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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-參見" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參見"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>參見</span> </div> </a> <ul id="toc-參見-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部連結" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部連結"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>外部連結</span> </div> </a> <ul id="toc-外部連結-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">球面幾何學</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。37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-37" 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">37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/%D9%87%D9%86%D8%AF%D8%B3%D8%A9_%D9%83%D8%B1%D9%88%D9%8A%D8%A9" title="هندسة كروية – 阿拉伯语" lang="ar" hreflang="ar" data-title="هندسة كروية" 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-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Сферычная геаметрыя – 白俄罗斯语" lang="be" hreflang="be" data-title="Сферычная геаметрыя" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Geometria_esf%C3%A8rica" title="Geometria esfèrica – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Geometria esfèrica" 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-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Sf%C3%A9rick%C3%A1_geometrie" title="Sférická geometrie – 捷克语" lang="cs" hreflang="cs" data-title="Sférická geometrie" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%C4%83%D0%BB%D0%BB%D0%B0_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8" title="Сферăлла геометри – 楚瓦什语" lang="cv" hreflang="cv" data-title="Сферăлла геометри" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什语" 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/Sph%C3%A4rische_Geometrie" title="Sphärische Geometrie – 德语" lang="de" hreflang="de" data-title="Sphärische Geometrie" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A3%CF%86%CE%B1%CE%B9%CF%81%CE%B9%CE%BA%CE%AE_%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1" title="Σφαιρική γεωμετρία – 希腊语" lang="el" hreflang="el" data-title="Σφαιρική γεωμετρία" data-language-autonym="Ελληνικά" data-language-local-name="希腊语" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Spherical_geometry" title="Spherical geometry – 英语" lang="en" hreflang="en" data-title="Spherical geometry" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Sfera_geometrio" title="Sfera geometrio – 世界语" lang="eo" hreflang="eo" data-title="Sfera geometrio" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Geometr%C3%ADa_esf%C3%A9rica" title="Geometría esférica – 西班牙语" lang="es" hreflang="es" data-title="Geometría esférica" 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-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D9%86%D8%AF%D8%B3%D9%87_%DA%A9%D8%B1%D9%88%DB%8C" title="هندسه کروی – 波斯语" lang="fa" hreflang="fa" data-title="هندسه کروی" 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/Pallogeometria" title="Pallogeometria – 芬兰语" lang="fi" hreflang="fi" data-title="Pallogeometria" 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/G%C3%A9om%C3%A9trie_sph%C3%A9rique" title="Géométrie sphérique – 法语" lang="fr" hreflang="fr" data-title="Géométrie sphérique" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Cruinneadaireachd" title="Cruinneadaireachd – 苏格兰盖尔语" lang="gd" hreflang="gd" data-title="Cruinneadaireachd" data-language-autonym="Gàidhlig" data-language-local-name="苏格兰盖尔语" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94_%D7%A1%D7%A4%D7%99%D7%A8%D7%99%D7%AA" title="גאומטריה ספירית – 希伯来语" lang="he" hreflang="he" data-title="גאומטריה ספירית" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A5%8B%E0%A4%B2%E0%A5%80%E0%A4%AF_%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A4%BF" title="गोलीय ज्यामिति – 印地语" lang="hi" hreflang="hi" data-title="गोलीय ज्यामिति" data-language-autonym="हिन्दी" data-language-local-name="印地语" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/G%C3%B6mbi_geometria" title="Gömbi geometria – 匈牙利语" lang="hu" hreflang="hu" data-title="Gömbi