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mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">外观</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=zh.wikipedia.org&uselang=zh" class=""><span>资助维基百科</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E7%A5%96%E5%86%B2%E4%B9%8B" title="我们推荐您创建账号并登录，但这不是强制性的" class=""><span>创建账号</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E7%A5%96%E5%86%B2%E4%B9%8B" title="建议你登录，尽管并非必须。[o]" accesskey="o" class=""><span>登录</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="更多选项" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="个人工具" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">个人工具</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="用户菜单" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=zh.wikipedia.org&uselang=zh"><span>资助维基百科</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E7%A5%96%E5%86%B2%E4%B9%8B" title="我们推荐您创建账号并登录，但这不是强制性的"><span 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=%E7%A5%96%E5%86%B2%E4%B9%8B" 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" 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-生平" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#生平"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>生平</span> </div> </a> <ul id="toc-生平-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-数学贡献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#数学贡献"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>数学贡献</span> </div> </a> <button aria-controls="toc-数学贡献-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>开关数学贡献子章节</span> </button> <ul id="toc-数学贡献-sublist" class="vector-toc-list"> <li id="toc-计算圆周率" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#计算圆周率"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>计算圆周率</span> </div> </a> <ul id="toc-计算圆周率-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-计算球体体积" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#计算球体体积"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>计算球体体积</span> </div> </a> <ul id="toc-计算球体体积-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-天文历法贡献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#天文历法贡献"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>天文历法贡献</span> </div> </a> <ul id="toc-天文历法贡献-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-机械制造贡献" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#机械制造贡献"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>机械制造贡献</span> </div> </a> <ul id="toc-机械制造贡献-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-家庭" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#家庭"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>家庭</span> </div> </a> <button aria-controls="toc-家庭-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>开关家庭子章节</span> </button> <ul id="toc-家庭-sublist" class="vector-toc-list"> <li id="toc-曾祖" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#曾祖"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>曾祖</span> </div> </a> <ul id="toc-曾祖-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-祖父" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#祖父"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>祖父</span> </div> </a> <ul id="toc-祖父-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-父亲" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#父亲"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>父亲</span> </div> </a> <ul id="toc-父亲-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-儿子" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#儿子"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>儿子</span> </div> </a> <ul id="toc-儿子-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-孙子" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#孙子"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>孙子</span> </div> </a> <ul id="toc-孙子-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-著作" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#著作"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>著作</span> </div> </a> <ul id="toc-著作-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-紀念" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#紀念"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>紀念</span> </div> </a> <ul id="toc-紀念-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参见" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参见"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>参见</span> </div> </a> <ul