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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">Indhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flyt til sidebjælken</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</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">Indledning</div> </a> </li> <li id="toc-Eksempler_på_anvendelser" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Eksempler_på_anvendelser"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Eksempler på anvendelser</span> </div> </a> <button aria-controls="toc-Eksempler_på_anvendelser-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Vis/skjul underafsnit Eksempler på anvendelser</span> </button> <ul id="toc-Eksempler_på_anvendelser-sublist" class="vector-toc-list"> <li id="toc-Omsætning_mellem_almindeligt_forekommende_vinkler" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Omsætning_mellem_almindeligt_forekommende_vinkler"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Omsætning mellem almindeligt forekommende vinkler</span> </div> </a> <ul id="toc-Omsætning_mellem_almindeligt_forekommende_vinkler-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Matematisk_konstant" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Matematisk_konstant"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Matematisk konstant</span> </div> </a> <ul id="toc-Matematisk_konstant-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historie"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Historie</span> </div> </a> <ul id="toc-Historie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referencer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referencer"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referencer</span> </div> </a> <ul id="toc-Referencer-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="Indhold" 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 indholdsfortegnelsen" > <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 indholdsfortegnelsen</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">Tørn</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 en artikel på et andet sprog. Tilgængelig på 25 sprog" > <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-25" 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">25 sprog</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AF%D9%88%D8%B1%D8%A9_(%D9%87%D9%86%D8%AF%D8%B3%D8%A9_%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A9)" title="دورة (هندسة رياضية) – arabisk" lang="ar" hreflang="ar" data-title="دورة (هندسة رياضية)" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%9F%E0%A6%BE%E0%A6%89_(%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE)" title="টাউ (সংখ্যা) – assamesisk" lang="as" hreflang="as" data-title="টাউ (সংখ্যা)" data-language-autonym="অসমীয়া" data-language-local-name="assamesisk" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D0%B1%D0%BE%D1%80%D0%BE%D1%82" title="Оборот – bulgarsk" lang="bg" hreflang="bg" data-title="Оборот" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%98%E0%A7%82%E0%A6%B0%E0%A7%8D%E0%A6%A3%E0%A6%A8_(%E0%A6%95%E0%A7%8B%E0%A6%A3)" title="ঘূর্ণন (কোণ) – bengali" lang="bn" hreflang="bn" data-title="ঘূর্ণন (কোণ)" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%C3%87%D0%B0%D0%B2%D1%80%C4%83%D0%BC_(%D0%B2%D0%B8%C3%A7%D0%B5%D0%B2_%D0%BF%C4%95%D1%80%D1%87%D0%B8)" title="Çаврăм (виçев пĕрчи) – tjuvasjisk" lang="cv" hreflang="cv" data-title="Çаврăм (виçев пĕрчи)" data-language-autonym="Чӑвашла" data-language-local-name="tjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Vollwinkel" title="Vollwinkel – tysk" lang="de" hreflang="de" data-title="Vollwinkel" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/%C3%80ngol_g%C3%AEr_(giumetr%C3%ACa)" title="Àngol gîr (giumetrìa) – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Àngol gîr (giumetrìa)" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Turn_(angle)" title="Turn (angle) – engelsk" lang="en" hreflang="en" data-title="Turn (angle)" 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/Vuelta_(%C3%A1ngulo)" title="Vuelta (ángulo) – spansk" lang="es" hreflang="es" data-title="Vuelta (ángulo)" data-language-autonym="Español" data-language-local-name="spansk" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Bira_(geometria)" title="Bira (geometria) – baskisk" lang="eu" hreflang="eu" data-title="Bira (geometria)" 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/%D8%AF%D9%88%D8%B1_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="دور (هندسه) – persisk" lang="fa" hreflang="fa" data-title="دور (هندسه)" 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/Tour_(angle)" title="Tour (angle) – fransk" lang="fr" hreflang="fr" data-title="Tour (angle)" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Putaran_(sudut)" title="Putaran (sudut) – indonesisk" lang="id" hreflang="id" data-title="Putaran (sudut)" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Angolo_giro" title="Angolo giro – italiensk" lang="it" hreflang="it" data-title="Angolo