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class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF" title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" 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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">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</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">序言</div> </a> </li> <li id="toc-参考文献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考文献"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>参考文献</span> </div> </a> <ul id="toc-参考文献-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="目录" 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="开关目录" > <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">开关目录</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">一般旋轮线</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="前往另一种语言写成的文章。15种语言可用" > <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-15" 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">15种语言</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%D8%AD%D8%B1%D9%88%D8%AC%D8%A9_(%D9%85%D9%86%D8%AD%D9%86%D9%89)" title="دحروجة (منحنى) – 阿拉伯语" lang="ar" hreflang="ar" data-title="دحروجة (منحنى)" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Ruleta_(geometria)" title="Ruleta (geometria) – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Ruleta (geometria)" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Roulette_(curve)" title="Roulette (curve) – 英语" lang="en" hreflang="en" data-title="Roulette (curve)" data-language-autonym="English" data-language-local-name="英语" 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/Ruleta_(curva)" title="Ruleta (curva) – 西班牙语" lang="es" hreflang="es" data-title="Ruleta (curva)" data-language-autonym="Español" data-language-local-name="西班牙语" 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/Erruleta_(geometria)" title="Erruleta (geometria) – 巴斯克语" lang="eu" hreflang="eu" data-title="Erruleta (geometria)" data-language-autonym="Euskara" data-language-local-name="巴斯克语" 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%BA%D9%84%D8%AA%D8%A7%D9%86" title="غلتان – 波斯语" lang="fa" hreflang="fa" data-title="غلتان" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Vierint%C3%A4k%C3%A4yr%C3%A4" title="Vierintäkäyrä – 芬兰语" lang="fi" hreflang="fi" data-title="Vierintäkäyrä" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Roulette_(courbe)" title="Roulette (courbe) – 法语" lang="fr" hreflang="fr" data-title="Roulette (courbe)" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Rulletta" title="Rulletta – 意大利语" lang="it" hreflang="it" data-title="Rulletta" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Rolete_(curva)" title="Rolete (curva) – 葡萄牙语" lang="pt" hreflang="pt" data-title="Rolete (curva)" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Rulet%C4%83_(curb%C4%83)" title="Ruletă (curbă) – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Ruletă (curbă)" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Ruleta_(krivulja)" title="Ruleta (krivulja) – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Ruleta (krivulja)" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AE%BF%E0%AE%B1%E0%AF%81%E0%AE%9A%E0%AE%BF%E0%AE%B2%E0%AF%8D%E0%AE%B2%E0%AE%BF" title="சிறுசில்லி – 泰米尔语" lang="ta" hreflang="ta" data-title="சிறுசில்லி" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" 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/Yuvarlanma_e%C4%9Frisi" title="Yuvarlanma eğrisi – 土耳其语" lang="tr" hreflang="tr" data-title="Yuvarlanma eğrisi" data-language-autonym="Türkçe" data-language-local-name="土耳其语" 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%A0%D1%83%D0%BB%D0%B5%D1%82%D0%B0" title="Рулета – 