id="toc-参见-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-注脚" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#注脚"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>注脚</span> </div> </a> <ul id="toc-注脚-sublist" class="vector-toc-list"> </ul> </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">10</span> <span>参考文献</span> </div> </a> <ul id="toc-参考文献-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-延伸阅读" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#延伸阅读"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>延伸阅读</span> </div> </a> <ul id="toc-延伸阅读-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" title="目录" > <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">祖冲之</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。34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-34" 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">34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%B2%D9%88_%D8%AA%D8%B4%D9%88%D9%86%D8%BA%D8%B2%D9%8A" title="زو تشونغزي – 阿拉伯语" lang="ar" hreflang="ar" data-title="زو تشونغزي" 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-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%B2%D9%88_%D8%AA%D8%B4%D9%88%D9%86%D8%AC%D8%B2%D9%89" title="زو تشونجزى – 埃及阿拉伯文" lang="arz" hreflang="arz" data-title="زو تشونجزى" data-language-autonym="مصرى" data-language-local-name="埃及阿拉伯文" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A6%D0%B7%D1%83_%D0%A7%D1%83%D0%BD%D1%87%D0%B6%D1%8B" title="Цзу Чунчжы – 白俄罗斯语" lang="be" hreflang="be" data-title="Цзу Чунчжы" 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/Zu_Chongzhi" title="Zu Chongzhi – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Zu Chongzhi" 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/Cu_%C4%8Cchung-%C4%8D%E2%80%99" title="Cu Čchung-č’ – 捷克语" lang="cs" hreflang="cs" data-title="Cu Čchung-č’" 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-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Zu_Chongzhi" title="Zu Chongzhi – 丹麦语" lang="da" hreflang="da" data-title="Zu Chongzhi" 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/Zu_Chongzhi" title="Zu Chongzhi – 德语" lang="de" hreflang="de" data-title="Zu Chongzhi" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Zu_Chongzhi" title="Zu Chongzhi – 英语" lang="en" hreflang="en" data-title="Zu Chongzhi" 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/Zu_%C4%88ong%C4%B5i" title="Zu Ĉongĵi – 世界语" lang="eo" hreflang="eo" data-title="Zu Ĉongĵi" 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/Zu_Chongzhi" title="Zu Chongzhi – 西班牙语" lang="es" hreflang="es" data-title="Zu Chongzhi" 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/Zu_Chongzhi" title="Zu Chongzhi – 巴斯克语" lang="eu" hreflang="eu" data-title="Zu Chongzhi" 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%AA%D8%B3%D9%88_%DA%86%D9%88%D9%86%DA%AF%DA%86%DB%8C" title="تسو چونگچی – 波斯语" lang="fa" hreflang="fa" data-title="تسو چونگچی" 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/Zu_Chongzhi" title="Zu Chongzhi – 芬兰语" lang="fi" hreflang="fi" data-title="Zu Chongzhi" 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/Zu_Chongzhi" title="Zu Chongzhi – 法语" lang="fr" hreflang="fr" data-title="Zu Chongzhi" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Cu_Csung-cse" title="Cu Csung-cse – 匈牙利语" lang="hu" hreflang="hu" data-title="Cu Csung-cse" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Zu_Chongzhi" title="Zu Chongzhi – 意大利语" lang="it" hreflang="it" data-title="Zu Chongzhi" 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%A5%96%E6%B2%96%E4%B9%8B" title="祖沖之 – 日语" lang="ja" hreflang="ja" data-title="祖沖之" 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/%EC%A1%B0%EC%B6%A9%EC%A7%80" title="조충지 – 韩语" lang="ko" hreflang="ko" data-title="조충지" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Zu_Chongzhi" title="Zu Chongzhi – 康沃尔语" lang="kw" hreflang="kw" data-title="Zu Chongzhi" data-language-autonym="Kernowek" data-language-local-name="康沃尔语" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Zu_Chongzhi" title="Zu Chongzhi – 荷兰语" lang="nl" hreflang="nl" data-title="Zu Chongzhi" 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/Zu_Chongzhi" title="Zu Chongzhi – 书面挪威语" lang="nb" hreflang="nb" data-title="Zu Chongzhi" 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-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Zu_Chongzhi" title="Zu Chongzhi – 皮埃蒙特文" lang="pms" hreflang="pms" data-title="Zu