geometria" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%88%D5%AC%D5%B8%D6%80%D5%BF%D5%A1%D5%B5%D5%AB%D5%B6_%D5%A5%D6%80%D5%AF%D6%80%D5%A1%D5%B9%D5%A1%D6%83%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Ոլորտային երկրաչափություն – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Ոլորտային երկրաչափություն" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Geometri_bola" title="Geometri bola – 印度尼西亚语" lang="id" hreflang="id" data-title="Geometri bola" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" 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/Geometria_sferica" title="Geometria sferica – 意大利语" lang="it" hreflang="it" data-title="Geometria sferica" 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-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%90%83%E9%9D%A2%E5%B9%BE%E4%BD%95%E5%AD%A6" title="球面幾何学 – 日语" lang="ja" hreflang="ja" data-title="球面幾何学" data-language-autonym="日本語" data-language-local-name="日语" 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/%EA%B5%AC%EB%A9%B4%EA%B8%B0%ED%95%98%ED%95%99" title="구면기하학 – 韩语" lang="ko" hreflang="ko" data-title="구면기하학" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Sf%C4%93risk%C4%81_%C4%A3eometrija" title="Sfēriskā ģeometrija – 拉脱维亚语" lang="lv" hreflang="lv" data-title="Sfēriskā ģeometrija" data-language-autonym="Latviešu" data-language-local-name="拉脱维亚语" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Bolmeetkunde" title="Bolmeetkunde – 荷兰语" lang="nl" hreflang="nl" data-title="Bolmeetkunde" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Sf%C3%A6risk_geometri" title="Sfærisk geometri – 书面挪威语" lang="nb" hreflang="nb" data-title="Sfærisk geometri" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Geometria_sferyczna" title="Geometria sferyczna – 波兰语" lang="pl" hreflang="pl" data-title="Geometria sferyczna" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Geometria_esf%C3%A9rica" title="Geometria esférica – 葡萄牙语" lang="pt" hreflang="pt" data-title="Geometria esférica" 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/Geometrie_sferic%C4%83" title="Geometrie sferică – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Geometrie sferică" 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-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Сферическая геометрия – 俄语" lang="ru" hreflang="ru" data-title="Сферическая геометрия" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Spherical_geometry" title="Spherical geometry – Simple English" lang="en-simple" hreflang="en-simple" data-title="Spherical geometry" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Sferna_geometrija" title="Sferna geometrija – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Sferna 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</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 typeof="mw:File/Thumb"><a href="/wiki/File:Triangles_(spherical_geometry).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Triangles_%28spherical_geometry%29.jpg/280px-Triangles_%28spherical_geometry%29.jpg" decoding="async" width="280" height="230" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Triangles_%28spherical_geometry%29.jpg/420px-Triangles_%28spherical_geometry%29.jpg 1.5x, 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84913072"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84913072"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84913072"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84913072"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist" style="background:white;"><tbody><tr><th class="sidebar-title"><a href="/wiki/%E5%87%A0%E4%BD%95%E5%AD%A6" title="几何学">几何学</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Stereographic_projection_in_3D.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Stereographic_projection_in_3D.png/220px-Stereographic_projection_in_3D.png" decoding="async" width="220" height="163" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Stereographic_projection_in_3D.png/330px-Stereographic_projection_in_3D.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Stereographic_projection_in_3D.png/440px-Stereographic_projection_in_3D.png 2x" data-file-width="640" data-file-height="473" /></a></span><div class="sidebar-caption">一个<a href="/wiki/%E7%90%83%E9%9D%A2" title="球面">球面</a>投射到一个<a href="/wiki/%E5%B9%B3%E9%9D%A2_(%E6%95%B0%E5%AD%A6)" title="平面 (数学)">平面</a>。