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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="サイト"> <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="目次" 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">目次</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">非表示</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">ページ先頭</div> </a> </li> <li id="toc-数学定数" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#数学定数"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>数学定数</span> </div> </a> <ul id="toc-数学定数-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-turnの分割" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#turnの分割"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>turnの分割</span> </div> </a> <ul id="toc-turnの分割-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-他の一般的な角度との比較" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#他の一般的な角度との比較"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>他の一般的な角度との比較</span> </div> </a> <ul id="toc-他の一般的な角度との比較-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-単位τの提案" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#単位τの提案"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>単位τの提案</span> </div> </a> <ul id="toc-単位τの提案-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-使用例" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#使用例"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>使用例</span> </div> </a> <ul id="toc-使用例-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-関連項目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#関連項目"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>関連項目</span> </div> </a> <ul id="toc-関連項目-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-出典" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#出典"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>出典</span> </div> </a> <ul id="toc-出典-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部リンク" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部リンク"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>外部リンク</span> </div> </a> <ul id="toc-外部リンク-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="目次" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="目次" > <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="目次の表示・非表示を切り替え" > <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">目次の表示・非表示を切り替え</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">turn (角度)</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="特定の記事の別の言語版に移動します。利用可能な言語25件" > <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の言語版</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="アラビア語: دورة (هندسة رياضية)" lang="ar" hreflang="ar" data-title="دورة (هندسة رياضية)" data-language-autonym="العربية" data-language-local-name="アラビア語" 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="アッサム語: টাউ (সংখ্যা)" lang="as" hreflang="as" data-title="টাউ (সংখ্যা)" data-language-autonym="অসমীয়া" data-language-local-name="アッサム語" 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="ブルガリア語: Оборот" lang="bg" hreflang="bg" data-title="Оборот" data-language-autonym="Български" data-language-local-name="ブルガリア語" 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="ベンガル語: ঘূর্ণন (কোণ)" lang="bn" hreflang="bn" data-title="ঘূর্ণন (কোণ)" data-language-autonym="বাংলা" data-language-local-name="ベンガル語" 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="チュヴァシ語: Çаврăм (виçев пĕрчи)" lang="cv" hreflang="cv" data-title="Çаврăм (виçев пĕрчи)" data-language-autonym="Чӑвашла" data-language-local-name="チュヴァシ語" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/T%C3%B8rn" title="デンマーク語: Tørn" lang="da" hreflang="da" data-title="Tørn" data-language-autonym="Dansk" data-language-local-name="デンマーク語" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Vollwinkel" title="ドイツ語: Vollwinkel" lang="de" hreflang="de" data-title="Vollwinkel" data-language-autonym="Deutsch" data-language-local-name="ドイツ語" 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="エミリア・ロマーニャ語: Àngol gîr (giumetrìa)" lang="egl" hreflang="egl" data-title="Àngol gîr (giumetrìa)" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="エミリア・ロマーニャ語" 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="英語: Turn (angle)" lang="en" hreflang="en" data-title="Turn (angle)" data-language-autonym="English" data-language-local-name="英語" 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="スペイン語: Vuelta (ángulo)" lang="es" hreflang="es" data-title="Vuelta (ángulo)" data-language-autonym="Español" data-language-local-name="スペイン語" 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="バスク語: Bira (geometria)" lang="eu" hreflang="eu" data-title="Bira (geometria)" data-language-autonym="Euskara" data-language-local-name="バスク語" 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="ペルシア語: دور (هندسه)" lang="fa" hreflang="fa" data-title="دور (هندسه)" data-language-autonym="فارسی" data-language-local-name="ペルシア語" 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="フランス語: Tour (angle)" lang="fr" hreflang="fr" data-title="Tour (angle)" data-language-autonym="Français" data-language-local-name="フランス語" 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="インドネシア語: Putaran (sudut)" lang="id" hreflang="id" data-title="Putaran (sudut)" data-language-autonym="Bahasa Indonesia" data-language-local-name="インドネシア語" 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="イタリア語: Angolo giro" lang="it" hreflang="it" data-title="Angolo giro" data-language-autonym="Italiano" data-language-local-name="イタリア語" class="interlanguage-link-target"><span>Italiano</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="韓国語: 바퀴 (각도)" lang="ko" hreflang="ko" data-title="바퀴 (각도)" data-language-autonym="한국어" data-language-local-name="韓国語" 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="ポルトガル語: Volta (geometria)" lang="pt" hreflang="pt" data-title="Volta (geometria)" data-language-autonym="Português" data-language-local-name="ポルトガル語" 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="ロシア語: Оборот (единица измерения)" lang="ru" hreflang="ru" data-title="Оборот (единица измерения)" data-language-autonym="Русский" data-language-local-name="ロシア語" 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="スウェーデン語: Varv (vinkelenhet)" lang="sv" hreflang="sv" data-title="Varv (vinkelenhet)" data-language-autonym="Svenska" data-language-local-name="スウェーデン語" 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="タミル語: சுற்று (வடிவவியல்)" lang="ta" hreflang="ta" data-title="சுற்று (வடிவவியல்)" data-language-autonym="தமிழ்" data-language-local-name="タミル語" 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="トルコ語: Devir (birim)" lang="tr" hreflang="tr" data-title="Devir (birim)" data-language-autonym="Türkçe" data-language-local-name="トルコ語" 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="ウクライナ語: Оберт" lang="uk" hreflang="uk" data-title="Оберт" data-language-autonym="Українська" data-language-local-name="ウクライナ語" 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="ベトナム語: Vòng (hình học)" lang="vi" hreflang="vi" data-title="Vòng (hình học)" data-language-autonym="Tiếng Việt" data-language-local-name="ベトナム語" 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="中国語: 轉 (角)" lang="zh" hreflang="zh" data-title="轉 (角)" data-language-autonym="中文" data-language-local-name="中国語" 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="広東語: 轉 (角)" lang="yue" hreflang="yue" data-title="轉 (角)" data-language-autonym="粵語" data-language-local-name="広東語" 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="言語間リンクを編集" 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href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Angle-fractions.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Angle-fractions.png/250px-Angle-fractions.png" decoding="async" width="250" height="262" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/45/Angle-fractions.png/375px-Angle-fractions.png 1.5x, //upload.wikimedia.org/wikipedia/commons/4/45/Angle-fractions.png 2x" data-file-width="430" data-file-height="450" /></a><figcaption>反時計回りに円の中心を1周することで 1 turn を表す</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r101304250">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%;font-size:90%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">このページ名「<b>Turn (角度)</b>」は<a href="/wiki/Template:%E6%9A%AB%E5%AE%9A%E8%A8%98%E4%BA%8B%E5%90%8D/doc" title="Template:暫定記事名/doc">暫定的なもの</a>です。<small>（<span title="2014年9月">2014年9月</span>）</small></div></td></tr></tbody></table> <p><b>turn</b>（ターン;回転という意味）は<a href="/wiki/%E8%A7%92%E5%BA%A6" title="角度">角度</a>の単位の一つ。 