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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" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <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="目录" 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-簡史" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#簡史"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>簡史</span> </div> </a> <ul id="toc-簡史-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-内容" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#内容"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>内容</span> </div> </a> <button aria-controls="toc-内容-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>开关内容子章节</span> </button> <ul id="toc-内容-sublist" class="vector-toc-list"> <li id="toc-基本课题" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#基本课题"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>基本课题</span> </div> </a> <ul id="toc-基本课题-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-其它课题" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#其它课题"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>其它课题</span> </div> </a> <ul id="toc-其它课题-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-相關條目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#相關條目"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>相關條目</span> </div> </a> <ul id="toc-相關條目-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">立体几何</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。51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-51" 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">51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-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8C%A0%E1%8C%A3%E1%88%AD_%E1%8C%82%E1%8B%8E%E1%88%9C%E1%89%B5%E1%88%AA" title="ጠጣር ጂዎሜትሪ – 阿姆哈拉语" lang="am" hreflang="am" data-title="ጠጣር ጂዎሜትሪ" data-language-autonym="አማርኛ" data-language-local-name="阿姆哈拉语" class="interlanguage-link-target"><span>አማርኛ</span></a></li><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%81%D8%B1%D8%A7%D8%BA%D9%8A%D8%A9" title="هندسة فراغية – 阿拉伯语" lang="ar" hreflang="ar" data-title="هندسة فراغية" 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-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Stereometriya" title="Stereometriya – 阿塞拜疆语" lang="az" hreflang="az" data-title="Stereometriya" data-language-autonym="Azərbaycanca" data-language-local-name="阿塞拜疆语" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%82%D1%8D%D1%80%D1%8D%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Стэрэаметрыя – 白俄罗斯语" lang="be" hreflang="be" data-title="Стэрэаметрыя" 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-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Стереометрия – 保加利亚语" lang="bg" hreflang="bg" data-title="Стереометрия" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Geometrijsko_tijelo" title="Geometrijsko tijelo – 波斯尼亚语" lang="bs" hreflang="bs" data-title="Geometrijsko tijelo" data-language-autonym="Bosanski" data-language-local-name="波斯尼亚语" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%95%D9%86%DB%95_%D8%A6%DB%95%D9%86%D8%AF%D8%A7%D8%B2%DB%95" title="تەنە ئەندازە – 中库尔德语" lang="ckb" hreflang="ckb" data-title="تەنە ئەندازە" data-language-autonym="کوردی" data-language-local-name="中库尔德语" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Stereometrie" title="Stereometrie – 捷克语" lang="cs" hreflang="cs" data-title="Stereometrie" 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%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8" title="Стереометри – 楚瓦什语" lang="cv" hreflang="cv" data-title="Стереометри" 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-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Rumgeometri" title="Rumgeometri – 丹麦语" lang="da" hreflang="da" data-title="Rumgeometri" data-language-autonym="Dansk" data-language-local-name="丹麦语" 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/Stereometrie" title="Stereometrie – 德语" lang="de" hreflang="de" data-title="Stereometrie" 