</div></td></tr><tr><td class="sidebar-above" style="border:none; background:#ddf;padding:0.4em 0 0.15em;text-align:center; display:block;margin:0 1px 0.4em;"> <div class="hlist"><ul><li><span class="ilh-all" data-orig-title="几何学纲要" data-lang-code="en" data-lang-name="英语" data-foreign-title="Outline of geometry"><span class="ilh-page"><a href="/w/index.php?title=%E5%87%A0%E4%BD%95%E5%AD%A6%E7%BA%B2%E8%A6%81&action=edit&redlink=1" class="new" title="几何学纲要（页面不存在）">纲要</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/Outline_of_geometry" class="extiw" title="en:Outline of geometry"><span lang="en" dir="auto">Outline of geometry</span></a></span>）</span></span></li><li><span class="ilh-all" data-orig-title="几何学历史" data-lang-code="en" data-lang-name="英语" data-foreign-title="History of geometry"><span class="ilh-page"><a href="/w/index.php?title=%E5%87%A0%E4%BD%95%E5%AD%A6%E5%8E%86%E5%8F%B2&action=edit&redlink=1" class="new" title="几何学历史（页面不存在）">历史</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/History_of_geometry" class="extiw" title="en:History of geometry"><span lang="en" dir="auto">History of geometry</span></a></span>）</span></span></li></ul></div></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;"><span class="ilh-all" data-orig-title="几何学议题列表" data-lang-code="en" data-lang-name="英语" data-foreign-title="List of geometry topics"><span class="ilh-page"><a href="/w/index.php?title=%E5%87%A0%E4%BD%95%E5%AD%A6%E8%AE%AE%E9%A2%98%E5%88%97%E8%A1%A8&action=edit&redlink=1" class="new" title="几何学议题列表（页面不存在）">分支</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/List_of_geometry_topics" class="extiw" title="en:List of geometry topics"><span lang="en" dir="auto">List of geometry topics</span></a></span>）</span></span></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="欧几里得几何">欧几里得</a></li> <li><a href="/wiki/%E9%9D%9E%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="非欧几里得几何">非欧几里得</a> <ul><li><a href="/wiki/%E9%BB%8E%E6%9B%BC%E5%87%A0%E4%BD%95" title="黎曼几何">椭圆</a> <ul><li><a class="mw-selflink selflink">球面</a></li></ul></li> <li><a href="/wiki/%E5%8F%8C%E6%9B%B2%E5%87%A0%E4%BD%95" title="双曲几何">双曲</a></li></ul></li> <li><a href="/wiki/%E5%B0%84%E5%BD%B1%E5%87%A0%E4%BD%95" title="射影几何">射影</a></li> <li><a href="/wiki/%E4%BB%BF%E5%B0%84%E5%87%A0%E4%BD%95%E5%AD%A6" title="仿射几何学">仿射</a></li> <li><span class="ilh-all" data-orig-title="合成几何学" data-lang-code="en" data-lang-name="英语" data-foreign-title="Synthetic geometry"><span class="ilh-page"><a href="/w/index.php?title=%E5%90%88%E6%88%90%E5%87%A0%E4%BD%95%E5%AD%A6&action=edit&redlink=1" class="new" title="合成几何学（页面不存在）">合成</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/Synthetic_geometry" class="extiw" title="en:Synthetic geometry"><span lang="en" dir="auto">Synthetic geometry</span></a></span>）</span></span></li> <li><a href="/wiki/%E8%A7%A3%E6%9E%90%E5%87%A0%E4%BD%95" title="解析几何">解析</a></li> <li><a href="/wiki/%E4%BB%A3%E6%95%B0%E5%87%A0%E4%BD%95" title="代数几何">代数</a> <ul><li><a href="/wiki/%E7%AE%97%E6%9C%AF%E5%87%A0%E4%BD%95" title="算术几何">算术几何</a></li></ul></li> <li><a href="/wiki/%E5%BE%AE%E5%88%86%E5%87%A0%E4%BD%95" title="微分几何">微分</a> <ul><li><a href="/wiki/%E9%BB%8E%E6%9B%BC%E5%87%A0%E4%BD%95" title="黎曼几何">黎曼</a></li> <li><a href="/wiki/%E8%BE%9B%E5%87%A0%E4%BD%95" title="辛几何">辛几何</a></li> <li><span class="ilh-all" data-orig-title="离散微分几何" data-lang-code="en" data-lang-name="英语" data-foreign-title="Discrete differential geometry"><span class="ilh-page"><a href="/w/index.php?title=%E7%A6%BB%E6%95%A3%E5%BE%AE%E5%88%86%E5%87%A0%E4%BD%95&action=edit&redlink=1" class="new" title="离散微分几何（页面不存在）">离散微分</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/Discrete_differential_geometry" class="extiw" title="en:Discrete differential geometry"><span lang="en" dir="auto">Discrete differential geometry</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E6%9C%89%E9%99%90%E5%B9%BE%E4%BD%95%E5%AD%B8" title="有限幾何學">有限</a></li> <li><a href="/wiki/%E9%87%8D%E5%90%88%E5%B9%BE%E4%BD%95" title="重合幾何">重合</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;"><div class="hlist"><ul><li>概念</li><li>特性</li></ul></div></div><div