1 turn は<a href="/wiki/%E5%BA%A6_(%E8%A7%92%E5%BA%A6)" title="度 (角度)">360°</a>、あるいは <a href="/wiki/%E3%83%A9%E3%82%B8%E3%82%A2%E3%83%B3" title="ラジアン">2<span lang="en" class="texhtml mvar" style="font-style:italic;">π</span> ラジアン</a>と等しい。turn は1回転することや回転運動などにも関係がある。一般的な角度を表現するには、1 turn を単位量として、1/2 turn（180°）、1/4 turn（90°、<a href="/wiki/%E7%9B%B4%E8%A7%92" title="直角">直角</a>）のように用いられる。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="数学定数"><span id=".E6.95.B0.E5.AD.A6.E5.AE.9A.E6.95.B0"></span>数学定数</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Turn_(%E8%A7%92%E5%BA%A6)&action=edit&section=1" title="節を編集: 数学定数"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>1 turn は <span class="nowrap">2π</span> (≈6.283185307179586)<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> <a href="/wiki/%E3%83%A9%E3%82%B8%E3%82%A2%E3%83%B3" title="ラジアン">ラジアン</a>と等しい。 </p> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:2pi-unrolled.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/2pi-unrolled.gif/400px-2pi-unrolled.gif" decoding="async" width="400" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/2pi-unrolled.gif/600px-2pi-unrolled.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/67/2pi-unrolled.gif/800px-2pi-unrolled.gif 2x" data-file-width="870" data-file-height="300" /></a><figcaption>（<a href="/wiki/%E5%8D%8A%E5%BE%84" title="半径">半径</a>が 1 の）<a href="/wiki/%E5%8D%98%E4%BD%8D%E5%86%86" title="単位円">単位円</a>の<a href="/wiki/%E5%91%A8%E9%95%B7" title="周長">周長</a>は 2<span lang="en" class="texhtml mvar" style="font-style:italic;">π</span> である。</figcaption></figure> <div style="clear:both;"></div> <div class="mw-heading mw-heading2"><h2 id="turnの分割"><span id="turn.E3.81.AE.E5.88.86.E5.89.B2"></span>turnの分割</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Turn_(%E8%A7%92%E5%BA%A6)&action=edit&section=2" title="節を編集: turnの分割"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>1 turn を100等分したものを 1 centiturn（センチターン）、1000等分したものを 1 milliturnと呼ぶ。1 milliturnは0.36°と等しく、21'36"とも表現できる。1 centiturnごとに目盛りを刻んだ<a href="/wiki/%E5%88%86%E5%BA%A6%E5%99%A8" title="分度器">分度器</a>をパーセント定規（percentage protractor）などと呼ぶ。 </p><p>また、航海士は伝統的に方位を32等分したものを用いている（⇒<a href="/wiki/%E7%BE%85%E9%87%9D%E5%9B%B3" title="羅針図">羅針図</a>）。 </p><p>turn の概念では平面上の回転が一般的に用いられる。英語では、1/2 turn と 1/4 turn は特に half-turn, quarter-turn と呼ばれている<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>。half-turn はしばしば reflection in a point（一点を中心とした対称移動）と呼ばれる。これらは 2 次元平面上での変換に対して同一であるからである。 </p> <div class="mw-heading mw-heading2"><h2 id="他の一般的な角度との比較"><span id=".E4.BB.96.E3.81.AE.E4.B8.80.E8.88.AC.E7.9A.84.E3.81.AA.E8.A7.92.E5.BA.A6.E3.81.A8.E3.81.AE.E6.AF.94.E8.BC.83"></span>他の一般的な角度との比較</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Turn_(%E8%A7%92%E5%BA%A6)&action=edit&section=3" title="節を編集: 他の一般的な角度との比較"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable" style="text-align:center;"> <tbody><tr> <th>単位</th> <th colspan="13">値 </th></tr> <tr> <td style="background:#f2f2f2; text-align:left;"><b>Turn</b>   </td> <td style="width:3em;">0 </td> <td style="width:3em;"><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}{24}}}"> <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>24</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{24}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b0e361e869e95bae64491e20b0b45b8c407bbe5" 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}{24}}}"></span> </td> <td style="width:3em;"><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;"><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;"><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;"><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;"><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;"><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;"><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}}}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9efc37d09854a3f8fb997e7de4331876bc49c2c0" 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}{3}}}"></span> </td> <td style="width:3em;"><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}}}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {2}{5}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edb22be2c480d6bb96c97cc2b6a1a796f8396489" 