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[r]" accesskey="r"><span>Siste endringar</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spesial:Tilfeldig_side" title="Vis ei tilfeldig side [x]" accesskey="x"><span>Tilfeldig side</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Hjelp:Innhald" title="Hjelp til å bruke alle funksjonane."><span>Hjelp</span></a></li><li id="n-kontakt" class="mw-list-item"><a href="/wiki/Wikipedia:Kontakt"><span>Kontakt</span></a></li> </ul> </div> </div> <div id="p-query" class="vector-menu mw-portlet mw-portlet-query emptyPortlet" > <div class="vector-menu-heading"> Eksterne søk </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> På andre prosjekt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Torus" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12510" title="Lenkje til tilknytt element [g]" accesskey="g"><span>Wikidata-element</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Hovudside" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; 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[o]" accesskey="o" class=""><span>Logg inn</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="Fleire val" > <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="Personlege verktøy" > <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">Personlege verktøy</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Brukarmeny" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_nn.wikipedia.org&uselang=nn"><span>Gåver</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Opprett_konto&returnto=Torus" title="Me oppfordrar til at du oppretter ein konto og loggar inn, men det er ikkje påkravd."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Opprett konto</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Logg_inn&returnto=Torus" title="Det er ikkje obligatorisk å logga inn, men medfører mange fordelar. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logg inn</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"> Sider for utlogga bidragsytarar <a href="/wiki/Hjelp:Introduksjon" aria-label="Lær meir om redigering"><span>lær meir</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/Spesial:Bidraga_mine" title="Liste over endringar gjorde frå denne IP-adressa [y]" accesskey="y"><span>Bidrag</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spesial:Diskusjonssida_mi" title="Diskusjon om endringar gjorde av denne ip-adressa [n]" accesskey="n"><span>Diskusjon</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="Nettstad"> <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="Innhald" 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">Innhald</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">gøym</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">Byrjinga</div> </a> </li> <li id="toc-Kjelder" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kjelder"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Kjelder</span> </div> </a> <ul id="toc-Kjelder-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="Innhald" 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="Vis/skjul innhaldslista" > <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">Vis/skjul innhaldslista</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">Torus</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="Gå til ein artikkel på eit anna språk. Tilgjengeleg på 68 språk" > <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-68" 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">68 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Torus" title="Torus – norsk bokmål" lang="nb" hreflang="nb" data-title="Torus" data-language-autonym="Norsk bokmål" data-language-local-name="norsk bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Torus" title="Torus – svensk" lang="sv" hreflang="sv" data-title="Torus" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Torus" title="Torus – dansk" lang="da" hreflang="da" data-title="Torus" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Torus" title="Torus – afrikaans" lang="af" hreflang="af" data-title="Torus" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B7%D8%A7%D8%B1%D8%A9_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="طارة (رياضيات) – arabisk" lang="ar" hreflang="ar" data-title="طارة (رياضيات)" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Tor_(h%C9%99nd%C9%99si_fiqur)" title="Tor (həndəsi fiqur) – aserbajdsjansk" lang="az" hreflang="az" data-title="Tor (həndəsi fiqur)" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D0%BE%D1%80_(%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F)" title="Тор (геаметрыя) – belarusisk" lang="be" hreflang="be" data-title="Тор (геаметрыя)" data-language-autonym="Беларуская" data-language-local-name="belarusisk" 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%A2%D0%BE%D1%80_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Тор (геометрия) – bulgarsk" lang="bg" hreflang="bg" data-title="Тор (геометрия)" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Torus" title="Torus – bosnisk" lang="bs" hreflang="bs" data-title="Torus" data-language-autonym="Bosanski" data-language-local-name="bosnisk" 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/Tor_(geometria)" title="Tor (geometria) – katalansk" lang="ca" hreflang="ca" data-title="Tor (geometria)" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D0%BE%D1%80_(%C3%A7%D0%B8%D0%B9)" title="Тор (çий) – tsjuvansk" lang="cv" hreflang="cv" data-title="Тор (çий)" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvansk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Torus" title="Torus – tsjekkisk" lang="cs" hreflang="cs" data-title="Torus" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Toru_(giumitria)" title="Toru (giumitria) – korsikansk" lang="co" hreflang="co" data-title="Toru (giumitria)" data-language-autonym="Corsu" data-language-local-name="korsikansk" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Torus" title="Torus – tysk" lang="de" hreflang="de" data-title="Torus" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Toor" title="Toor – estisk" lang="et" hreflang="et" data-title="Toor" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CF%8C%CF%81%CE%BF%CF%82" title="Τόρος – gresk" lang="el" hreflang="el" data-title="Τόρος" data-language-autonym="Ελληνικά" data-language-local-name="gresk" 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/Torus" title="Torus – engelsk" lang="en" hreflang="en" data-title="Torus" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Toro_(geometr%C3%ADa)" title="Toro (geometría) – spansk" lang="es" hreflang="es" data-title="Toro (geometría)" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Toro_(geometrio)" title="Toro (geometrio) – esperanto" lang="eo" hreflang="eo" data-title="Toro (geometrio)" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Toru" title="Toru – baskisk" lang="eu" hreflang="eu" data-title="Toru" data-language-autonym="Euskara" data-language-local-name="baskisk" 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%86%D9%86%D8%A8%D8%B1%D9%87" title="چنبره – persisk" lang="fa" hreflang="fa" data-title="چنبره" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Tore" title="Tore – fransk" lang="fr" hreflang="fr" data-title="Tore" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/T%C3%B3ras" title="Tóras – irsk" lang="ga" hreflang="ga" data-title="Tóras" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Toro_(xeometr%C3%ADa_e_topolox%C3%ADa)" title="Toro (xeometría e topoloxía) – galisisk" lang="gl" hreflang="gl" data-title="Toro (xeometría e topoloxía)" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/Mbiriga_(mathabu)" title="Mbiriga (mathabu) – kikuyu" lang="ki" hreflang="ki" data-title="Mbiriga (mathabu)" data-language-autonym="Gĩkũyũ" data-language-local-name="kikuyu" class="interlanguage-link-target"><span>Gĩkũyũ</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%A2%D0%BE%D1%80" title="Тор – kalmykisk" lang="xal" hreflang="xal" data-title="Тор" data-language-autonym="Хальмг" data-language-local-name="kalmykisk" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9B%90%ED%99%98%EB%A9%B4" title="원환면 – koreansk" lang="ko" hreflang="ko" data-title="원환면" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%B8%D6%80_(%D5%B4%D5%A1%D5%AF%D5%A5%D6%80%D6%87%D5%B8%D6%82%D5%B5%D5%A9)" title="Տոր (մակերևույթ) – armensk" lang="hy" hreflang="hy" data-title="Տոր (մակերևույթ)" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%9F%E0%A5%89%E0%A4%B0%E0%A4%B8" title="टॉरस – hindi" lang="hi" hreflang="hi" data-title="टॉरस" 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/Torus" title="Torus – kroatisk" lang="hr" hreflang="hr" data-title="Torus" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Toro" title="Toro – ido" lang="io" hreflang="io" data-title="Toro" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Torus" title="Torus – indonesisk" lang="id" hreflang="id" data-title="Torus" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Toro" title="Toro – interlingua" lang="ia" hreflang="ia" data-title="Toro" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Toro_(geometria)" title="Toro (geometria) – italiensk" lang="it" hreflang="it" data-title="Toro (geometria)" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%98%D7%95%D7%A8%D7%95%D7%A1" title="טורוס – hebraisk" lang="he" hreflang="he" data-title="טורוס" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A2%E1%83%9D%E1%83%A0%E1%83%98_(%E1%83%92%E1%83%94%E1%83%9D%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98%E1%83%90)" title="ტორი (გეომეტრია) – georgisk" lang="ka" hreflang="ka" data-title="ტორი (გეომეტრია)" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Torus_(mathematica)" title="Torus (mathematica) – latin" lang="la" hreflang="la" data-title="Torus (mathematica)" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Tors_(%C4%A3eometrija)" title="Tors (ģeometrija) – latvisk" lang="lv" hreflang="lv" data-title="Tors (ģeometrija)" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Torus" title="Torus – luxemburgsk" lang="lb" hreflang="lb" data-title="Torus" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemburgsk" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Toras_(geometrija)" title="Toras (geometrija) – litauisk" lang="lt" hreflang="lt" data-title="Toras (geometrija)" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/T%C3%B3rusz" title="Tórusz – ungarsk" lang="hu" hreflang="hu" data-title="Tórusz" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%BE%D1%80_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Тор (геометрија) – makedonsk" lang="mk" hreflang="mk" data-title="Тор (геометрија)" data-language-autonym="Македонски" data-language-local-name="makedonsk" 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%9F%E0%B5%8B%E0%B4%B1%E0%B4%B8%E0%B5%8D" title="ടോറസ് – malayalam" lang="ml" hreflang="ml" data-title="ടോറസ്" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Torus" title="Torus – malayisk" lang="ms" hreflang="ms" data-title="Torus" data-language-autonym="Bahasa Melayu" data-language-local-name="malayisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Torus" title="Torus – nederlandsk" lang="nl" hreflang="nl" data-title="Torus" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%88%E3%83%BC%E3%83%A9%E3%82%B9" title="トーラス – japansk" lang="ja" hreflang="ja" data-title="トーラス" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Ring_(Geometrii)" title="Ring (Geometrii) – nordfrisisk" lang="frr" hreflang="frr" data-title="Ring (Geometrii)" data-language-autonym="Nordfriisk" data-language-local-name="nordfrisisk" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/T%C3%B2r_(geometria)" title="Tòr (geometria) – oksitansk" lang="oc" hreflang="oc" data-title="Tòr (geometria)" data-language-autonym="Occitan" data-language-local-name="oksitansk" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Tor_(jism)" title="Tor (jism) – usbekisk" lang="uz" hreflang="uz" data-title="Tor (jism)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Torus_(matematyka)" title="Torus (matematyka) – polsk" lang="pl" hreflang="pl" data-title="Torus (matematyka)" data-language-autonym="Polski" data-language-local-name="polsk" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Toro_(topologia)" title="Toro (topologia) – portugisisk" lang="pt" hreflang="pt" data-title="Toro (topologia)" data-language-autonym="Português" data-language-local-name="portugisisk" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Tor" title="Tor – rumensk" lang="ro" hreflang="ro" data-title="Tor" data-language-autonym="Română" data-language-local-name="rumensk" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%BE%D1%80_(%D0%BF%D0%BE%D0%B2%D0%B5%D1%80%D1%85%D0%BD%D0%BE%D1%81%D1%82%D1%8C)" title="Тор (поверхность) – russisk" lang="ru" hreflang="ru" data-title="Тор (поверхность)" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Torusi" title="Torusi – albansk" lang="sq" hreflang="sq" data-title="Torusi" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Toru_(giometr%C3%ACa)" title="Toru (giometrìa) – siciliansk" lang="scn" hreflang="scn" data-title="Toru (giometrìa)" data-language-autonym="Sicilianu" data-language-local-name="siciliansk" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Torus" title="Torus – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Torus" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" 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/Torus_(geometria)" title="Torus (geometria) – slovakisk" lang="sk" hreflang="sk" data-title="Torus (geometria)" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" 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/Torus" title="Torus – slovensk" lang="sl" hreflang="sl" data-title="Torus" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%BE%D1%80%D1%83%D1%81" title="Торус – serbisk" lang="sr" hreflang="sr" data-title="Торус" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Torus" title="Torus – serbokroatisk" lang="sh" hreflang="sh" data-title="Torus" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Torus" title="Torus – finsk" lang="fi" hreflang="fi" data-title="Torus" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%89%E0%AE%B0%E0%AF%81%E0%AE%B3%E0%AF%8D%E0%AE%B5%E0%AE%B3%E0%AF%88%E0%AE%AF%E0%AE%AE%E0%AF%8D" title="உருள்வளையம் – tamil" lang="ta" hreflang="ta" data-title="உருள்வளையம்" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%AD%E0%B8%A3%E0%B8%B1%E0%B8%AA_(%E0%B9%80%E0%B8%A3%E0%B8%82%E0%B8%B2%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95)" title="ทอรัส (เรขาคณิต) – thai" lang="th" hreflang="th" data-title="ทอรัส (เรขาคณิต)" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Simit_(geometri)" title="Simit (geometri) – tyrkisk" lang="tr" hreflang="tr" data-title="Simit (geometri)" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%BE%D1%80_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F)" title="Тор (геометрія) – ukrainsk" lang="uk" hreflang="uk" data-title="Тор (геометрія)" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%ACnh_xuy%E1%BA%BFn" title="Hình xuyến – vietnamesisk" lang="vi" hreflang="vi" data-title="Hình xuyến" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E7%8E%AF%E9%9D%A2" title="环面 – wu" lang="wuu" hreflang="wuu" data-title="环面" data-language-autonym="吴语" data-language-local-name="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%8E%AF%E9%9D%A2" title="环面 – kinesisk" lang="zh" hreflang="zh" data-title="环面" data-language-autonym="中文" data-language-local-name="kinesisk" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12510#sitelinks-wikipedia" title="Endra mellomspråklege lenkjer" class="wbc-editpage">Endra lenkjer</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namnerom"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Torus" title="Vis innhaldssida [c]" accesskey="c"><span>Artikkel</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskusjon:Torus&action=edit&redlink=1" rel="discussion" class="new" title="Diskusjon om