class="sidebar-list-content mw-collapsible-content hlist"><a href="/wiki/%E7%B6%AD%E5%BA%A6" title="維度">維度</a> <ul><li><a href="/wiki/%E5%B0%BA%E8%A7%84%E4%BD%9C%E5%9B%BE" title="尺规作图">尺规作图</a></li></ul> <ul><li><a href="/wiki/%E8%A7%92%E5%BA%A6" class="mw-redirect" title="角度">角度</a></li> <li><a href="/wiki/%E6%9B%B2%E7%BA%BF" title="曲线">曲线</a></li> <li><a href="/wiki/%E5%B0%8D%E8%A7%92%E7%B7%9A" title="對角線">对角线</a></li> <li><a href="/wiki/%E5%B9%B3%E8%A1%8C" title="平行">平行</a></li> <li><a href="/wiki/%E5%9E%82%E7%9B%B4" title="垂直">垂直</a></li> <li><a href="/wiki/%E9%A0%82%E9%BB%9E_(%E5%B9%BE%E4%BD%95)" title="頂點 (幾何)">顶点</a></li></ul> <ul><li><a href="/wiki/%E5%85%A8%E7%AD%89_(%E5%B9%BE%E4%BD%95)" class="mw-redirect" title="全等 (幾何)">全等</a></li> <li><a href="/wiki/%E7%9B%B8%E4%BC%BC_(%E5%B9%BE%E4%BD%95)" title="相似 (幾何)">相似</a></li> <li><a href="/wiki/%E5%AF%B9%E7%A7%B0" class="mw-redirect" title="对称">对称</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;">零 / <a href="/wiki/%E4%B8%80%E7%BB%B4%E7%A9%BA%E9%97%B4" title="一维空间">一维</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E7%82%B9" title="点">点</a></li> <li><a href="/wiki/%E7%9B%B4%E7%BA%BF" title="直线">直线</a> <ul><li><a href="/wiki/%E7%BA%BF%E6%AE%B5" title="线段">线段</a></li> <li><a href="/wiki/%E5%B0%84%E7%BA%BF" title="射线">射线</a></li></ul></li> <li><a href="/wiki/%E9%95%BF%E5%BA%A6" title="长度">长度</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;"><a href="/wiki/%E4%BA%8C%E7%BB%B4%E7%A9%BA%E9%97%B4" title="二维空间">二维</a></div><div class="sidebar-list-content mw-collapsible-content hlist" style="padding-bottom:0;"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E5%B9%B3%E9%9D%A2_(%E6%95%B0%E5%AD%A6)" title="平面 (数学)">平面</a></li> <li><a href="/wiki/%E9%9D%A2%E7%A7%AF" title="面积">面积</a></li> <li><a href="/wiki/%E5%A4%9A%E8%BE%B9%E5%BD%A2" title="多边形">多边形</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> <a href="/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形">三角形</a></th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Altitude_(triangle)&action=edit&redlink=1" class="new" title="Altitude (triangle)（页面不存在）">Altitude</a></li> <li><a href="/wiki/%E6%96%9C%E9%82%8A" title="斜邊">斜边</a></li> <li><a href="/wiki/%E8%BE%B9%E9%95%BF" class="mw-redirect" title="边长">邊長</a></li> <li><a href="/wiki/%E5%8B%BE%E8%82%A1%E5%AE%9A%E7%90%86" title="勾股定理">勾股定理</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> <a href="/wiki/%E5%B9%B3%E8%A1%8C%E5%9B%9B%E8%BE%B9%E5%BD%A2" title="平行四边形">平行四边形</a></th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E6%AD%A3%E6%96%B9%E5%BD%A2" title="正方形">正方形</a></li> <li><a href="/wiki/%E4%B8%89%E8%A7%92%E5%BD%A2" title="三角形">三角形</a></li> <li><a href="/wiki/%E8%8F%B1%E5%BD%A2" title="菱形">菱形</a></li> <li><a href="/wiki/%E5%B9%B3%E8%A1%8C%E5%9B%9B%E8%BE%B9%E5%BD%A2" title="平行四边形">平行四边形</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> <a href="/wiki/%E5%9B%9B%E8%BE%B9%E5%BD%A2" class="mw-redirect" title="四边形">四边形</a></th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E6%A2%AF%E5%BD%A2" title="梯形">梯形</a> <ul><li><a href="/wiki/%E7%AD%89%E8%85%B0%E6%A2%AF%E5%BD%A2" title="等腰梯形">等腰梯形</a></li></ul></li> <li><a href="/wiki/%E9%B7%82%E5%BD%A2" title="鷂形">筝形</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> <a href="/wiki/%E5%9C%86%E5%BD%A2" class="mw-redirect" title="圆形">圆形</a></th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E7%9B%B4%E5%BE%84" title="直径">直径</a></li> <li><a href="/wiki/%E5%91%A8%E9%95%BF" title="周长">周长</a></li> <li><a href="/wiki/%E5%9C%86%E7%9A%84%E9%9D%A2%E7%A7%AF" title="圆的面积">面积</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;"><a href="/wiki/%E4%B8%89%E7%BB%B4%E7%A9%BA%E9%97%B4" class="mw-redirect" title="三维空间">三维</a></div><div class="sidebar-list-content mw-collapsible-content hlist"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E7%A9%BA%E9%96%93" title="空間">空間</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> <a href="/wiki/%E5%A4%9A%E9%9D%A2%E9%AB%94" class="mw-redirect" title="多面體">多面體</a></th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E4%BD%93%E7%A7%AF" title="体积">体积</a></li> <li><a href="/wiki/%E8%A1%A8%E9%9D%A2%E7%A9%8D" title="表面積">表面積</a></li> <li><a