Chongzhi" data-language-autonym="Piemontèis" data-language-local-name="皮埃蒙特文" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Tsu_Ch%27ung_Chih" title="Tsu Ch'ung Chih – 葡萄牙语" lang="pt" hreflang="pt" data-title="Tsu Ch'ung Chih" 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-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A6%D0%B7%D1%83_%D0%A7%D1%83%D0%BD%D1%87%D0%B6%D0%B8" title="Цзу Чунчжи – 俄语" lang="ru" hreflang="ru" data-title="Цзу Чунчжи" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Zu_Chongzhi" title="Zu Chongzhi – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Zu Chongzhi" 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/Zu_Chongzhi" title="Zu Chongzhi – Simple English" lang="en-simple" hreflang="en-simple" data-title="Zu Chongzhi" 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/Dzu_%C4%8Congd%C5%BEi" title="Dzu Čongdži – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Dzu Čongdži" 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-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Zu_Chongzhi" title="Zu Chongzhi – 他加禄语" lang="tl" hreflang="tl" data-title="Zu Chongzhi" 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%A6%D0%B7%D1%83_%D0%A7%D1%83%D0%BD%D1%87%D0%B6%D0%B8" title="Цзу Чунчжи – 乌克兰语" lang="uk" hreflang="uk" data-title="Цзу Чунчжи" 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-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%E1%BB%95_Xung_Chi" title="Tổ Xung Chi – 越南语" lang="vi" hreflang="vi" data-title="Tổ Xung Chi" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Zu_Chongzhi" title="Zu Chongzhi – 瓦瑞语" lang="war" hreflang="war" data-title="Zu Chongzhi" data-language-autonym="Winaray" data-language-local-name="瓦瑞语" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-za mw-list-item"><a href="https://za.wikipedia.org/wiki/Cuj_Cungciz" title="Cuj Cungciz – 壮语" lang="za" hreflang="za" data-title="Cuj Cungciz" data-language-autonym="Vahcuengh" data-language-local-name="壮语" class="interlanguage-link-target"><span>Vahcuengh</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E7%A5%96%E6%B2%96%E4%B9%8B" title="祖沖之 – 文言文" lang="lzh" hreflang="lzh" data-title="祖沖之" data-language-autonym="文言" data-language-local-name="文言文" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%A5%96%E6%B2%96%E4%B9%8B" title="祖沖之 – 粤语" lang="yue" hreflang="yue" data-title="祖沖之" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q227444#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 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hreflang="en"><span>维基共享资源</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://zh.wikiquote.org/wiki/%E7%A5%96%E6%B2%96%E4%B9%8B" hreflang="zh"><span>维基语录</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/Q227444" 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"><span class="mw-redirectedfrom">（重定向自<a href="/w/index.php?title=%E7%A5%96%E6%B2%96%E4%B9%8B&redirect=no" class="mw-redirect" title="祖沖之">祖沖之</a>）</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r83732082">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}body.skin-minerva .mw-parser-output .infobox-header,body.skin-minerva .mw-parser-output .infobox-subheader,body.skin-minerva .mw-parser-output .infobox-above,body.skin-minerva .mw-parser-output .infobox-title,body.skin-minerva .mw-parser-output .infobox-image,body.skin-minerva .mw-parser-output .infobox-full-data,body.skin-minerva .mw-parser-output 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div.NavHead:not(.notheme)[style]{background:transparent!important}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox vcard"><tbody><tr><th colspan="2" class="infobox-above fn" style="background-color: #FFFFDD">祖冲之</th></tr><tr><td colspan="2" class="infobox-subheader" style="background-color:#CDDBE8"><a href="/wiki/%E7%A7%91%E5%AD%B8%E5%AE%B6" class="mw-redirect" title="科學家">科學家</a></td></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:%E7%A5%96%E5%86%B2%E4%B9%8B%E9%93%9C%E5%83%8F.jpg" class="mw-file-description" title="祖冲之"><img alt="祖冲之" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/%E7%A5%96%E5%86%B2%E4%B9%8B%E9%93%9C%E5%83%8F.jpg/200px-%E7%A5%96%E5%86%B2%E4%B9%8B%E9%93%9C%E5%83%8F.jpg" decoding="async" width="200" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/%E7%A5%96%E5%86%B2%E4%B9%8B%E9%93%9C%E5%83%8F.jpg/300px-%E7%A5%96%E5%86%B2%E4%B9%8B%E9%93%9C%E5%83%8F.