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 {2}{5}}}"></span> </td> <td style="width:3em;"><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;"><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;">1 </td></tr> <tr> <td style="background:#f2f2f2; text-align:left;"><b><a href="/wiki/%E3%83%A9%E3%82%B8%E3%82%A2%E3%83%B3" title="ラジアン">ラジアン</a></b>（弧度法） </td> <td>0 </td> <td><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 {\pi }{12}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>12</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\pi }{12}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4003cb335c111eff28d24f990d71ce744bdbce2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.48ex; height:3.176ex;" alt="{\displaystyle {\tfrac {\pi }{12}}}"></span> </td> <td><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 {\pi }{6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>6</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\pi }{6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75bc23c5dc0aac6e2066ae76ee4a5cf52fd3e19b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.778ex; height:3.343ex;" alt="{\displaystyle {\tfrac {\pi }{6}}}"></span> </td> <td><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 {\pi }{5}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>5</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\pi }{5}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3dc8ac67580c4e2439889672d4b14d9b5ad67720" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.778ex; height:3.343ex;" alt="{\displaystyle {\tfrac {\pi }{5}}}"></span> </td> <td><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 {\pi }{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\pi }{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1f065c03576345b1b536c3cd513af53e8c35c5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.778ex; height:3.176ex;" alt="{\displaystyle {\tfrac {\pi }{4}}}"></span> </td> <td><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 {\pi }{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>3</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\pi }{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35e0953cd4cd6fa5a3f4b473c8bd0cf32bbb5c7e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:1.778ex; height:3.343ex;" alt="{\displaystyle {\tfrac {\pi }{3}}}"></span> </td> <td><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\pi }{5}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>5</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {2\pi }{5}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5508e6906bf83215949906383498fa5b3402b730" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.6ex; height:3.676ex;" alt="{\displaystyle {\tfrac {2\pi }{5}}}"></span> </td> <td><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 {\pi }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4e31a202557dfbf326b44ebcc914ba3ab08fff1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:1.778ex; height:3.176ex;" alt="{\displaystyle {\tfrac {\pi }{2}}}"></span> </td> <td><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\pi }{3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {2\pi }{3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d347f5b40db81e556675c27ed6da65079059c5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.6ex; height:3.676ex;" alt="{\displaystyle {\tfrac {2\pi }{3}}}"></span> </td> <td><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 {4\pi }{5}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mn>5</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {4\pi }{5}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb0e3d29f4753f7eb135a2dcade23e0dae258423" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.6ex; height:3.676ex;" alt="{\displaystyle {\tfrac {4\pi }{5}}}"></span> </td> <td><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><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\pi }{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mn>3</mn> <mi>π</mi> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {3\pi }{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d3931916b7162c3b40be4327140f391b5d495b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.6ex; height:3.509ex;" alt="{\displaystyle {\tfrac {3\pi }{2}}}"></span> </td> <td><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> <td style="background:#f2f2f2; text-align:left;"><b><a href="/wiki/%E5%BA%A6_(%E8%A7%92%E5%BA%A6)" title="度 (角度)">度</a></b>（度数法）   </td> <td style="width:3em;">0° </td> <td style="width:3em;">15° </td> <td style="width:3em;">30° </td> <td style="width:3em;">36° </td> <td style="width:3em;">45° </td> <td style="width:3em;">60° </td> <td style="width:3em;">72° </td> <td style="width:3em;">90° </td> <td style="width:3em;">120° </td> <td style="width:3em;">144° </td> <td style="width:3em;">180° </td> <td style="width:3em;">270° </td> <td style="width:3em;">360° </td></tr> <tr> <td style="background:#f2f2f2; text-align:left;"><b><a href="/wiki/%E3%82%B0%E3%83%A9%E3%83%BC%E3%83%89_(%E5%8D%98%E4%BD%8D)" title="グラード (単位)">グラード</a></b> </td> <td>0<sup>g</sup> </td> <td>16⅔<sup>g</sup> </td> <td>33⅓<sup>g</sup> </td> <td>40<sup>g</sup> </td> <td>50<sup>g</sup> </td> <td>66⅔<sup>g</sup> </td> <td>80<sup>g</sup> </td> <td>100<sup>g</sup> </td> <td>133⅓<sup>g</sup> </td> <td>160<sup>g</sup> </td> <td>200<sup>g</sup> </td> <td>300<sup>g</sup> </td> <td>400<sup>g</sup> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="単位τの提案"><span id=".E5.8D.98.E4.BD.8D.CF.84.E3.81.AE.E6.8F.90.E6.A1.88"></span>単位τの提案</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Turn_(%E8%A7%92%E5%BA%A6)&action=edit&section=4" title="節を編集: 単位τの提案"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Circle_radians_tau.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Circle_radians_tau.gif/200px-Circle_radians_tau.gif" decoding="async" width="200" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Circle_radians_tau.gif/300px-Circle_radians_tau.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Circle_radians_tau.gif/400px-Circle_radians_tau.gif 2x" data-file-width="430" data-file-height="430" /></a><figcaption>円の半径と同じ長さの弧は1ラジアンの角度に対応する。全円は1 turn、6.28ラジアンと対応しており、これをギリシャ文字タウ(<span style="font-family:'Times New Roman',serif;font-size:118%">τ</span>)を用いて表す。</figcaption></figure> <p>2001年、Robert Palaisは数学をより単純でわかりやすくするために基本的な円の定数である<a href="/wiki/%E5%86%86%E5%91%A8%E7%8E%87" title="円周率"><span lang="en" class="texhtml mvar" style="font-style:italic;">π</span></a>（半円のラジアン値）の代わりとしてturnでラジアンの値を表すことを提案した。このとき提案した記号は<span lang="en" class="texhtml mvar" style="font-style:italic;">π</span>の足を2本から3本に増やしたものであった(<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 \!\;\!\!\!\pi =2\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mspace width="negativethinmathspace" /> <mspace width="thickmathspace" /> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mspace width="negativethinmathspace" /> <mi>π</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi \!\;\!\!\!\pi =2\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0c1447252a4e997ca26dc5d429a0aec5b16a47b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.354ex; height:2.176ex;" alt="{\displaystyle \pi \!\;\!\!\!\pi =2\pi }"></span>)<sup id="cite_ref-palais_3-0" class="reference"><a href="#cite_note-palais-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>2010年には、Michael Hartlはこの3本足の<span lang="en" class="texhtml mvar" style="font-style:italic;">π</span>を2つの理由からギリシャ文字の<a href="/wiki/%CE%A4_(%E6%95%B0%E5%AD%A6%E5%AE%9A%E6%95%B0)" title="Τ (数学定数)"><span style="font-family:'Times New Roman',serif;font-size:118%">τ</span></a>で代用することを提案した。それはまず <span style="font-family:'Times New Roman',serif;font-size:118%">τ</span> ラジアンは円の1周 (1 turn) に対応し、<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}}}"> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {2}{5}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edb22be2c480d6bb96c97cc2b6a1a796f8396489" 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 {2}{5}}}"></span> turn あるいは <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 {4}{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>4</mn> <mn>5</mn> </mfrac> </mstyle> </mrow> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {4}{5}}\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8cb1209b6daa75b437df957c20bf319166d44fc" 