href="/wiki/%E6%AD%A3%E5%A4%9A%E9%9D%A2%E9%AB%94" title="正多面體">正多面體</a> <ul><li><a href="/wiki/%E5%87%B8%E6%AD%A3%E5%A4%9A%E9%9D%A2%E9%AB%94" class="mw-redirect" title="凸正多面體">凸正多面體</a></li></ul></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> <a href="/wiki/%E5%85%AD%E9%9D%A2%E9%AB%94" title="六面體">六面體</a></th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E7%AB%8B%E6%96%B9%E9%AB%94" title="立方體">立方體</a> <ul><li><a href="/wiki/%E9%95%B7%E6%96%B9%E9%AB%94" title="長方體">長方體</a></li></ul></li> <li><a href="/wiki/%E5%9B%9B%E8%A7%92%E6%9F%B1" title="四角柱">四角柱</a></li> <li><a href="/wiki/%E5%B9%B3%E8%A1%8C%E5%85%AD%E9%9D%A2%E4%BD%93" title="平行六面体">平行六面體</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> <a href="/wiki/%E5%B9%BE%E4%BD%95%E9%AB%94" class="mw-redirect" title="幾何體">幾何體</a></th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E6%A3%B1%E9%94%A5" title="棱锥">棱锥</a> <ul><li><a href="/wiki/%E5%9C%86%E9%94%A5" title="圆锥">圆锥体</a></li></ul></li> <li><a href="/wiki/%E6%A3%B1%E6%9F%B1" title="棱柱">棱柱</a> <ul><li><a href="/wiki/%E5%9C%86%E6%9F%B1%E4%BD%93" title="圆柱体">圆柱体</a></li></ul></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> <a href="/wiki/%E7%90%83_(%E6%95%B0%E5%AD%A6)" title="球 (数学)">球體</a></th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E7%9B%B4%E5%BE%84" title="直径">直径</a></li> <li><a href="/wiki/%E7%90%83%E9%9D%A2" title="球面">體積與表面積</a></li> <li><a href="/wiki/%E7%90%83%E7%BC%BA" title="球缺">球缺</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;"><a href="/wiki/%E5%9B%9B%E7%BB%B4%E7%A9%BA%E9%97%B4" title="四维空间">四维</a>- / 其他维度</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E5%A4%9A%E8%83%9E%E5%BD%A2" title="多胞形">多胞形</a></li> <li><a href="/wiki/%E5%9B%9B%E7%BB%B4%E5%87%B8%E6%AD%A3%E5%A4%9A%E8%83%9E%E4%BD%93" title="四维凸正多胞体">四维凸正多胞体</a> <ul><li><a href="/wiki/%E5%9B%9B%E7%B6%AD%E8%B6%85%E6%AD%A3%E6%96%B9%E9%AB%94" title="四維超正方體">四維超正方體</a></li></ul></li> <li><a href="/wiki/%E8%B6%85%E7%90%83%E4%BD%93" class="mw-redirect" title="超球体">超球體</a></li></ul></div></div></td> </tr><tr><th class="sidebar-heading" style="padding-bottom:0.2em;"> <a href="/wiki/%E5%87%A0%E4%BD%95%E5%AD%A6%E5%AE%B6%E5%88%97%E8%A1%A8" title="几何学家列表">几何学家</a></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;">按照姓名</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E4%BC%9A%E7%94%B0%E5%AE%89%E6%98%8E" title="会田安明">会田安明</a></li> <li><a href="/wiki/%E9%98%BF%E8%80%B6%E6%B3%A2%E5%A4%9A" title="阿耶波多">阿耶波多</a></li> <li><a href="/w/index.php?title=Ahmes&action=edit&redlink=1" class="new" title="Ahmes（页面不存在）">Ahmes</a></li> <li><a href="/wiki/%E6%B5%B7%E4%BB%80%E6%9C%A8" class="mw-redirect" title="海什木">海什木</a></li> <li><a href="/wiki/%E9%98%BF%E6%B3%A2%E7%BD%97%E5%B0%BC%E5%A5%A5%E6%96%AF" title="阿波罗尼奥斯">阿波罗尼奥斯</a></li> <li><a href="/wiki/%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7" title="阿基米德">阿基米德</a></li> <li><a href="/wiki/%E8%BF%88%E5%85%8B%E5%B0%94%C2%B7%E9%98%BF%E8%92%82%E4%BA%9A" title="迈克尔·阿蒂亚">阿蒂亚</a></li> <li><a href="/w/index.php?title=Baudhayana&action=edit&redlink=1" class="new" title="Baudhayana（页面不存在）">Baudhayana</a></li> <li><a href="/wiki/%E9%B2%8D%E8%80%B6%C2%B7%E4%BA%9A%E8%AF%BA%E4%BB%80" title="鲍耶·亚诺什">鲍耶</a></li> <li><a href="/w/index.php?title=Brahmagupta&action=edit&redlink=1" class="new" title="Brahmagupta（页面不存在）">Brahmagupta</a></li> <li><a href="/wiki/%C3%89lie_Cartan" class="mw-redirect" title="Élie Cartan">Cartan</a></li> <li><a href="/w/index.php?title=Ren%C3%A9_Descartes&action=edit&redlink=1" class="new" title="René Descartes（页面不存在）">Descartes</a></li> <li><a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97" title="欧几里得">欧几里得</a></li> <li><a href="/wiki/%E8%90%8A%E6%98%82%E5%93%88%E5%BE%B7%C2%B7%E6%AD%90%E6%8B%89" title="萊昂哈德·歐拉">欧拉</a></li> <li><a href="/wiki/%E5%8D%A1%E7%88%BE%C2%B7%E5%BC%97%E9%87%8C%E5%BE%B7%E9%87%8C%E5%B8%8C%C2%B7%E9%AB%98%E6%96%AF" title="卡爾·弗里德里希·高斯">高斯</a></li> <li><a href="/wiki/%E7%B1%B3%E5%93%88%E4%BC%8A%E5%B0%94%C2%B7%E6%A0%BC%E7%BD%97%E8%8E%AB%E5%A4%AB" title="米哈伊尔·格罗莫夫">格罗莫夫</a></li> <li><a href="/wiki/%E5%A4%A7%E5%8D%AB%C2%B7%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9" title="大卫·希尔伯特">希尔伯特</a></li> <li><a