乌克兰语" lang="uk" hreflang="uk" data-title="Рулета" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</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/Q2810237#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</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="命名空间"> <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/%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF" title="浏览条目正文[c]" accesskey="c"><span>条目</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Talk:%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF&action=edit&redlink=1" rel="discussion" class="new" title="关于此页面的讨论（页面不存在）[t]" accesskey="t"><span>讨论</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " > <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="更改语言变体" > <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">不转换</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="selected ca-variants-zh mw-list-item"><a href="/zh/%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF" lang="zh" hreflang="zh"><span>不转换</span></a></li><li id="ca-varlang-1" class="ca-variants-zh-Hans mw-list-item"><a href="/zh-hans/%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF" lang="zh-Hans" hreflang="zh-Hans"><span>简体</span></a></li><li id="ca-varlang-2" class="ca-variants-zh-Hant mw-list-item"><a href="/zh-hant/%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF" lang="zh-Hant" hreflang="zh-Hant"><span>繁體</span></a></li><li id="ca-varlang-3" class="ca-variants-zh-Hans-CN mw-list-item"><a href="/zh-cn/%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF" lang="zh-Hans-CN" hreflang="zh-Hans-CN"><span>大陆简体</span></a></li><li id="ca-varlang-4" class="ca-variants-zh-Hant-HK mw-list-item"><a href="/zh-hk/%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF" lang="zh-Hant-HK" hreflang="zh-Hant-HK"><span>香港繁體</span></a></li><li id="ca-varlang-5" class="ca-variants-zh-Hant-MO mw-list-item"><a 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<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">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隐藏</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">维基百科，自由的百科全书</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="zh" dir="ltr"><figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/File:RouletteAnim.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d8/RouletteAnim.gif" decoding="async" width="326" height="327" class="mw-file-element" data-file-width="326" data-file-height="327" /></a><figcaption><a href="/wiki/%E8%94%93%E5%8F%B6%E7%BA%BF" title="蔓叶线">蔓叶线</a>为旋轮线的一种，可以通过一条抛物线在另一条抛物线上滚动而构造</figcaption></figure> <p><b>一般旋轮线</b>（英語：<span lang="en">roulette</span>），又称为<b>转迹线</b>、<b>轮转曲线</b>等，是一类<a href="/wiki/%E6%9B%B2%E7%BA%BF" title="曲线">曲线</a>的统称，指一条动曲线沿一条定曲线无滑动地滚动时，动曲线上的一定点所形成的轨迹，包括<a href="/wiki/%E6%91%86%E7%BA%BF" title="摆线">摆线</a>、<a href="/wiki/%E5%A4%96%E6%91%86%E7%BA%BF" title="外摆线">外摆线</a>、<a href="/wiki/%E5%85%A7%E6%93%BA%E7%B7%9A" class="mw-redirect" title="內擺線">内摆线</a>、<a href="/wiki/%E6%AC%A1%E6%91%86%E7%BA%BF" title="次摆线">次摆线</a>、<a href="/wiki/%E6%B8%90%E4%BC%B8%E7%BA%BF" class="mw-redirect" title="渐伸线">渐伸线</a>等。<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>常见的旋轮线有： </p> <table class="wikitable"> <tbody><tr> <th>定曲线 </th> <th>动曲线 </th> <th>定点 </th> <th>名称 </th></tr> <tr> <td>任意曲线 </td> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td>直线上点 </td> <td>曲线的<a href="/wiki/%E6%B8%90%E4%BC%B8%E7%BA%BF" class="mw-redirect" title="渐伸线">渐伸线</a> </td></tr> <tr> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td><a href="/wiki/%E5%9C%86" title="圆">圆</a> </td> <td>任意点 </td> <td><a href="/wiki/%E6%AC%A1%E6%91%86%E7%BA%BF" title="次摆线">次摆线</a> </td></tr> <tr> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td><a href="/wiki/%E5%9C%86" title="圆">圆</a> </td> <td>直线上点 </td> <td><a href="/wiki/%E6%91%86%E7%BA%BF" title="摆线">摆线</a> </td></tr> <tr> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td><a href="/wiki/%E5%9C%86%E9%94%A5%E6%9B%B2%E7%BA%BF" title="圆锥曲线">圆锥曲线</a> </td> <td>圆锥曲线中心 </td> <td>斯图姆旋轮线（Sturm