiws <a href="/wiki/Anfeidraidd" class="mw-redirect" title="Anfeidraidd">anfeidraidd</a>, sydd a'i ganolbwynt yn "bwynt anfeidraidd" (<i>point at infinity</i>).<sup id="cite_ref-Woods266_3-0" class="reference"><a href="#cite_note-Woods266-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Gellir rhoi pwyntiau sffêr gyda radiws <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> a'i ganol <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> ar baramedr, drwy: </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 \varphi \;\cos \theta \\y&=y_{0}+r\sin \varphi \;\sin \theta \qquad (-{\pi }/2\leq \varphi \leq {\pi }/2,\;0\leq \theta <2\pi )\\z&=z_{0}+r\cos \varphi \,\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>φ</mi> <mspace width="thickmathspace"></mspace> <mi>cos</mi> <mo>⁡</mo> <mi>θ</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>φ</mi> <mspace width="thickmathspace"></mspace> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mspace width="2em"></mspace> <mo stretchy="false">(</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo>≤</mo> <mi>φ</mi> <mo>≤</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo>,</mo> <mspace width="thickmathspace"></mspace> <mn>0</mn> <mo>≤</mo> <mi>θ</mi> <mo><</mo> <mn>2</mn> <mi>π</mi> <mo stretchy="false">)</mo> </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>φ</mi> <mspace width="thinmathspace"></mspace> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x&=x_{0}+r\sin \varphi \;\cos \theta \\y&=y_{0}+r\sin \varphi \;\sin \theta \qquad (-{\pi }/2\leq \varphi \leq {\pi }/2,\;0\leq \theta <2\pi )\\z&=z_{0}+r\cos \varphi \,\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30797d673aa83c6f92b4834c1cabe45cb65a6d19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:57.694ex; height:9.176ex;" alt="{\displaystyle {\begin{aligned}x&=x_{0}+r\sin \varphi \;\cos \theta \\y&=y_{0}+r\sin \varphi \;\sin \theta \qquad (-{\pi }/2\leq \varphi \leq {\pi }/2,\;0\leq \theta <2\pi )\\z&=z_{0}+r\cos \varphi \,\end{aligned}}}" /></span><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Mae sffêr gyda'i radiws wedi'i ganoli ar sero yn arwyneb integrol o'r ffurf wahaniaethol ganlynol: </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\,dx+y\,dy+z\,dz=0.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>x</mi> <mo>+</mo> <mi>y</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>y</mi> <mo>+</mo> <mi>z</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>z</mi> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\,dx+y\,dy+z\,dz=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9cfcc379e60de9faca3aa371dc3f6b3ea23e965" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.544ex; height:2.509ex;" alt="{\displaystyle x\,dx+y\,dy+z\,dz=0.}" /></span></dd></dl> <p>Mae'r hafaliad hwn yn adlewyrchu safle a fectorau cyflymder pwynt, <span class="texhtml">(<i>x</i>, <i>y</i>, <i>z</i>)</span> a <span class="texhtml">(<i>dx</i>, <i>dy</i>, <i>dz</i>)</span>, sy'n teithio ar y sffêr, ac sydd bob amser yn orthogonol i'w gilydd. </p> <div class="mw-heading mw-heading2"><h2 id="Cyfaint_mewnol">Cyfaint mewnol</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sff%C3%AAr&veaction=edit&section=2" title="Golygu'r adran: Cyfaint mewnol" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Sff%C3%AAr&action=edit&section=2" title="Edit section's source code: Cyfaint mewnol"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Delwedd:Esfera_Arqu%C3%ADmedes0.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Esfera_Arqu%C3%ADmedes0.svg/220px-Esfera_Arqu%C3%ADmedes0.svg.png" decoding="async" width="220" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Esfera_Arqu%C3%ADmedes0.svg/330px-Esfera_Arqu%C3%ADmedes0.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f1/Esfera_Arqu%C3%ADmedes0.svg/440px-Esfera_Arqu%C3%ADmedes0.svg.png 2x" data-file-width="9954" data-file-height="10536" /></a><figcaption>Sffêr (mewn coch), gyda'i silindr amgylchol (mewn glas golau).</figcaption></figure> <p>Mewn gofod tri dimensiwn, mae <a href="/wiki/Cyfaint" title="Cyfaint">cyfaint</a> oddi mewn i sffêr (sef cyfaint pêl) yn: </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}{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/07808adf2ca4b2aeb69b6c15fb6251a3a3617c91" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.319ex; height:5.176ex;" alt="{\displaystyle V={\frac {4}{3}}\pi r^{3}}" /></span></dd></dl> <p>lle mae <span class="texhtml mvar" style="font-style:italic;">r</span> yn radiws y sffêr. <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> a luniodd y fformiwla hon yn gyntaf, gan fynegi fod y cyfaint y tu mewn i sffêr ddwywaith y gwahaniaeth cyfaint y sffêr a chyfaint y silindr sy'n ei amgylchynu. </p><p>Yn fyr, gellir canfod fformiwla ei gyfaint drwy ddefnyddio cyfesurynnau sfferig, gydag elfennau'r cyfaint yn </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 dV=r^{2}\sin \theta \,dr\,d\theta \,d\varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>V</mi> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>r</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>θ</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dV=r^{2}\sin \theta \,dr\,d\theta \,d\varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7baab55bb4d5559e61d50df77cca1d7f6befc27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.393ex; height:3.176ex;" alt="{\displaystyle dV=r^{2}\sin \theta \,dr\,d\theta \,d\varphi }" /></span></dd></dl> <p>fel bod </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=\int _{0}^{2\pi }\int _{0}^{\pi }\int _{0}^{r}r'^{2}\sin \theta \,dr'\,d\theta \,d\varphi =2\pi \int _{0}^{\pi }\int _{0}^{r}r'^{2}\sin \theta \,dr'\,d\theta =4\pi \int _{0}^{r}r'^{2}\,dr'\ ={\frac {4}{3}}\pi r^{3}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>π</mi> </mrow> </msubsup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> </mrow> </msubsup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msubsup> <msup> <mi>r</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <msup> <mi>r</mi> <mo>′</mo> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>θ</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>φ</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> </mrow> </msubsup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msubsup> <msup> <mi>r</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mspace width="thinmathspace"></mspace> <mi>d</mi> <msup> <mi>r</mi> <mo>′</mo> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <mi>θ</mi> <mo>=</mo> <mn>4</mn> <mi>π</mi> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msubsup> <msup> <mi>r</mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mi>d</mi> <msup> <mi>r</mi> <mo>′</mo> </msup> <mtext> </mtext> <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> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=\int _{0}^{2\pi }\int _{0}^{\pi }\int _{0}^{r}r'^{2}\sin \theta \,dr'\,d\theta \,d\varphi =2\pi \int _{0}^{\pi }\int _{0}^{r}r'^{2}\sin \theta \,dr'\,d\theta =4\pi \int _{0}^{r}r'^{2}\,dr'\ ={\frac {4}{3}}\pi r^{3}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16b51d4bd953c2d8ddb0b746770be5d790eb6e01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:86.604ex; height:6.176ex;" alt="{\displaystyle V=\int _{0}^{2\pi }\int _{0}^{\pi }\int _{0}^{r}r'^{2}\sin \theta \,dr'\,d\theta \,d\varphi =2\pi \int _{0}^{\pi }\int _{0}^{r}r'^{2}\sin \theta \,dr'\,d\theta =4\pi \int _{0}^{r}r'^{2}\,dr'\ ={\frac {4}{3}}\pi r^{3}.}" /></span></dd></dl> <p>Yn ymarferol, ac fel brasamcan, mae cyfaint mewnol sffêr yn 52.4% o gyfaint y <a href="/wiki/Ciwb" title="Ciwb">ciwb</a>, gan fod <span class="texhtml"><i>V</i> = <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;"><span class="texhtml">π</span></span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">6</span></span> <i>d</i><sup>3</sup></span>, ble <span class="texhtml mvar" style="font-style:italic;">d</span> yw diamedr y sffêr a hyd ochr y ciwb a <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; margin:0 0.1em;"><span class="texhtml">π</span></span><span class="visualhide">/</span><span style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">6</span></span> ≈ 0.5236. Er enghraifft, mae gan sffêr gyda diamedr o 1 fetr 52.4% o gyfaint y ciwb sydd a hyd ei ymylon yn 1 fetr, neu tua 0.524 m<sup>3</sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Arwynebedd">Arwynebedd</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sff%C3%AAr&veaction=edit&section=3" title="Golygu'r adran: Arwynebedd" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Sff%C3%AAr&action=edit&section=3" title="Edit section's source code: Arwynebedd"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Arwynebedd sffêr gyda'i radiws yn <span class="texhtml mvar" style="font-style:italic;">r</span> yw: </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> <mo>.</mo> </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/95625828c519b36791d56af65d21b8448472650d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.086ex; height:2.676ex;" alt="{\displaystyle A=4\pi r^{2}.}" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Cyfeiriadau">Cyfeiriadau</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sff%C3%AAr&veaction=edit&section=4" title="Golygu'r adran: Cyfeiriadau" class="mw-editsection-visualeditor"><span>golygu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Sff%C3%AAr&action=edit&section=4" title="Edit section's source code: Cyfeiriadau"><span>golygu cod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dsfai%3Dra^">σφαῖρα</a>, Henry George Liddell, Robert Scott, <i>A Greek-English Lexicon</i>, on Perseus</span> </li> <li id="cite_note-Albert54-2"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-Albert54_2-0">2.0</a></sup> <sup><a href="#cite_ref-Albert54_2-1">2.1</a></sup></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> </ol></div></div>    </div><noscript><img src="https://auth.wikimedia.org/loginwiki/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Wedi dod o "<a dir="ltr" href="https://cy.wikipedia.org/w/index.php?title=Sffêr&oldid=10881269">https://cy.wikipedia.org/w/index.php?title=Sffêr&oldid=10881269</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Arbennig:Categories" title="Arbennig:Categories">Categorïau</a>: <ul><li><a href="/wiki/Categori:Arwynebau" title="Categori:Arwynebau">Arwynebau</a></li><li><a href="/wiki/Categori:Geometreg_Euclidaidd" title="Categori:Geometreg Euclidaidd">Geometreg Euclidaidd</a></li><li><a href="/wiki/Categori:Siapau_elfennol" title="Categori:Siapau elfennol">Siapau elfennol</a></li><li><a href="/wiki/Categori:Strwythur" title="Categori:Strwythur">Strwythur</a></li><li><a href="/wiki/Categori:Topoleg" title="Categori:Topoleg">Topoleg</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Golygwyd y dudalen hon ddiwethaf ar 24 Chwefror 2021, am 07:55.</li> <li id="footer-info-copyright">Mae'r testun ar gael o dan <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-ShareAlike License</a>; gall telerau ychwanegol fod yn berthnasol. 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