href="/w/index.php?title=Jye%E1%B9%A3%E1%B9%ADhadeva&action=edit&redlink=1" class="new" title="Jyeṣṭhadeva（页面不存在）">Jyeṣṭhadeva</a></li> <li><a href="/w/index.php?title=K%C4%81ty%C4%81yana&action=edit&redlink=1" class="new" title="Kātyāyana（页面不存在）">Kātyāyana</a></li> <li><a href="/w/index.php?title=Omar_Khayy%C3%A1m&action=edit&redlink=1" class="new" title="Omar Khayyám（页面不存在）">Khayyám</a></li> <li><a href="/wiki/%E8%8F%B2%E5%88%A9%E5%85%8B%E6%96%AF%C2%B7%E5%85%8B%E8%8E%B1%E5%9B%A0" class="mw-redirect" title="菲利克斯·克莱因">克莱因</a></li> <li><a href="/wiki/%E5%B0%BC%E5%8F%A4%E6%8B%89%C2%B7%E7%BD%97%E5%B7%B4%E5%88%87%E5%A4%AB%E6%96%AF%E5%9F%BA" title="尼古拉·罗巴切夫斯基">罗巴切夫斯基</a></li> <li><a href="/w/index.php?title=Manava&action=edit&redlink=1" class="new" title="Manava（页面不存在）">Manava</a></li> <li><a href="/wiki/%E8%B5%AB%E5%B0%94%E6%9B%BC%C2%B7%E9%97%B5%E5%8F%AF%E5%A4%AB%E6%96%AF%E5%9F%BA" title="赫尔曼·闵可夫斯基">闵可夫斯基</a></li> <li><a href="/wiki/%E6%98%8E%E5%AE%89%E5%9C%96" title="明安圖">明安图</a></li> <li><a href="/wiki/%E5%B8%83%E8%8E%B1%E5%85%B9%C2%B7%E5%B8%95%E6%96%AF%E5%8D%A1" class="mw-redirect" title="布莱兹·帕斯卡">帕斯卡</a></li> <li><a href="/wiki/%E6%AF%95%E8%BE%BE%E5%93%A5%E6%8B%89%E6%96%AF" title="毕达哥拉斯">毕达哥拉斯</a></li> <li><a href="/w/index.php?title=Parameshvara&action=edit&redlink=1" class="new" title="Parameshvara（页面不存在）">Parameshvara</a></li> <li><a href="/wiki/%E5%84%92%E5%8B%92%C2%B7%E6%98%82%E5%88%A9%C2%B7%E5%BA%9E%E5%8A%A0%E8%8E%B1" class="mw-redirect" title="儒勒·昂利·庞加莱">庞加莱</a></li> <li><a href="/wiki/%E6%B3%A2%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC" class="mw-redirect" title="波恩哈德·黎曼">黎曼</a></li> <li><a href="/w/index.php?title=Sakabe_K%C5%8Dhan&action=edit&redlink=1" class="new" title="Sakabe Kōhan（页面不存在）">Sakabe</a></li> <li><a href="/w/index.php?title=Sijzi&action=edit&redlink=1" class="new" title="Sijzi（页面不存在）">Sijzi</a></li> <li><a href="/wiki/%E7%BA%B3%E8%A5%BF%E5%B0%94%E4%B8%81%C2%B7%E5%9B%BE%E8%A5%BF" class="mw-redirect" title="纳西尔丁·图西">图西</a></li> <li><a href="/wiki/%E5%A5%A7%E6%96%AF%E7%93%A6%E7%88%BE%E5%BE%B7%C2%B7%E7%B6%AD%E5%B8%83%E5%80%AB" title="奧斯瓦爾德·維布倫">維布倫</a></li> <li><a href="/w/index.php?title=Virasena&action=edit&redlink=1" class="new" title="Virasena（页面不存在）">Virasena</a></li> <li><a href="/wiki/%E6%9D%A8%E8%BE%89" title="杨辉">杨辉</a></li> <li><a href="/w/index.php?title=Ibn_al-Yasamin&action=edit&redlink=1" class="new" title="Ibn al-Yasamin（页面不存在）">al-Yasamin</a></li> <li><a href="/wiki/%E5%BC%A0%E8%A1%A1" title="张衡">张衡</a></li> <li><a href="/wiki/%E5%87%A0%E4%BD%95%E5%AD%A6%E5%AE%B6%E5%88%97%E8%A1%A8" title="几何学家列表">几何学家列表</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddf; text-align:center;">按照时期</div><div class="sidebar-list-content mw-collapsible-content hlist" style="padding-bottom:0;"><table class="sidebar nomobile nowraplinks" style="background-color: transparent; color: var( --color-base ); border-collapse:collapse; border-spacing:0px; border:none; width:100%; margin:0px; font-size:100%; clear:none; float:none"><tbody><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> <a href="/wiki/%E5%85%AC%E5%85%83" title="公元">公元前</a></th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Ahmes&action=edit&redlink=1" class="new" title="Ahmes（页面不存在）">Ahmes</a></li> <li><a href="/w/index.php?title=Baudhayana&action=edit&redlink=1" class="new" title="Baudhayana（页面不存在）">Baudhayana</a></li> <li><a href="/w/index.php?title=Manava&action=edit&redlink=1" class="new" title="Manava（页面不存在）">Manava</a></li> <li><a href="/wiki/%E6%AF%95%E8%BE%BE%E5%93%A5%E6%8B%89%E6%96%AF" title="毕达哥拉斯">毕达哥拉斯</a></li> <li><a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97" title="欧几里得">欧几里得</a></li> <li><a href="/wiki/%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7" title="阿基米德">阿基米德</a></li> <li><a href="/wiki/%E9%98%BF%E6%B3%A2%E7%BD%97%E5%B0%BC%E5%A5%A5%E6%96%AF" title="阿波罗尼奥斯">阿波罗尼奥斯</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> 1–1400年代</th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E5%BC%A0%E8%A1%A1" title="张衡">张衡</a></li> <li><a href="/w/index.php?title=K%C4%81ty%C4%81yana&action=edit&redlink=1" class="new" title="Kātyāyana（页面不存在）">Kātyāyana</a></li> <li><a href="/wiki/%E9%98%BF%E8%80%B6%E6%B3%A2%E5%A4%9A" title="阿耶波多">阿耶波多</a></li> <li><a