roulette）<sup id="cite_ref-sturm_2-0" class="reference"><a href="#cite_note-sturm-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td><a href="/wiki/%E5%9C%86%E9%94%A5%E6%9B%B2%E7%BA%BF" title="圆锥曲线">圆锥曲线</a> </td> <td>圆锥曲线焦点 </td> <td>德洛内旋轮线（Delaunay roulette）<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> </td></tr> <tr> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td><a href="/wiki/%E6%8A%9B%E7%89%A9%E7%BA%BF" title="抛物线">抛物线</a> </td> <td>抛物线焦点 </td> <td><a href="/wiki/%E6%82%AC%E9%93%BE%E7%BA%BF" title="悬链线">悬链线</a><sup id="cite_ref-2dcurves_roulettede_4-0" class="reference"><a href="#cite_note-2dcurves_roulettede-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td><a href="/wiki/%E6%A4%AD%E5%9C%86" title="椭圆">椭圆</a> </td> <td>椭圆焦点 </td> <td>椭圆悬链线<sup id="cite_ref-2dcurves_roulettede_4-1" class="reference"><a href="#cite_note-2dcurves_roulettede-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td><a href="/wiki/%E5%8F%8C%E6%9B%B2%E7%BA%BF" title="双曲线">双曲线</a> </td> <td>双曲线焦点 </td> <td>双曲悬链线<sup id="cite_ref-2dcurves_roulettede_4-2" class="reference"><a href="#cite_note-2dcurves_roulettede-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td><a href="/wiki/%E5%8F%8C%E6%9B%B2%E7%BA%BF" title="双曲线">双曲线</a> </td> <td>双曲线中心 </td> <td>直角弹性线（rectangular elastica）<sup id="cite_ref-sturm_2-1" class="reference"><a href="#cite_note-sturm-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> </td> <td><a href="/wiki/%E5%A4%96%E6%91%86%E7%BA%BF" title="外摆线">外摆线</a>或<a href="/wiki/%E5%85%A7%E6%93%BA%E7%B7%9A" class="mw-redirect" title="內擺線">内摆线</a> </td> <td>中心 </td> <td><a href="/wiki/%E6%A4%AD%E5%9C%86" title="椭圆">椭圆</a><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> </td></tr> <tr> <td><a href="/wiki/%E5%9C%86" title="圆">圆</a> </td> <td><a href="/wiki/%E5%9C%86" title="圆">圆</a> </td> <td>任意点 </td> <td>同心次摆线（centered trochoid）<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> </td></tr> <tr> <td><a href="/wiki/%E6%8A%9B%E7%89%A9%E7%BA%BF" title="抛物线">抛物线</a> </td> <td>与定抛物线形状相同、方向相反 </td> <td>抛物线极点 </td> <td><a href="/wiki/%E8%94%93%E5%8F%B6%E7%BA%BF" title="蔓叶线">蔓叶线</a><sup id="cite_ref-2dcurves_cubicc_7-0" class="reference"><a href="#cite_note-2dcurves_cubicc-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="参考文献"><span id=".E5.8F.82.E8.80.83.E6.96.87.E7.8C.AE"></span>参考文献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF&action=edit&section=1" title="编辑章节：参考文献"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation book">沈以淡 (编). 《简明数学词典》. 北京理工大学出版社. 2003.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF&rft.au=%E6%B2%88%E4%BB%A5%E6%B7%A1&rft.btitle=%E3%80%8A%E7%AE%80%E6%98%8E%E6%95%B0%E5%AD%A6%E8%AF%8D%E5%85%B8%E3%80%8B&rft.date=2003&rft.genre=book&rft.pub=%E5%8C%97%E4%BA%AC%E7%90%86%E5%B7%A5%E5%A4%A7%E5%AD%A6%E5%87%BA%E7%89%88%E7%A4%BE&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-sturm-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-sturm_2-0"><sup><b>2.0</b></sup></a> <a href="#cite_ref-sturm_2-1"><sup><b>2.1</b></sup></a></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.mathcurve.com/courbes2d/sturm/sturm.shtml"><span style="padding-left:0.2em;">"</span>Sturm's roulette" on www.mathcurve.com</a>. <span class="reference-accessdate"> [<span class="nowrap">2016-10-05</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190916001505/http://www.mathcurve.com/courbes2d/sturm/sturm.shtml">存档</a>于2019-09-16）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF&rft.btitle=%22Sturm%27s+roulette%22+on+www.mathcurve.com&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.mathcurve.com%2Fcourbes2d%2Fsturm%2Fsturm.shtml&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.mathcurve.com/courbes2d/delaunay/delaunay.shtml"><span style="padding-left:0.2em;">"</span>Delaunay's roulette" on www.mathcurve.com</a>. <span class="reference-accessdate"> [<span