giro" data-language-autonym="Italiano" data-language-local-name="italiensk" 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/Turn_(%E8%A7%92%E5%BA%A6)" title="Turn (角度) – japansk" lang="ja" hreflang="ja" data-title="Turn (角度)" 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-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%94%ED%80%B4_(%EA%B0%81%EB%8F%84)" title="바퀴 (각도) – koreansk" lang="ko" hreflang="ko" data-title="바퀴 (각도)" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Volta_(geometria)" title="Volta (geometria) – portugisisk" lang="pt" hreflang="pt" data-title="Volta (geometria)" data-language-autonym="Português" data-language-local-name="portugisisk" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D0%B1%D0%BE%D1%80%D0%BE%D1%82_(%D0%B5%D0%B4%D0%B8%D0%BD%D0%B8%D1%86%D0%B0_%D0%B8%D0%B7%D0%BC%D0%B5%D1%80%D0%B5%D0%BD%D0%B8%D1%8F)" title="Оборот (единица измерения) – russisk" lang="ru" hreflang="ru" data-title="Оборот (единица измерения)" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Varv_(vinkelenhet)" title="Varv (vinkelenhet) – svensk" lang="sv" hreflang="sv" data-title="Varv (vinkelenhet)" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%81%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AF%81_(%E0%AE%B5%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D)" title="சுற்று (வடிவவியல்) – tamil" lang="ta" hreflang="ta" data-title="சுற்று (வடிவவியல்)" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Devir_(birim)" title="Devir (birim) – tyrkisk" lang="tr" hreflang="tr" data-title="Devir (birim)" 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%9E%D0%B1%D0%B5%D1%80%D1%82" title="Оберт – ukrainsk" lang="uk" hreflang="uk" data-title="Оберт" 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/V%C3%B2ng_(h%C3%ACnh_h%E1%BB%8Dc)" title="Vòng (hình học) – vietnamesisk" lang="vi" hreflang="vi" data-title="Vòng (hình học)" 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-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%BD%89_(%E8%A7%92)" title="轉 (角) – kinesisk" lang="zh" hreflang="zh" data-title="轉 (角)" data-language-autonym="中文" data-language-local-name="kinesisk" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%BD%89_(%E8%A7%92)" title="轉 (角) – kantonesisk" lang="yue" hreflang="yue" data-title="轉 (角)" data-language-autonym="粵語" data-language-local-name="kantonesisk" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q304479#sitelinks-wikipedia" title="Redigér sproglinks" class="wbc-editpage">Redigér links</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="Navnerum"> <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/T%C3%B8rn" title="Se indholdssiden [c]" accesskey="c"><span>Artikel</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskussion:T%C3%B8rn&action=edit&redlink=1" rel="discussion" class="new" title="Diskussion om indholdet på siden (ikke skrevet endnu) [t]" accesskey="t"><span>Diskussion</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Ændr sprogvariant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">dansk</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Visninger"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/T%C3%B8rn"><span>Læs</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=T%C3%B8rn&veaction=edit" title="Redigér denne side [v]" accesskey="v"><span>Redigér</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=T%C3%B8rn&action=edit" title="Rediger kildekoden for denne side [e]" accesskey="e"><span>Rediger kildekode</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=T%C3%B8rn&action=history" title="Tidligere versioner af denne side [h]" accesskey="h"><span>Se historik</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sideværktøjer"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Værktøjer" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Værktøjer</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">Værktøjer</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">flyt til sidebjælken</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skjul</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Flere muligheder" > <div class="vector-menu-heading"> Handlinger </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/T%C3%B8rn"><span>Læs</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=T%C3%B8rn&veaction=edit" title="Redigér denne side [v]" accesskey="v"><span>Redigér</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=T%C3%B8rn&action=edit" title="Rediger kildekoden for denne side [e]" accesskey="e"><span>Rediger kildekode</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=T%C3%B8rn&action=history"><span>Se historik</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generelt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciel:Hvad_linker_hertil/T%C3%B8rn" title="Liste med alle sider som henviser hertil [j]" accesskey="j"><span>Hvad henviser hertil</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciel:Relaterede_%C3%A6ndringer/T%C3%B8rn" rel="nofollow" title="Seneste ændringer af sider som denne side henviser til [k]" accesskey="k"><span>Beslægtede ændringer</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=da&campaign=dk" title="Upload filer [u]" accesskey="u"><span>Upload fil</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speciel:Specialsider" title="Liste over alle specialsider [q]" accesskey="q"><span>Specialsider</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=T%C3%B8rn&oldid=10955604" title="Permanent link til denne version af denne side"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=T%C3%B8rn&action=info" title="Yderligere oplysninger om denne side"><span>Sideinformation</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speciel:Citer&page=T%C3%B8rn&id=10955604&wpFormIdentifier=titleform" title="Information om, hvordan man kan citere denne side"><span>Referer til denne side</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speciel:UrlShortener&url=https%3A%2F%2Fda.wikipedia.org%2Fwiki%2FT%25C3%25B8rn"><span>Hent forkortet URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speciel:QrCode&url=https%3A%2F%2Fda.wikipedia.org%2Fwiki%2FT%25C3%25B8rn"><span>Download QR-kode</span></a></li> </ul> </div> </div> <div id="p-Organisation" class="vector-menu mw-portlet mw-portlet-Organisation" > <div class="vector-menu-heading"> Organisation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-contact" class="mw-list-item"><a href="/wiki/Wikipedia:Kontakt_Wikipedia"><span>Kontakt Wikipedia</span></a></li><li id="n-Wikimedia-Danmark" class="mw-list-item"><a href="https://dk.wikimedia.org/wiki/"><span>Wikimedia Danmark</span></a></li><li id="n-GLAM" class="mw-list-item"><a href="/wiki/Wikipedia:GLAM"><span>GLAM</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"> Udskriv/eksportér </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=Speciel:Bog&bookcmd=book_creator&referer=T%C3%B8rn"><span>Lav en bog</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speciel:DownloadAsPdf&page=T%C3%B8rn&action=show-download-screen"><span>Download som PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=T%C3%B8rn&printable=yes" title="Printervenlig udgave af denne side [p]" accesskey="p"><span>Udskriftsvenlig udgave</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> I andre projekter </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q304479" title="Link til tilknyttet emne i Wikidata [g]" accesskey="g"><span>Wikidata-element</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="Sideværktøjer"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Udseende"> <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">Udseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flyt til sidebjælken</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skjul</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">Fra Wikipedia, den frie encyklopædi</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="da" dir="ltr"><p>En <b>tørn</b> er en enhed til måling af vinkler og svarer til en hel omgang eller 360° eller 2<a href="/wiki/%CE%A0" class="mw-redirect" title="Π">π</a> radianer. En tørn kan inddeles i 100 <b>centitørn</b> eller 1000 <b>millitørn</b>, hvor hver millitørn svarer til en vinkel på 0.36°, hvilket også kan skrives 21'36". </p><p>Det er også almindeligt at lave binære inddelinger af en tørn. Således har søfolk traditionelt inddelt en tørn i 32 streger. En binær grad, også kaldet en binær radian er 1/256 tørn <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>. Binære grader bruges mest i programmering hvor det er en fordel at kunne repræsentere en vinkel med en enkelt byte. </p><p>Begrebet tørn bruges mest i forbindelse med plane rotationer. En rotation på 180° kaldes en halvtørn eller en refleksion i et punkt. En rotation på 90° kaldes en kvarttørn. </p><p>En tørn kaldes også en <b>hel omgang</b>. </p><p>Afhængigt af anvendelsen betegnes 1 tørn <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 \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }"></span>, rev eller rot. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Eksempler_på_anvendelser"><span id="Eksempler_p.C3.A5_anvendelser"></span>Eksempler på anvendelser</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=T%C3%B8rn&veaction=edit&section=1" title="Redigér afsnit: Eksempler på anvendelser" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=T%C3%B8rn&action=edit&section=1" title="Edit section's source code: Eksempler på anvendelser"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Som enhed for vinkelmålinger er tørn specielt velegnet til store vinkler. Summen af ydre vinkler i en polygon er 1 tørn. </p><p>I <a href="/w/index.php?title=Lagkagediagrammer&action=edit&redlink=1" class="new" title="Lagkagediagrammer (ikke skrevet endnu)">lagkagediagrammer</a> illustrerer man procentvis andel med den tilsvarende vinkel målt i centitørn. </p> <div class="mw-heading mw-heading3"><h3 id="Omsætning_mellem_almindeligt_forekommende_vinkler"><span id="Oms.C3.A6tning_mellem_almindeligt_forekommende_vinkler"></span>Omsætning mellem almindeligt forekommende