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 {4}{5}}\pi }"></span> を表すのに <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}}\tau }"> <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>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {2}{5}}\tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe5e9c22600f12e677a675267abbb496d5dd4093" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.86ex; height:3.676ex;" alt="{\displaystyle {\tfrac {2}{5}}\tau }"></span> のようなturnの分数が使えること、次に<span style="font-family:'Times New Roman',serif;font-size:118%">τ</span>は<span lang="en" class="texhtml mvar" style="font-style:italic;">π</span>と見た目が似ていて円の定数であることがそこから連想されることである。<sup id="cite_ref-tauday_4-0" class="reference"><a href="#cite_note-tauday-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Hartlの <i>Tau Manifesto</i>（タウの宣言）は<span lang="en" class="texhtml mvar" style="font-style:italic;">π</span>の代わりに<span style="font-family:'Times New Roman',serif;font-size:118%">τ</span>を用いればたくさんの式が簡単になることが示されている<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><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> </p> <div class="mw-heading mw-heading2"><h2 id="使用例"><span id=".E4.BD.BF.E7.94.A8.E4.BE.8B"></span>使用例</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Turn_(%E8%A7%92%E5%BA%A6)&action=edit&section=5" title="節を編集: 使用例"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>角度の単位として、turnやrevolution（いずれも回転を意味する）は大きな角度を表すのに便利である。例えば<a href="/wiki/%E3%82%B3%E3%82%A4%E3%83%AB" title="コイル">コイル</a>や<a href="/wiki/%E5%9B%9E%E8%BB%A2%E9%81%8B%E5%8B%95" class="mw-redirect" title="回転運動">回転運動</a>などがあげられる。<a href="/wiki/%E5%9B%9E%E8%BB%A2%E6%95%B0_(%E6%95%B0%E5%AD%A6)" title="回転数 (数学)">回転数</a>も参照。</li> <li><a href="/wiki/%E5%8E%9F%E5%8B%95%E6%A9%9F" title="原動機">エンジン</a>のような機械類の回転の角速度は一般に <a href="/wiki/Rpm_(%E5%8D%98%E4%BD%8D)" title="Rpm (単位)">rpm</a> で計測される。これは1分間に何回転するかを表す単位である。</li> <li>turn は <a href="https://en.wikipedia.org/wiki/External_ray" class="extiw" title="en:External ray">external</a>、internal angle に対して<a href="/wiki/%E8%A4%87%E7%B4%A0%E5%8A%9B%E5%AD%A6%E7%B3%BB" title="複素力学系">複素力学系</a>で使用される。多角形の外角の和は 1 turn （360°）である。<a href="https://en.wikipedia.org/wiki/Dyadic_transformation" class="extiw" title="en:Dyadic transformation">Dyadic transformation</a> が用いられる。</li> <li><a href="/wiki/%E5%86%86%E3%82%B0%E3%83%A9%E3%83%95" title="円グラフ">円グラフ</a>の比率はturnの分数である。1 % は 1 centiturn である。</li> <li><a href="/wiki/Cascading_Style_Sheets" title="Cascading Style Sheets">CSS 3</a> では角度の表現法の1つとして turn がサポートされている。</li></ul> <div class="mw-heading mw-heading2"><h2 id="関連項目"><span id=".E9.96.A2.E9.80.A3.E9.A0.85.E7.9B.AE"></span>関連項目</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Turn_(%E8%A7%92%E5%BA%A6)&action=edit&section=6" title="節を編集: 関連項目"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E5%BA%A6_(%E8%A7%92%E5%BA%A6)" title="度 (角度)">度 (角度)</a></li> <li><a href="/wiki/%E3%83%A9%E3%82%B8%E3%82%A2%E3%83%B3" title="ラジアン">ラジアン</a></li> <li><a href="/wiki/%E3%82%B0%E3%83%A9%E3%83%BC%E3%83%89_(%E5%8D%98%E4%BD%8D)" title="グラード (単位)">グラード (単位)</a></li> <li><a href="/wiki/%E5%8B%BE%E9%85%8D" title="勾配">勾配</a></li> <li><a href="/wiki/%E7%9B%B4%E8%A7%92" title="直角">直角</a></li> <li><a href="/wiki/%E6%99%82%E8%A7%92" title="時角">時角</a></li> <li><a href="/wiki/Rpm_(%E5%8D%98%E4%BD%8D)" title="Rpm (単位)">rpm (単位)</a></li> <li><a href="/wiki/%CE%A4_(%E6%95%B0%E5%AD%A6%E5%AE%9A%E6%95%B0)" title="Τ (数学定数)">τ (数学定数)</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="出典"><span id=".E5.87.BA.E5.85.B8"></span>出典</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Turn_(%E8%A7%92%E5%BA%A6)&action=edit&section=7" title="節を編集: 出典"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="-moz-column-count:auto; -webkit-column-count:auto; column-count:auto; -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><b><a href="#cite_ref-1">^</a></b> <span class="reference-text">Sequence <a rel="nofollow" class="external text" href="//oeis.org/A019692">A019692</a>.