class="nowrap">2016-10-05</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190913204355/http://www.mathcurve.com/courbes2d/delaunay/delaunay.shtml">存档</a>于2019-09-13）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF&rft.btitle=%22Delaunay%27s+roulette%22+on+www.mathcurve.com&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.mathcurve.com%2Fcourbes2d%2Fdelaunay%2Fdelaunay.shtml&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2dcurves_roulettede-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-2dcurves_roulettede_4-0"><sup><b>4.0</b></sup></a> <a href="#cite_ref-2dcurves_roulettede_4-1"><sup><b>4.1</b></sup></a> <a href="#cite_ref-2dcurves_roulettede_4-2"><sup><b>4.2</b></sup></a></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.2dcurves.com/roulette/roulettede.html"><span style="padding-left:0.2em;">"</span>Delaunay's roulette" on www.2dcurves.com</a>. <span class="reference-accessdate"> [<span class="nowrap">2016-10-05</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190212033521/http://www.2dcurves.com/roulette/roulettede.html">存档</a>于2019-02-12）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF&rft.btitle=%22Delaunay%27s+roulette%22+on+www.2dcurves.com&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.2dcurves.com%2Froulette%2Froulettede.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.mathcurve.com/courbes2d/roulette/roulette.shtml"><span style="padding-left:0.2em;">"</span>Roulette with straight fixed curve" on www.mathcurve.com</a>. <span class="reference-accessdate"> [<span class="nowrap">2016-10-05</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190913173531/http://www.mathcurve.com/courbes2d/roulette/roulette.shtml">存档</a>于2019-09-13）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF&rft.btitle=%22Roulette+with+straight+fixed+curve%22+on+www.mathcurve.com&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.mathcurve.com%2Fcourbes2d%2Froulette%2Froulette.shtml&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.mathcurve.com/courbes2d/trochoid/trochoidacentre.shtml"><span style="padding-left:0.2em;">"</span>Centered trochoid" on mathcurve.com</a>. <span class="reference-accessdate"> [<span class="nowrap">2016-10-05</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190921235232/http://www.mathcurve.com/courbes2d/trochoid/trochoidacentre.shtml">存档</a>于2019-09-21）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF&rft.btitle=%22Centered+trochoid%22+on+mathcurve.com&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.mathcurve.com%2Fcourbes2d%2Ftrochoid%2Ftrochoidacentre.shtml&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2dcurves_cubicc-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-2dcurves_cubicc_7-0">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.2dcurves.com/cubic/cubicc.html"><span style="padding-left:0.2em;">"</span>Cissoid" on www.2dcurves.com</a>. <span class="reference-accessdate"> [<span class="nowrap">2016-10-05</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20191230011051/http://www.2dcurves.com/cubic/cubicc.html">存档</a>于2019-12-30）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E4%B8%80%E8%88%AC%E6%97%8B%E8%BD%AE%E7%BA%BF&rft.btitle=%22Cissoid%22+on+www.2dcurves.com&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.2dcurves.com%2Fcubic%2Fcubicc.html&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r84265675">.mw-parser-output .hlist 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.navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Differential_transforms_of_plane_curves" title="Template:Differential transforms of plane curves"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:Differential_transforms_of_plane_curves&action=edit&redlink=1" class="new" title="Template talk:Differential transforms of plane curves（页面不存在）"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:Differential_transforms_of_plane_curves" title="Special:编辑页面/Template:Differential