vinkler</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=T%C3%B8rn&veaction=edit&section=2" title="Redigér afsnit: Omsætning mellem almindeligt forekommende vinkler" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=T%C3%B8rn&action=edit&section=2" title="Edit section's source code: Omsætning mellem almindeligt forekommende vinkler"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <th>Enheder</th> <th colspan="10">Værdier </th></tr> <tr valign="top"> <td style="background:#f2f2f2"><b>Tørn</b>   </td> <td style="width:3em; text-align:center">0 </td> <td style="width:3em; text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{12}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>12</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{12}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/421fdcb29205f9b03bdbda76332610e37742d54b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.48ex; height:3.509ex;" alt="{\displaystyle {\tfrac {1}{12}}}"></span> </td> <td style="width:3em; text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{10}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>10</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{10}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca1de894f8f238d18b9d57b742b8dcc52eadb493" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.48ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{10}}}"></span> </td> <td style="width:3em; text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{8}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>8</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{8}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78ec678ab485e2409f2fd6bfa86c8e3a56f9e028" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{8}}}"></span> </td> <td style="width:3em; text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bc02e655226b1a0e18922e932efff50531c48eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{6}}}"></span> </td> <td style="width:3em; text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{5}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{5}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cba10df075ad5061b732c02e1101b8f9237558e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{5}}}"></span> </td> <td style="width:3em; text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4825cd2a1ca51dfc4d53042434f6d3733370a57f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.658ex; height:3.509ex;" alt="{\displaystyle {\tfrac {1}{4}}}"></span> </td> <td style="width:3em; text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edef8290613648790a8ac1a95c2fb7c3972aea2f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.658ex; height:3.509ex;" alt="{\displaystyle {\tfrac {1}{2}}}"></span> </td> <td style="width:3em; text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {3}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {3}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8ec6051ef87eb0dafdaeaacd61f340052fcbf2bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.658ex; height:3.509ex;" alt="{\displaystyle {\tfrac {3}{4}}}"></span> </td> <td style="width:3em; text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.162ex; height:2.176ex;" alt="{\displaystyle 1}"></span> </td></tr> <tr valign="top"> <td style="background:#f2f2f2"><b>Grader</b>   </td> <td style="width:3em; text-align:center">0° </td> <td style="width:3em; text-align:center">30° </td> <td style="width:3em; text-align:center">36° </td> <td style="width:3em; text-align:center">45° </td> <td style="width:3em; text-align:center">60° </td> <td style="width:3em; text-align:center">72° </td> <td style="width:3em; text-align:center">90° </td> <td style="width:3em; text-align:center">180° </td> <td style="width:3em; text-align:center">270° </td> <td style="width:3em; text-align:center">360° </td></tr> <tr valign="top"> <td style="background:#f2f2f2"><b>Radianer</b> </td> <td style="text-align:center">0 </td> <td style="text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{6}}\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </mstyle> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{6}}\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56e1124294a23e49fc06fe471d666bd4814552e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.99ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{6}}\pi }"></span> </td> <td style="text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{5}}\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> </mstyle> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{5}}\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61d3a78418fda368bb0ae7c6466a93f5384a6542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.99ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{5}}\pi }"></span> </td> <td style="text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{4}}\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{4}}\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27b0601b4596e0a8c688b1fd39f1ccb9465c120f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.99ex; height:3.509ex;" alt="{\displaystyle {\tfrac {1}{4}}\pi }"></span> </td> <td style="text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{3}}\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mstyle> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{3}}\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c955aec170febff465815e3c038cf56f0c6d153" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.99ex; height:3.676ex;" alt="{\displaystyle {\tfrac {1}{3}}\pi }"></span> </td> <td style="text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {2}{5}}\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>2</mn> <mn>5</mn> </mfrac> </mstyle> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {2}{5}}\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd30d4ac332dc2ea0f3bad427caf4b28fc9bf6e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.99ex; height:3.676ex;" alt="{\displaystyle {\tfrac {2}{5}}\pi }"></span> </td> <td style="text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {1}{2}}\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{2}}\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfe27b6e44239efb1973b09f9eae178854860d5e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.99ex; height:3.509ex;" alt="{\displaystyle {\tfrac {1}{2}}\pi }"></span> </td> <td style="text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b64589f24cc8e145d021afa17d6564d55ea5a95c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.719ex; height:1.676ex;" alt="{\displaystyle \pi \,}"></span> </td> <td style="text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {3}{2}}\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {3}{2}}\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2945aa548a3aca4e2ba73153d448917714861055" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.99ex; height:3.509ex;" alt="{\displaystyle {\tfrac {3}{2}}\pi }"></span> </td> <td style="text-align:center"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\pi \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff0831f5ce22f8358436ea655ec0d0ef2534e1d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.882ex; height:2.176ex;" alt="{\displaystyle 2\pi \,}"></span> </td></tr> <tr valign="top"> <td style="background:#f2f2f2"><b>Nygrader</b> </td> <td style="text-align:center">0<sup>g</sup> </td> <td style="text-align:center">33⅓<sup>g</sup> </td> <td style="text-align:center">40<sup>g</sup> </td> <td style="text-align:center">50<sup>g</sup> </td> <td style="text-align:center">66⅔<sup>g</sup> </td> <td style="text-align:center">80<sup>g</sup> </td> <td style="text-align:center">100<sup>g</sup> </td> <td style="text-align:center">200<sup>g</sup> </td> <td style="text-align:center">300<sup>g</sup> </td> <td style="text-align:center">400<sup>g</sup> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Matematisk_konstant">Matematisk konstant</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=T%C3%B8rn&veaction=edit&section=3" title="Redigér afsnit: Matematisk konstant" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=T%C3%B8rn&action=edit&section=3" title="Edit section's source code: Matematisk konstant"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En halv tørn identificeres ofte med den matematiske konstant <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 \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> idet 1/2 tørn er <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 \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> radianer. Tilsvarende kan 1 tørn identificeres med <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2\pi =\tau \approx 6.283185307}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> <mo>=</mo> <mi>τ</mi> <mo>≈</mo> <mn>6.283185307</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi =\tau \approx 6.283185307}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/781eb9055336d7a911c86f5ec815e6f74fa6fa03" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:22.165ex; height:2.176ex;" alt="{\displaystyle 2\pi =\tau \approx 6.283185307}"></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Historie">Historie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=T%C3%B8rn&veaction=edit&section=4" title="Redigér afsnit: Historie" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=T%C3%B8rn&action=edit&section=4" title="Edit section's source code: Historie"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ordet tørn stammer via latin, fransk og engelsk fra det græske ord <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 \tau \mathrm {o} \rho \nu \mathrm {o} \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> </mrow> <mi>ρ</mi> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">o</mi> </mrow> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau \mathrm {o} \rho \nu \mathrm {o} \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51972ba4629131fff0cba261f962cb34021e027b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.291ex; height:2.176ex;" alt="{\displaystyle \tau \mathrm {o} \rho \nu \mathrm {o} \sigma }"></span> (tornos, som betyder en drejebænk). </p><p>Det geometriske begreb en tørn stammer fra søfolkenes betegnelser for dele af knob, hvor en tørn betyder at rebet er snoet omgang rundt om en puller, om sig selv eller en omgang i en kvejl. På dansk anvendes til søs betegnelserne tørn, rundtørn og dobbelt rundtørn, men disse betegnelser svarer ikke præcis til den geometriske brug af ordet. På tysk er der en mere eksakt sammenhæng mellem den geometriske anvendelse af ordet og brugen i forbindelse med knob.