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%84%CE%B5%CF%81%CE%B5%CE%BF%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1" title="Στερεομετρία – 希腊语" lang="el" hreflang="el" data-title="Στερεομετρία" 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/Solid_geometry" title="Solid geometry – 英语" lang="en" hreflang="en" data-title="Solid 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-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Geometr%C3%ADa_del_espacio" title="Geometría del espacio – 西班牙语" lang="es" hreflang="es" data-title="Geometría del espacio" 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-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Stereomeetria" title="Stereomeetria – 爱沙尼亚语" lang="et" hreflang="et" data-title="Stereomeetria" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target"><span>Eesti</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_%D9%81%D8%B6%D8%A7%DB%8C%DB%8C" title="هندسه فضایی – 波斯语" lang="fa" hreflang="fa" data-title="هندسه فضایی" 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/Avaruusgeometria" title="Avaruusgeometria – 芬兰语" lang="fi" hreflang="fi" data-title="Avaruusgeometria" 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_dans_l%27espace" title="Géométrie dans l'espace – 法语" lang="fr" hreflang="fr" data-title="Géométrie dans l'espace" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Geoim%C3%A9adracht_sholadach" title="Geoiméadracht sholadach – 爱尔兰语" lang="ga" hreflang="ga" data-title="Geoiméadracht sholadach" data-language-autonym="Gaeilge" data-language-local-name="爱尔兰语" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%A0%D7%93%D7%A1%D7%AA_%D7%94%D7%9E%D7%A8%D7%97%D7%91" title="הנדסת המרחב – 希伯来语" lang="he" hreflang="he" data-title="הנדסת המרחב" 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%A0%E0%A5%8B%E0%A4%B8_%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="ठोस ज्यामिति – 印地语" lang="hi" hreflang="hi" data-title="ठोस 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-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Geometrijsko_tijelo" title="Geometrijsko tijelo – 克罗地亚语" lang="hr" hreflang="hr" data-title="Geometrijsko tijelo" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%A1%D6%80%D5%A1%D5%AE%D5%A1%D5%B9%D5%A1%D6%83%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Տարածաչափություն – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Տարածաչափություն" 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_padat" title="Geometri padat – 印度尼西亚语" lang="id" hreflang="id" data-title="Geometri padat" 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_solida" title="Geometria solida – 意大利语" lang="it" hreflang="it" data-title="Geometria solida" 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%A9%BA%E9%96%93%E5%B9%BE%E4%BD%95%E5%AD%A6" title="空間幾何学 – 日语" lang="ja" hreflang="ja" data-title="空間幾何学" 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-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A1%E1%83%A2%E1%83%94%E1%83%A0%E1%83%94%E1%83%9D%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98%E1%83%90" title="სტერეომეტრია – 格鲁吉亚语" lang="ka" hreflang="ka" data-title="სტერეომეტრია" data-language-autonym="ქართული" data-language-local-name="格鲁吉亚语" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D0%B5" title="Стереометрие – 卡巴尔德语" lang="kbd" hreflang="kbd" data-title="Стереометрие" data-language-autonym="Адыгэбзэ" data-language-local-name="卡巴尔德语" class="interlanguage-link-target"><span>Адыгэбзэ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Стереометрия – 哈萨克语" lang="kk" hreflang="kk" data-title="Стереометрия" data-language-autonym="Қазақша" data-language-local-name="哈萨克语" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Stereometrija" title="Stereometrija – 拉脱维亚语" lang="lv" hreflang="lv" data-title="Stereometrija" 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-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D1%81%D1%8C" title="Стереометриясь – 莫克沙语" lang="mdf" hreflang="mdf" data-title="Стереометриясь" data-language-autonym="Мокшень" data-language-local-name="莫克沙语" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Стереометрија – 马其顿语" lang="mk" hreflang="mk" data-title="Стереометрија" data-language-autonym="Македонски" data-language-local-name="马其顿语" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Ruimtemeetkunde" title="Ruimtemeetkunde – 荷兰语" lang="nl" hreflang="nl" data-title="Ruimtemeetkunde" 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-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Romgeometri" title="Romgeometri – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Romgeometri" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Ji%E2%80%99oomeetirii_jabaa" title="Ji’oomeetirii jabaa – 奥罗莫语" lang="om" hreflang="om" data-title="Ji’oomeetirii jabaa" data-language-autonym="Oromoo" data-language-local-name="奥罗莫语" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Stereometria" title="Stereometria – 波兰语" lang="pl" hreflang="pl" data-title="Stereometria" 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_espacial" title="Geometria espacial – 葡萄牙语" lang="pt" hreflang="pt" data-title="Geometria espacial" 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_%C3%AEn_spa%C8%9Biu" title="Geometrie în spațiu – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Geometrie în spațiu" 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%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Стереометрия – 俄语" lang="ru" hreflang="ru" data-title="Стереометрия" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/S%C3%B2lidu_(giomitr%C3%ACa)" title="Sòlidu (giomitrìa) – 西西里语" lang="scn" hreflang="scn" data-title="Sòlidu (giomitrìa)" data-language-autonym="Sicilianu" data-language-local-name="西西里语" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Stereometrija" title="Stereometrija – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Stereometrija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Solid_geometry" title="Solid geometry – Simple English" lang="en-simple" hreflang="en-simple" data-title="Solid 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Stereometria" title="Stereometria – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Stereometria" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Stereometrija" title="Stereometrija – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Stereometrija" 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-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0" title="Стереометрија – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Стереометрија" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Rymdgeometri" title="Rymdgeometri – 瑞典语" lang="sv" hreflang="sv" data-title="Rymdgeometri" data-language-autonym="Svenska" data-language-local-name="瑞典语" 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%A4%E0%AE%BF%E0%AE%A3%E0%AF%8D%E0%AE%AE%E0%AE%AE%E0%AF%8D_(%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="திண்மம் (வடிவவியல்) – 泰米尔语" lang="ta" hreflang="ta" data-title="திண்மம் (வடிவவியல்)" 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-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Heometriyang_pangsolido" title="Heometriyang pangsolido – 他加禄语" lang="tl" hreflang="tl" data-title="Heometriyang pangsolido" data-language-autonym="Tagalog" data-language-local-name="他加禄语" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F" title="Стереометрія – 乌克兰语" lang="uk" hreflang="uk" data-title="Стереометрія" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Stereometriya" title="Stereometriya – 乌兹别克语" lang="uz" hreflang="uz" data-title="Stereometriya" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="乌兹别克语" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%ACnh_h%E1%BB%8Dc_kh%C3%B4ng_gian" title="Hình học không gian – 越南语" lang="vi" hreflang="vi" data-title="Hình 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mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> 打印/导出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E7%AB%8B%E4%BD%93%E5%87%A0%E4%BD%95&action=show-download-screen"><span>下载为PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="本页面的可打印版本[p]" accesskey="p"><span>打印页面</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 