transforms of plane curves"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="平面曲線的微分變換" style="font-size:110%;margin:0 5em"><a href="/wiki/%E6%9B%B2%E7%BA%BF%E7%9A%84%E5%BE%AE%E5%88%86%E5%87%A0%E4%BD%95" title="曲线的微分几何">平面曲線</a>的微分變換</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E4%B8%80%E5%85%83%E9%81%8B%E7%AE%97" title="一元運算">一元運算</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%B8%90%E5%B1%88%E7%BA%BF" title="渐屈线">渐屈线</a></li> <li><a href="/wiki/%E6%BC%B8%E4%BC%B8%E7%B7%9A" title="漸伸線">漸伸線</a></li> <li><span class="ilh-all" data-orig-title="對偶曲線" data-lang-code="en" data-lang-name="英语" data-foreign-title="Dual curve"><span class="ilh-page"><a href="/w/index.php?title=%E5%B0%8D%E5%81%B6%E6%9B%B2%E7%B7%9A&action=edit&redlink=1" class="new" title="對偶曲線（页面不存在）">對偶曲線</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Dual_curve" class="extiw" title="en:Dual curve"><span lang="en" dir="auto">Dual curve</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="反曲線" data-lang-code="en" data-lang-name="英语" data-foreign-title="Inverse curve"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%8D%E6%9B%B2%E7%B7%9A&action=edit&redlink=1" class="new" title="反曲線（页面不存在）">反曲線</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Inverse_curve" class="extiw" title="en:Inverse curve"><span lang="en" dir="auto">Inverse curve</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="平行曲線" data-lang-code="en" data-lang-name="英语" data-foreign-title="Parallel curve"><span class="ilh-page"><a href="/w/index.php?title=%E5%B9%B3%E8%A1%8C%E6%9B%B2%E7%B7%9A&action=edit&redlink=1" class="new" title="平行曲線（页面不存在）">平行曲線</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Parallel_curve" class="extiw" title="en:Parallel curve"><span lang="en" dir="auto">Parallel curve</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="isoptic" data-lang-code="en" data-lang-name="英语" data-foreign-title="Isoptic"><span class="ilh-page"><a href="/w/index.php?title=Isoptic&action=edit&redlink=1" class="new" title="Isoptic（页面不存在）">isoptic</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Isoptic" class="extiw" title="en:Isoptic"><span lang="en" dir="auto">Isoptic</span></a></span>）</span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">由一個點定義的一元運算</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%9E%82%E8%B6%B3%E6%9B%B2%E7%BA%BF" title="垂足曲线">垂足曲線</a></li> <li><span class="ilh-all" data-orig-title="負垂足曲線" data-lang-code="en" data-lang-name="英语" data-foreign-title="Negative pedal curve"><span class="ilh-page"><a href="/w/index.php?title=%E8%B2%A0%E5%9E%82%E8%B6%B3%E6%9B%B2%E7%B7%9A&action=edit&redlink=1" class="new" title="負垂足曲線（页面不存在）">負垂足曲線</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Negative_pedal_curve" class="extiw" title="en:Negative pedal curve"><span lang="en" dir="auto">Negative pedal curve</span></a></span>）</span></span></li> <li><a href="/wiki/%E8%BF%BD%E8%B8%AA%E6%9B%B2%E7%BA%BF" title="追踪曲线">追踪曲线</a></li> <li><a href="/wiki/%E7%84%A6%E6%95%A3%E7%BA%BF" title="焦散线">焦散曲線</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">由二個點定義的一元運算</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%92%B0%E7%B4%A2%E7%B7%9A" title="環索線">環索線</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">由一個點定義的<a href="/wiki/%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97" title="二元运算">二元运算</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a class="mw-selflink selflink">一般旋轮线</a></li> <li><a href="/wiki/%E8%94%93%E5%8F%B6%E7%BA%BF" title="蔓叶线">蔓叶线</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">曲線族的<a href="/wiki/%E8%BF%90%E7%AE%97" title="运算">运算</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%8C%85%E7%B5%A1%E7%B7%9A" title="包絡線">包絡線</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: 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