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>. </p><p>I 1697 brugte David Gregory <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 \pi /\rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi /\rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58b533ab3cc11547d616b91fb44af44160db481b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.696ex; height:2.843ex;" alt="{\displaystyle \pi /\rho }"></span> som betegnelse for omkredsen af en cirkel divideret med radius.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><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>, og <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 \pi /\delta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>δ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi /\delta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc74bcfb2fdecf74df7d5f9abf0b3c23a8ff2696" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.543ex; height:2.843ex;" alt="{\displaystyle \pi /\delta }"></span> blev brugt af <a href="/w/index.php?title=Oughtred&action=edit&redlink=1" class="new" title="Oughtred (ikke skrevet endnu)">Oughtred</a> i 1647 til at betegne forholdet mellem en cirkels omkreds og dens diameter. Den første anvendelse af symbolet <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 \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> i sin nuværende betydning finder vi hos <a href="/w/index.php?title=William_Jones_(mathematician)&action=edit&redlink=1" class="new" title="William Jones (mathematician) (ikke skrevet endnu)">William Jones</a> i 1706.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>, og <a href="/wiki/Euler" class="mw-redirect" title="Euler">Euler</a> overtog symbolet 1737. </p><p>Robert Palais foreslog anvendelse af et "trebenet pi" som betegnelse for 1 tørn <sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>, men dette symbol var ikke tilgængeligt i almindelige tekstbahandlingsprogrammer, så siden har nogle matematikere slået til lyd for at bruge <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 \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }"></span> (tau) som betegnelse for 1 tørn. </p> <div class="mw-heading mw-heading2"><h2 id="Referencer">Referencer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=T%C3%B8rn&veaction=edit&section=5" title="Redigér afsnit: Referencer" class="mw-editsection-visualeditor"><span>redigér</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=T%C3%B8rn&action=edit&section=5" title="Edit section's source code: Referencer"><span>rediger kildetekst</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r11780210">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <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.oopic.com/pgchap15.htm">ooPIC Programmer's Guide</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20080628051746/http://www.oopic.com/pgchap15.htm">Arkiveret</a> 28. juni 2008 hos <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> <i>www.oopic.com</i></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">^</a></span> <span class="reference-text"><a href="https://de.wikipedia.org/wiki/Rundt%C3%B6rn" class="extiw" title="de:Rundtörn">de:Rundtörn</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">^</a></span> <span class="reference-text">Beckmann, P., A History of Pi. Barnes & Noble Publishing, 1989.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">^</a></span> <span class="reference-text">Schwartzman, S., The Words of Mathematics. The Mathematical Association of America,1994. Page 165</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">^</a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r11752076">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120306173803/http://www.veling.nl/anne/templars/Pi_through_the_ages.html">"Pi through the ages"</a>. Arkiveret fra <a rel="nofollow" class="external text" href="http://www.veling.nl/anne/templars/Pi_through_the_ages.html">originalen</a> 6. marts 2012<span class="reference-accessdate">. Hentet 2. december 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Pi+through+the+ages&rft_id=http%3A%2F%2Fwww.veling.nl%2Fanne%2Ftemplars%2FPi_through_the_ages.html&rfr_id=info%3Asid%2Fda.wikipedia.org%3AT%C3%B8rn" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">^</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.math.utah.edu/%7Epalais/pi.pdf">Palais, R. 2001: Pi is Wrong, The Mathematical Intelligencer. Springer-Verlag New York. 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