</span> </li> <li id="cite_note-2"><b><a href="#cite_ref-2">^</a></b> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.cut-the-knot.org/Curriculum/Geometry/HalfTurn.shtml">Half Turn, Reflection in Point</a> cut-the-knot.org</span> </li> <li id="cite_note-palais-3"><b><a href="#cite_ref-palais_3-0">^</a></b> <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. Volume 23, Number 3, pp. 7–8</a></span> </li> <li id="cite_note-tauday-4"><b><a href="#cite_ref-tauday_4-0">^</a></b> <span class="reference-text"><cite class="citation web" style="font-style:normal">Michael Hartl (March 14, 2013). “<a rel="nofollow" class="external text" href="http://tauday.com/tau-manifesto">The Tau Manifesto</a>”. <span title="">September 14, 2013</span>閲覧。</cite></span> </li> <li id="cite_note-5"><b><a href="#cite_ref-5">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="citation" id="CITEREFAron2011">Aron, Jacob (8 January 2011), “Interview: Michael Hartl: It's time to kill off pi”, <i><a href="/wiki/%E3%83%8B%E3%83%A5%E3%83%BC%E3%83%BB%E3%82%B5%E3%82%A4%E3%82%A8%E3%83%B3%E3%83%86%E3%82%A3%E3%82%B9%E3%83%88" title="ニュー・サイエンティスト">New Scientist</a></i> <b>209</b> (2794), <a href="/wiki/Bibcode_(%E8%AD%98%E5%88%A5%E5%AD%90)" class="mw-redirect" title="Bibcode (識別子)">Bibcode</a>: <a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011NewSc.209...23A/abstract">2011NewSc.209...23A</a>, <a href="/wiki/Doi_(%E8%AD%98%E5%88%A5%E5%AD%90)" class="mw-redirect" title="Doi (識別子)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0262-4079%2811%2960036-5">10.1016/S0262-4079(11)60036-5</a></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Interview%3A+Michael+Hartl%3A+It%27s+time+to+kill+off+pi&rft.jtitle=%5B%5B%E3%83%8B%E3%83%A5%E3%83%BC%E3%83%BB%E3%82%B5%E3%82%A4%E3%82%A8%E3%83%B3%E3%83%86%E3%82%A3%E3%82%B9%E3%83%88%7CNew+Scientist%5D%5D&rft.aulast=Aron&rft.aufirst=Jacob&rft.au=Aron%2C%26%2332%3BJacob&rft.date=8+January+2011&rft.volume=209&rft.issue=2794&rft_id=info:bibcode/2011NewSc.209...23A&rft_id=info:doi/10.1016%2FS0262-4079%2811%2960036-5&rfr_id=info:sid/ja.wikipedia.org:Turn_(%E8%A7%92%E5%BA%A6)"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-6"><b><a href="#cite_ref-6">^</a></b> <span class="reference-text"><cite style="font-style:normal" class="citation" id="CITEREFLandau2011">Landau, Elizabeth (14 March 2011), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110315004034/http://edition.cnn.com/2011/TECH/innovation/03/14/pi.tau.math/index.html">“On Pi Day, is 'pi' under attack?”</a>, <i>cnn.com</i>,  <a rel="nofollow" class="external text" href="http://edition.cnn.com/2011/TECH/innovation/03/14/pi.tau.math/index.html">オリジナル</a>の2011/03/15時点におけるアーカイブ。<span style="display:none;">, <a rel="nofollow" class="external free" href="https://web.archive.org/web/20110315004034/http://edition.cnn.com/2011/TECH/innovation/03/14/pi.tau.math/index.html">https://web.archive.org/web/20110315004034/http://edition.cnn.com/2011/TECH/innovation/03/14/pi.tau.math/index.html</a></span></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+Pi+Day%2C+is+%27pi%27+under+attack%3F&rft.jtitle=cnn.com&rft.aulast=Landau&rft.aufirst=Elizabeth&rft.au=Landau%2C%26%2332%3BElizabeth&rft.date=14+March+2011&rft_id=https%3A%2F%2Fweb.archive.org%2Fweb%2F20110315004034%2Fhttp%3A%2F%2Fedition.cnn.com%2F2011%2FTECH%2Finnovation%2F03%2F14%2Fpi.tau.math%2Findex.html&rfr_id=info:sid/ja.wikipedia.org:Turn_(%E8%A7%92%E5%BA%A6)"><span style="display: none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="外部リンク"><span id=".E5.A4.96.E9.83.A8.E3.83.AA.E3.83.B3.E3.82.AF"></span>外部リンク</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Turn_(%E8%A7%92%E5%BA%A6)&action=edit&section=8" title="節を編集: 外部リンク"><span>編集</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.math.utah.edu/%7Epalais/pi.pdf">"π Is Wrong!" by Bob Palais</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">「<a dir="ltr" href="https://ja.wikipedia.org/w/index.php?title=Turn_(角度)&oldid=86405944">https://ja.wikipedia.org/w/index.php?title=Turn_(角度)&oldid=86405944</a>」から取得</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%82%AB%E3%83%86%E3%82%B4%E3%83%AA" title="特別:カテゴリ">カテゴリ</a>: <ul><li><a href="/wiki/Category:%E8%A7%92%E5%BA%A6" title="Category:角度">角度</a></li><li><a href="/wiki/Category:%E8%A7%92%E5%BA%A6%E3%81%AE%E5%8D%98%E4%BD%8D" title="Category:角度の単位">角度の単位</a></li><li><a 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