href="/w/index.php?title=Brahmagupta&action=edit&redlink=1" class="new" title="Brahmagupta（页面不存在）">Brahmagupta</a></li> <li><a href="/w/index.php?title=Virasena&action=edit&redlink=1" class="new" title="Virasena（页面不存在）">Virasena</a></li> <li><a href="/wiki/%E6%B5%B7%E4%BB%80%E6%9C%A8" class="mw-redirect" title="海什木">海什木</a></li> <li><a href="/w/index.php?title=Sijzi&action=edit&redlink=1" class="new" title="Sijzi（页面不存在）">Sijzi</a></li> <li><a href="/w/index.php?title=Omar_Khayy%C3%A1m&action=edit&redlink=1" class="new" title="Omar Khayyám（页面不存在）">Khayyám</a></li> <li><a href="/w/index.php?title=Ibn_al-Yasamin&action=edit&redlink=1" class="new" title="Ibn al-Yasamin（页面不存在）">al-Yasamin</a></li> <li><a href="/w/index.php?title=Nasir_al-Din_al-Tusi&action=edit&redlink=1" class="new" title="Nasir al-Din al-Tusi（页面不存在）">al-Tusi</a></li> <li><a href="/wiki/%E6%9D%A8%E8%BE%89" title="杨辉">杨辉</a></li> <li><a href="/w/index.php?title=Parameshvara&action=edit&redlink=1" class="new" title="Parameshvara（页面不存在）">Parameshvara</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> 1400–1700年代</th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/w/index.php?title=Jye%E1%B9%A3%E1%B9%ADhadeva&action=edit&redlink=1" class="new" title="Jyeṣṭhadeva（页面不存在）">Jyeṣṭhadeva</a></li> <li><a href="/w/index.php?title=Ren%C3%A9_Descartes&action=edit&redlink=1" class="new" title="René Descartes（页面不存在）">Descartes</a></li> <li><a href="/wiki/%E5%B8%83%E8%8E%B1%E5%85%B9%C2%B7%E5%B8%95%E6%96%AF%E5%8D%A1" class="mw-redirect" title="布莱兹·帕斯卡">帕斯卡</a></li> <li><a href="/wiki/%E6%98%8E%E5%AE%89%E5%9C%96" title="明安圖">明安图</a></li> <li><a href="/wiki/%E8%90%8A%E6%98%82%E5%93%88%E5%BE%B7%C2%B7%E6%AD%90%E6%8B%89" title="萊昂哈德·歐拉">欧拉</a></li> <li><a href="/w/index.php?title=Sakabe_K%C5%8Dhan&action=edit&redlink=1" class="new" title="Sakabe Kōhan（页面不存在）">Sakabe</a></li> <li><a href="/wiki/%E4%BC%9A%E7%94%B0%E5%AE%89%E6%98%8E" title="会田安明">会田安明</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> 1700–1900年代</th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E5%8D%A1%E7%88%BE%C2%B7%E5%BC%97%E9%87%8C%E5%BE%B7%E9%87%8C%E5%B8%8C%C2%B7%E9%AB%98%E6%96%AF" title="卡爾·弗里德里希·高斯">高斯</a></li> <li><a href="/wiki/%E5%B0%BC%E5%8F%A4%E6%8B%89%C2%B7%E7%BD%97%E5%B7%B4%E5%88%87%E5%A4%AB%E6%96%AF%E5%9F%BA" title="尼古拉·罗巴切夫斯基">罗巴切夫斯基</a></li> <li><a href="/wiki/%E9%B2%8D%E8%80%B6%C2%B7%E4%BA%9A%E8%AF%BA%E4%BB%80" title="鲍耶·亚诺什">鲍耶</a></li> <li><a href="/wiki/%E6%B3%A2%E6%81%A9%E5%93%88%E5%BE%B7%C2%B7%E9%BB%8E%E6%9B%BC" class="mw-redirect" title="波恩哈德·黎曼">黎曼</a></li> <li><a href="/wiki/%E8%8F%B2%E5%88%A9%E5%85%8B%E6%96%AF%C2%B7%E5%85%8B%E8%8E%B1%E5%9B%A0" class="mw-redirect" title="菲利克斯·克莱因">克莱因</a></li> <li><a href="/wiki/%E5%84%92%E5%8B%92%C2%B7%E6%98%82%E5%88%A9%C2%B7%E5%BA%9E%E5%8A%A0%E8%8E%B1" class="mw-redirect" title="儒勒·昂利·庞加莱">庞加莱</a></li> <li><a href="/wiki/%E5%A4%A7%E5%8D%AB%C2%B7%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9" title="大卫·希尔伯特">希尔伯特</a></li> <li><a href="/wiki/%E8%B5%AB%E5%B0%94%E6%9B%BC%C2%B7%E9%97%B5%E5%8F%AF%E5%A4%AB%E6%96%AF%E5%9F%BA" title="赫尔曼·闵可夫斯基">闵可夫斯基</a></li> <li><a href="/wiki/%C3%89lie_Cartan" class="mw-redirect" title="Élie Cartan">Cartan</a></li> <li><a href="/wiki/%E5%A5%A7%E6%96%AF%E7%93%A6%E7%88%BE%E5%BE%B7%C2%B7%E7%B6%AD%E5%B8%83%E5%80%AB" title="奧斯瓦爾德·維布倫">維布倫</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="background:#e6e6ff; font-weight:normal;"> 现代</th></tr><tr><td class="sidebar-content" style="padding:0.2em 0.4em 0.6em;"> <ul><li><a href="/wiki/%E8%BF%88%E5%85%8B%E5%B0%94%C2%B7%E9%98%BF%E8%92%82%E4%BA%9A" title="迈克尔·阿蒂亚">阿蒂亚</a></li> <li><a href="/wiki/%E7%B1%B3%E5%93%88%E4%BC%8A%E5%B0%94%C2%B7%E6%A0%BC%E7%BD%97%E8%8E%AB%E5%A4%AB" title="米哈伊尔·格罗莫夫">格罗莫夫</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-below"> <span class="noviewer" typeof="mw:File"><a href="/wiki/File:Crystal_Clear_app_3d.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Crystal_Clear_app_3d.png/28px-Crystal_Clear_app_3d.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Crystal_Clear_app_3d.png/42px-Crystal_Clear_app_3d.