innhaldssida (sida finst ikkje) [t]" accesskey="t"><span>Diskusjon</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" 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for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Verktøy</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Verktøy</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">gøym</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Flere alternativer" > <div class="vector-menu-heading"> Handlingar </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Torus"><span>Les</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Torus&veaction=edit" title="Endre sida [v]" accesskey="v"><span>Endre</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Torus&action=edit" title="Endre kjeldekoden til sida [e]" accesskey="e"><span>Endre wikiteksten</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Torus&action=history"><span>Sjå historikken</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Ålment </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spesial:Lenkjer_hit/Torus" title="Liste over alle wikisidene som har lenkjer hit [j]" accesskey="j"><span>Lenkjer hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesial:Relaterte_endringar/Torus" rel="nofollow" title="Nylege endringar på sider denne sida lenkjar til [k]" accesskey="k"><span>Relaterte endringar</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=nn" title="Last opp filer [u]" accesskey="u"><span>Last opp fil</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Spesial:Spesialsider" title="Liste over spesialsider [q]" accesskey="q"><span>Spesialsider</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Torus&oldid=2803688" title="Fast lenkje til denne versjonen av sida"><span>Fast lenkje</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Torus&action=info" title="Meir informasjon om sida"><span>Sideinformasjon</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spesial:Siter&page=Torus&id=2803688&wpFormIdentifier=titleform" title="Informasjon om korleis ein siterer denne sida"><span>Siter denne sida</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spesial:UrlShortener&url=https%3A%2F%2Fnn.wikipedia.org%2Fwiki%2FTorus"><span>Hent kort URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Spesial:QrCode&url=https%3A%2F%2Fnn.wikipedia.org%2Fwiki%2FTorus"><span>Last ned QR-kode</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Skriv ut/eksporter </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Spesial:Bok&bookcmd=book_creator&referer=Torus"><span>Opprett ei bok</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Spesial:DownloadAsPdf&page=Torus&action=show-download-screen"><span>Last ned som PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Torus&printable=yes" title="Utskriftsversjon av sida [p]" accesskey="p"><span>Utskriftsversjon</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utsjånad"> <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">Utsjånad</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">gøym</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">Frå Wikipedia – det frie oppslagsverket</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="nn" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Torus.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Torus.png/220px-Torus.png" decoding="async" width="220" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Torus.png/330px-Torus.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Torus.png/440px-Torus.png 2x" data-file-width="784" data-file-height="502" /></a><figcaption>Ein torus</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Sphere-like_degenerate_torus.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Sphere-like_degenerate_torus.gif/220px-Sphere-like_degenerate_torus.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/e/e7/Sphere-like_degenerate_torus.gif 1.5x" data-file-width="240" data-file-height="180" /></a><figcaption>Når avstanden til rotasjonsaksen minkar, vert torusringen ein torusspindel og så ei kule.</figcaption></figure> <p><b>Torus</b>, <b>sirkelring</b> eller <b>ankerring</b> er ei «<a href="/wiki/Smultring" title="Smultring">smultringforma</a>» flate som skildrast av ein sirkel når han roterer om ein <a href="/wiki/Akse" class="mw-disambig" title="Akse">akse</a> i planet til sirkelen som ikkje skjerer sirkelen. </p><p>Matematisk kan ein lage ein torus ved: </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(u,v)=(R+r\cos {v})\cos {u}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(u,v)=(R+r\cos {v})\cos {u}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab9470ae59c91d22ae36a83a92715cb1155e0d75" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.806ex; height:2.843ex;" alt="{\displaystyle x(u,v)=(R+r\cos {v})\cos {u}\,}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y(u,v)=(R+r\cos {v})\sin {u}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> <mo stretchy="false">)</mo> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y(u,v)=(R+r\cos {v})\sin {u}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f8c4ed3a5ead836a3674244d8bb479d3de473bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.376ex; height:2.843ex;" alt="{\displaystyle y(u,v)=(R+r\cos {v})\sin {u}\,}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z(u,v)=r\sin {v}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>r</mi> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z(u,v)=r\sin {v}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c4a814d2a4afc823c9bc0f95ffa8772ba0ecb58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.68ex; height:2.843ex;" alt="{\displaystyle z(u,v)=r\sin {v}\,}"></span></dd></dl> <p>der </p> <dl><dd><i>u</i>, <i>v</i> ∈ [0, 2π),</dd> <dd><i>R</i> er avstanden frå senteret av torusen til ytterkanten.