在其他项目中 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Solid_geometry" hreflang="en"><span>维基共享资源</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q207648" title="链接到连接的数据仓库项目[g]" accesskey="g"><span>维基数据项目</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="外观"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">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"><p><a href="/wiki/%E6%95%B0%E5%AD%A6" title="数学">数学</a>上，<b>立体几何</b>（英語：<span lang="en">solid geometry</span>，德語：<span lang="de">Stereometrie</span>，<a href="/wiki/%E5%B8%8C%E8%87%98%E8%AA%9E" class="mw-redirect" title="希臘語">希臘語</a>：<span lang="el">Στερεομετρία</span>）是三维<a href="/wiki/%E6%AD%90%E5%B9%BE%E9%87%8C%E5%BE%97%E7%A9%BA%E9%96%93" class="mw-redirect" title="歐幾里得空間">歐幾里得空間</a>的<a href="/wiki/%E5%87%A0%E4%BD%95" class="mw-redirect" title="几何">几何</a>的传统名称。实践上这大致上就是一般生活的<a href="/wiki/%E7%A9%BA%E9%97%B4" class="mw-redirect" title="空间">空间</a>。一般作为<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>的后续课程。其研究對象是<b>立体</b>（簡稱<b>体</b>）——占据一定<a href="/wiki/%E4%B8%89%E7%BB%B4%E7%A9%BA%E9%97%B4" class="mw-redirect" title="三维空间">三维空间</a>，具有非零<a href="/wiki/%E4%BD%93%E7%A7%AF" title="体积">体积</a>的物体。 </p><p><b>立体测绘</b>（<span lang="en">stereometry</span>）处理不同<a href="/wiki/%E5%BD%A2%E4%BD%93" class="mw-redirect" title="形体">形体</a>的<a href="/wiki/%E4%BD%93%E7%A7%AF" title="体积">体积</a>的<a href="/wiki/%E6%B5%8B%E9%87%8F" class="mw-redirect mw-disambig" title="测量">测量</a>问题。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="簡史"><span id=".E7.B0.A1.E5.8F.B2"></span>簡史</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AB%8B%E4%BD%93%E5%87%A0%E4%BD%95&action=edit&section=1" title="编辑章节：簡史"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r85100532">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">主条目：<span class="ilh-all" data-orig-title="几何学史" 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%8F%B2&action=edit&redlink=1" class="new" title="几何学史（页面不存在）">几何学史</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></div> <p><a href="/wiki/%E6%AF%95%E8%BE%BE%E5%93%A5%E6%8B%89%E6%96%AF%E5%AD%A6%E6%B4%BE" class="mw-redirect" title="毕达哥拉斯学派">毕达哥拉斯学派</a>就处理过球和<a href="/wiki/%E6%9F%8F%E6%8B%89%E5%9C%96%E7%AB%8B%E9%AB%94" title="柏拉圖立體">正多面体</a>，但是<a href="/wiki/%E6%A3%B1%E9%94%A5" title="棱锥">棱锥</a>、<a href="/wiki/%E6%A3%B1%E6%9F%B1" title="棱柱">棱柱</a>、<a href="/wiki/%E5%9C%86%E9%94%A5" title="圆锥">圆锥</a>和<a href="/wiki/%E5%9C%86%E6%9F%B1" class="mw-redirect" title="圆柱">圆柱</a>在<a href="/wiki/%E6%9F%8F%E6%8B%89%E5%9B%BE%E4%B8%BB%E4%B9%89" title="柏拉图主义">柏拉图学派</a>着手处理之前人们所知甚少。<a href="/wiki/%E6%AC%A7%E5%A4%9A%E5%85%8B%E7%B4%A2%E6%96%AF" title="欧多克索斯">欧多克索斯</a>建立了它们的测量法，证明锥是等底等高的柱体积的三分之一，可能也是第一个证明球体积和其半径的立方成正比的。 </p> <div class="mw-heading mw-heading2"><h2 id="内容"><span id=".E5.86.85.E5.AE.B9"></span>内容</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AB%8B%E4%BD%93%E5%87%A0%E4%BD%95&action=edit&section=2" title="编辑章节：内容"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="基本课题"><span id=".E5.9F.BA.E6.9C.AC.E8.AF.BE.E9.A2.98"></span>基本课题</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AB%8B%E4%BD%93%E5%87%A0%E4%BD%95&action=edit&section=3" title="编辑章节：基本课题"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r79074265">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="div-col" style="column-count:2; column-width:auto;"> <ul><li><a href="/wiki/%E5%B9%B3%E9%9D%A2_(%E6%95%B0%E5%AD%A6)" title="平面 (数学)">面</a>和<a href="/wiki/%E7%9B%B4%E7%B7%9A" class="mw-redirect" title="直線">直線</a>的重合</li> <li><a href="/wiki/%E4%B8%A4%E9%9D%A2%E8%A7%92" class="mw-redirect" title="两面角">两面角</a>和<a href="/wiki/%E7%AB%8B%E4%BD%93%E8%A7%92" class="mw-redirect" title="立体角">立体角</a></li> <li><a href="/wiki/%E7%AB%8B%E6%96%B9%E9%AB%94" title="立方體">方块</a>、<a href="/wiki/%E9%95%BF%E6%96%B9%E4%BD%93" class="mw-redirect" title="长方体">长方体</a>、<a href="/wiki/%E5%B9%B3%E8%A1%8C%E5%85%AD%E9%9D%A2%E4%BD%93" title="平行六面体">平行六面体</a></li> <li><a