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Crystal_Clear_app_3d.png/56px-Crystal_Clear_app_3d.png 2x" data-file-width="128" data-file-height="128" /></a></span> <a href="/wiki/Portal:%E5%87%A0%E4%BD%95%E5%AD%A6" title="Portal:几何学">几何学主题</a></td></tr><tr><td class="sidebar-navbar" style="line-height:1.6"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84244141">.mw-parser-output .navbar{display:inline;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:110%;margin:0 8em}.mw-parser-output .navbar-ct-mini{font-size:110%;margin:0 5em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:General_geometry" title="Template:General geometry"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:General_geometry" title="Template talk:General geometry"><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:General_geometry" title="Special:编辑页面/Template:General geometry"><abbr title="编辑该模板">编</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>球面幾何學</b>（英語：<span lang="en">Spherical geometry</span>），简称<b>球面几何</b>，是在<a href="/wiki/%E4%BA%8C%E7%B6%AD" class="mw-redirect" title="二維">二維</a>的<a href="/wiki/%E7%90%83%E9%9D%A2" title="球面">球面</a>表面上的<a href="/wiki/%E5%B9%BE%E4%BD%95%E5%AD%B8" class="mw-redirect" title="幾何學">幾何學</a>，也是<a href="/wiki/%E9%9D%9E%E6%AC%A7%E5%87%A0%E4%BD%95" class="mw-redirect" title="非欧几何">非欧几何</a>的一個例子。 </p><p>在<a href="/wiki/%E5%B9%B3%E9%9D%A2%E5%87%A0%E4%BD%95" class="mw-redirect" title="平面几何">平面几何</a> 中，基本的觀念是<a href="/wiki/%E9%BB%9E" class="mw-redirect" title="點">點</a>和<a href="/wiki/%E7%B7%9A" class="mw-redirect mw-disambig" title="線">線</a>。在球面上，<a href="/wiki/%E9%BB%9E" class="mw-redirect" title="點">點</a>的觀念和定義依舊不變，但線不再是“<a href="/wiki/%E7%9B%B4%E7%B7%9A" class="mw-redirect" title="直線">直線</a>”，而是兩點之間最短的距離，稱為<a href="/wiki/%E6%B5%8B%E5%9C%B0%E7%BA%BF" title="测地线">測地線</a>。在球面上，最短線是<a href="/wiki/%E5%A4%A7%E5%9C%93" class="mw-redirect" title="大圓">大圓</a>的弧，所以平面幾何中的<a href="/wiki/%E7%B7%9A" class="mw-redirect mw-disambig" title="線">線</a>在球面幾何中被<a href="/wiki/%E5%A4%A7%E5%9C%93" class="mw-redirect" title="大圓">大圓</a>所取代。同樣的，在球面幾何中的<a href="/wiki/%E8%A7%92" title="角">角</a>被定義在兩個大圓之間。結果是<a href="/wiki/%E7%90%83%E9%9D%A2%E4%B8%89%E8%A7%92%E5%AD%B8" title="球面三角學">球面三角學</a>和平常的<a href="/wiki/%E4%B8%89%E8%A7%92%E5%AD%B8" class="mw-redirect" title="三角學">三角學</a>有諸多不同之處。例如：球面三角形的內角和大於180°。 </p><p>對比於通過一個點至少有兩條平行線，甚至無窮多條平行線的<a href="/wiki/%E5%8F%8C%E6%9B%B2%E5%87%A0%E4%BD%95" title="双曲几何">雙曲幾何</a>，通過特定的點沒有平行線的球面幾何學是<a href="/w/index.php?title=%E6%A9%A2%E5%9C%93%E5%B9%BE%E4%BD%95%E5%AD%B8&action=edit&redlink=1" class="new" title="橢圓幾何學（页面不存在）">橢圓幾何學</a>中最簡單的模式。 </p><p>球面幾何學在<a href="/wiki/%E8%88%AA%E6%B5%B7%E5%AD%A6" class="mw-redirect" title="航海学">航海學</a>和<a href="/wiki/%E5%A4%A9%E6%96%87%E5%AD%B8" title="天文學">天文學</a>都有實際且重要的用途。 </p><p><a href="/wiki/%E5%AE%9E%E5%B0%84%E5%BD%B1%E5%B9%B3%E9%9D%A2" title="实射影平面">实射影平面</a>是與球面密切相關的另一種幾何結構，將球面上每對正相反的<a href="/wiki/%E5%B0%8D%E8%B9%A0%E9%BB%9E" title="對蹠點">對蹠點</a>（同一直徑兩端相對的點）合二為一，視為同一個點，則得到實射影平面。<a href="/wiki/%E5%B1%80%E9%83%A8%E6%80%A7%E8%B4%A8" title="局部性质">局部地</a>，投影平面具有球面幾何所有的特性，但有不同的總體特性，特別是它<a href="/wiki/%E5%8F%AF%E5%AE%9A%E5%90%91%E6%80%A7" title="可定向性">不可定向</a>。 </p> <div class="mw-heading mw-heading2"><h2 id="參見"><span id=".E5.8F.83.E8.A6.8B"></span>參見</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%90%83%E9%9D%A2%E5%B9%BE%E4%BD%95%E5%AD%B8&action=edit&section=1" title="编辑章节：參見"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E7%90%83%E9%9D%A2%E4%B8%89%E8%A7%92%E5%AD%B8" title="球面三角學">球面三角學</a></li> <li><a href="/wiki/%E5%A4%A7%E5%9C%86%E8%B7%9D%E7%A6%BB" title="大圆距离">大圆距离</a></li> <li><a href="/wiki/%E5%8F%8C%E6%9B%B2%E5%87%A0%E4%BD%95" title="双曲几何">双曲几何</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="外部連結"><span id=".E5.A4.96.E9.83.A8.E9.80.A3.E7.B5.90"></span>外部連結</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%90%83%E9%9D%A2%E5%B9%BE%E4%BD%95%E5%AD%B8&action=edit&section=2" title="编辑章节：外部連結"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://episte.math.ntu.edu.tw/articles/ar/ar_wy_geo_07/">《基礎幾何學》：球面幾何和球面三角學</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210416153016/http://episte.math.ntu.edu.tw/articles/ar/ar_wy_geo_07/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84261037">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output 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