</dd> <dd><i>r</i> er radius av den vesle sirkelen</dd></dl> <p>Vi ser av diagrammet til høgre at forholdet mellom R og r endrar utsjånaden på forma. R > r gjev ein <i>torusring</i>, R = r gjev eit <i>torushorn</i> og R < r gjev ein <i>torusspindel</i>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Torus-circle.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Torus-circle.jpg/220px-Torus-circle.jpg" decoding="async" width="220" height="267" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/Torus-circle.jpg/330px-Torus-circle.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/9/94/Torus-circle.jpg 2x" data-file-width="359" data-file-height="436" /></a><figcaption>torus</figcaption></figure> <p>Vi utleiar a og c: </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 r=c-a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mi>c</mi> <mo>−</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=c-a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2346354a31d40a2c201ed24c4630623757710e21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.224ex; height:2.176ex;" alt="{\displaystyle r=c-a}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=c+a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mi>c</mi> <mo>+</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=c+a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e32aa26bed3374a88063db803a0af63542575e3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.94ex; height:2.343ex;" alt="{\displaystyle R=c+a}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a={\frac {1}{2}}(R-r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>R</mi> <mo>−</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a={\frac {1}{2}}(R-r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7dacf784c992d1285ebe38961db262f78bc4eca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.789ex; height:5.176ex;" alt="{\displaystyle a={\frac {1}{2}}(R-r)}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c={\frac {1}{2}}(R+r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c={\frac {1}{2}}(R+r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4da41959d14cc881e6bc0200506ef2c6c90675ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:13.566ex; height:5.176ex;" alt="{\displaystyle c={\frac {1}{2}}(R+r)}"></span></dd></dl> <p>Av dette får vi flateareal <i>A</i> og volumet <i>V</i>: </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=(2\pi a)(2\pi c)=4\pi ^{2}ac=\pi ^{2}(R-r)(R+r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mi>a</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mi>c</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>4</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>a</mi> <mi>c</mi> <mo>=</mo> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>R</mi> <mo>−</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=(2\pi a)(2\pi c)=4\pi ^{2}ac=\pi ^{2}(R-r)(R+r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f46dfd3727fc8f28c1b4ffc0eb8dd7d6fbdbfaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:44.983ex; height:3.176ex;" alt="{\displaystyle A=(2\pi a)(2\pi c)=4\pi ^{2}ac=\pi ^{2}(R-r)(R+r)}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V=(\pi a^{2})(2\pi c)=2\pi ^{2}a^{2}c={\frac {1}{4}}\pi ^{2}(R-r)^{2}(R+r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mi>π</mi> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>π</mi> <mi>c</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>c</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>R</mi> <mo>−</mo> <mi>r</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>R</mi> <mo>+</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=(\pi a^{2})(2\pi c)=2\pi ^{2}a^{2}c={\frac {1}{4}}\pi ^{2}(R-r)^{2}(R+r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a44d0ffc1d41a8bf6910fe58180afe7b0c1c8b86" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:49.026ex; height:5.176ex;" alt="{\displaystyle V=(\pi a^{2})(2\pi c)=2\pi ^{2}a^{2}c={\frac {1}{4}}\pi ^{2}(R-r)^{2}(R+r)}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Kjelder">Kjelder</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Torus&veaction=edit&section=1" title="Endre bolk: Kjelder" class="mw-editsection-visualeditor"><span>endre</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Torus&action=edit&section=1" title="Rediger kildekoden til seksjonen Kjelder"><span>endre wikiteksten</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small"> <ul><li><i>Denne artikkelen bygger på «<a href="https://no.wikipedia.org/wiki/Torus" class="extiw" title="nb:Torus">Torus</a>» frå <a href="https://no.wikipedia.org/wiki/Hovedside" class="extiw" title="nb:Hovedside">Wikipedia på bokmål</a>, den 15. februar 2012.</i></li></ul> </div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r3515230">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output 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