href="/wiki/%E6%A3%B1%E9%94%A5" title="棱锥">棱锥</a></li> <li><a href="/wiki/%E6%A3%B1%E6%9F%B1" title="棱柱">棱柱</a></li> <li><a href="/wiki/%E6%A3%B1%E5%8F%B0" class="mw-redirect" title="棱台">棱台</a></li> <li><a href="/wiki/%E6%AD%A3%E5%A4%9A%E9%9D%A2%E4%BD%93" class="mw-redirect" title="正多面体">正多面体</a></li> <li><a href="/wiki/%E5%9C%86%E9%94%A5" title="圆锥">圆锥</a>、<a href="/wiki/%E5%9C%86%E6%9F%B1" class="mw-redirect" title="圆柱">圆柱</a></li> <li><a href="/wiki/%E7%90%83_(%E6%95%B0%E5%AD%A6)" title="球 (数学)">球</a></li> <li><a href="/wiki/%E4%BA%8C%E6%AC%A1%E6%9B%B2%E9%9D%A2" title="二次曲面">二次曲面</a>：<a href="/wiki/%E9%A1%9E%E7%90%83%E9%9D%A2" title="類球面">類球面</a>、<a href="/wiki/%E6%A4%AD%E7%90%83" title="椭球">椭球</a>、<a href="/wiki/%E6%8A%9B%E7%89%A9%E9%9D%A2" title="抛物面">抛物面</a>、<a href="/wiki/%E5%8F%8C%E6%9B%B2%E9%9D%A2" class="mw-redirect" title="双曲面">双曲面</a></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="其它课题"><span id=".E5.85.B6.E5.AE.83.E8.AF.BE.E9.A2.98"></span>其它课题</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AB%8B%E4%BD%93%E5%87%A0%E4%BD%95&action=edit&section=4" title="编辑章节：其它课题"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>较高级的研究有： </p> <ul><li>三维的<a href="/wiki/%E5%B0%84%E5%BD%B1%E5%87%A0%E4%BD%95" title="射影几何">射影几何</a></li> <li>用增加一个维度的方法的<a href="/wiki/%E7%AC%9B%E6%B2%99%E6%A0%BC%E5%AE%9A%E7%90%86" title="笛沙格定理">笛沙格定理</a>的证明</li> <li>更多的<a href="/wiki/%E5%A4%9A%E9%9D%A2%E4%BD%93" title="多面体">多面体</a></li> <li>描述几何</li></ul> <p><a href="/wiki/%E8%A7%A3%E6%9E%90%E5%87%A0%E4%BD%95" title="解析几何">解析几何</a>和<a href="/wiki/%E5%90%91%E9%87%8F" title="向量">向量</a>技术通过允许系统的使用<a href="/wiki/%E7%BA%BF%E6%80%A7%E6%96%B9%E7%A8%8B%E7%BB%84" title="线性方程组">线性方程组</a>和<a href="/wiki/%E7%9F%A9%E9%98%B5" title="矩阵">矩阵</a>代数带来了重大的冲击；这在高维变得更为重要。研究这个主题的一个重要应用是<a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E5%9B%BE%E5%BD%A2%E5%AD%A6" title="计算机图形学">计算机图形学</a>，这意味着<a href="/wiki/%E7%AE%97%E6%B3%95" title="算法">算法</a>变得重要起来。 </p> <div class="mw-heading mw-heading2"><h2 id="相關條目"><span id=".E7.9B.B8.E9.97.9C.E6.A2.9D.E7.9B.AE"></span>相關條目</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%AB%8B%E4%BD%93%E5%87%A0%E4%BD%95&action=edit&section=5" title="编辑章节：相關條目"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E7%90%83_(%E6%95%B0%E5%AD%A6)" title="球 (数学)">球 (数学)</a></li> <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">欧几里得几何</a></li> <li><a href="/wiki/%E7%B6%AD%E5%BA%A6" title="維度">維度</a></li> <li><a href="/wiki/%E7%82%B9" title="点">点</a></li> <li><span class="ilh-all" data-orig-title="平面測繪" data-lang-code="en" data-lang-name="英语" data-foreign-title="Planimetry"><span class="ilh-page"><a href="/w/index.php?title=%E5%B9%B3%E9%9D%A2%E6%B8%AC%E7%B9%AA&action=edit&redlink=1" class="new" title="平面測繪（页面不存在）">平面測繪</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/Planimetry" class="extiw" title="en:Planimetry"><span lang="en" dir="auto">Planimetry</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%BD%A2%E7%8B%80" title="形狀">形狀</a></li> <li><span class="ilh-all" data-orig-title="形狀列表" data-lang-code="en" data-lang-name="英语" data-foreign-title="Lists of shapes"><span class="ilh-page"><a href="/w/index.php?title=%E5%BD%A2%E7%8B%80%E5%88%97%E8%A1%A8&action=edit&redlink=1" class="new" title="形狀列表（页面不存在）">形狀列表</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/Lists_of_shapes" class="extiw" title="en:Lists of shapes"><span lang="en" dir="auto">Lists of shapes</span></a></span>）</span></span></li> <li><span class="ilh-all ilh-blue" data-orig-title="曲面" data-lang-code="en" data-lang-name="英语" data-foreign-title="Surface (mathematics)"><span class="ilh-page"><a href="/wiki/%E6%9B%B2%E9%9D%A2" title="曲面">曲面</a></span></span></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/%E9%98%BF%E5%9F%BA%E7%B1%B3%E5%BE%B7" title="阿基米德">阿基米德</a></li></ul> <table class="metadata plainlinks stub" role="presentation" style="background:transparent"><tbody><tr class="noresize"><td><span 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