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/%E7%A5%96%E5%86%B2%E4%B9%8B%E9%93%9C%E5%83%8F.jpg/400px-%E7%A5%96%E5%86%B2%E4%B9%8B%E9%93%9C%E5%83%8F.jpg 2x" data-file-width="3344" data-file-height="5024" /></a></span></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;;">國家</th><td class="infobox-data country-name" style=""><a href="/wiki/%E5%88%98%E5%AE%8B" title="刘宋">刘宋</a>（429-479）<br /><a href="/wiki/%E5%8D%97%E9%BD%8A" class="mw-redirect" title="南齊">南齊</a>（479-500）</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;;">時代</th><td class="infobox-data" style=""><a href="/wiki/%E5%8D%97%E5%8C%97%E6%9C%9D" title="南北朝">南北朝</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;;"><a href="/wiki/%E6%B0%91%E6%97%8F" title="民族">族裔</a></th><td class="infobox-data" style=""><a href="/wiki/%E6%BC%A2%E6%97%8F" class="mw-redirect" title="漢族">漢族</a></td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;;">出生</th><td class="infobox-data" style="">公元429年</td></tr><tr><th scope="row" class="infobox-label" style="white-space: nowrap;;">逝世</th><td class="infobox-data" style="">公元500年(70-71歲)</td></tr><tr><td colspan="2" class="infobox-full-data" style=""><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r83732082"></td></tr><tr><td colspan="2" class="infobox-full-data" style=""><link rel="mw-deduplicated-inline-style" 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(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-subgroup,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-pretitle,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-heading,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-above,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-below{background:inherit!important;color:inherit!important;border-color:#54595d!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar a:not(.new):not(.mw-selflink):link{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks hlist" style="width:200px"><tbody><tr><th class="sidebar-title" style="font-size:130%;"><a href="/wiki/%E5%9C%93%E5%91%A8%E7%8E%87" title="圓周率">圓周率</a></th></tr><tr><td class="sidebar-image"><span class="mw-default-size" typeof="mw:File/Frameless"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pi-unrolled-720.gif/220px-Pi-unrolled-720.gif" decoding="async" width="220" height="70" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pi-unrolled-720.gif/330px-Pi-unrolled-720.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pi-unrolled-720.gif/440px-Pi-unrolled-720.gif 2x" data-file-width="720" data-file-height="228" /></span></span></td></tr><tr><td class="sidebar-content"> <b><span style="white-space:nowrap">3.14159<span style="margin-left:0.25em">26535</span><span style="margin-left:0.25em">89793</span><span style="margin-left:0.25em">23846</span><span style="margin-left:0.25em">26433...</span></span></b></td> </tr><tr><th class="sidebar-heading" style="border-top:#aaa 1px solid;"> 運用</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/%E5%9C%86%E7%9A%84%E9%9D%A2%E7%A7%AF" title="圆的面积">圓的面積</a></li> <li><a href="/wiki/%E5%9C%93%E5%91%A8" title="圓周">周長</a></li> <li><a href="/wiki/%E5%90%AB%E5%9C%86%E5%91%A8%E7%8E%87%E7%9A%84%E5%85%AC%E5%BC%8F%E5%88%97%E8%A1%A8" title="含圆周率的公式列表">含圆周率的公式列表</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="border-top:#aaa 1px solid;"> 證明</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/%E8%AF%81%E6%98%8E%CF%80%E6%98%AF%E6%97%A0%E7%90%86%E6%95%B0" title="证明π是无理数">無理性</a></li> <li><a href="/w/index.php?title=%E6%9E%97%E5%BE%B7%E6%9B%BC%E2%80%94%E9%AD%8F%E7%88%BE%E6%96%AF%E7%89%B9%E6%8B%89%E6%96%AF%E5%AE%9A%E7%90%86&action=edit&redlink=1" class="new" title="林德曼—魏爾斯特拉斯定理（页面不存在）">超越性</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="border-top:#aaa 1px solid;"> 值</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/%E7%BA%A6%E7%8E%87" title="约率">約率</a>（<a href="/wiki/%E8%AD%89%E6%98%8E22/7%E5%A4%A7%E6%96%BC%CF%80" title="證明22/7大於π">證明22/7大於π</a>）</li> <li><a href="/wiki/%E5%AF%86%E7%8E%87" title="密率">密率</a></li> <li><a href="/wiki/%E5%9C%86%E5%91%A8%E7%8E%87%E8%BF%91%E4%BC%BC%E5%80%BC" title="圆周率近似值">近似值</a></li> <li><a href="/wiki/%E5%89%B2%E5%9C%86%E6%9C%AF_(%E5%88%98%E5%BE%BD)" title="割圆术 (刘徽)">割圓術</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="border-top:#aaa 1px solid;"> 人物</th></tr><tr><td class="sidebar-content"> <ul><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/%E5%88%98%E5%BE%BD" title="刘徽">刘徽</a></li> <li><a class="mw-selflink selflink">祖冲之</a></li> <li><span class="ilh-all" data-orig-title="玛达瓦" data-lang-code="en" data-lang-name="英语" data-foreign-title="Madhava of Sangamagrama"><span class="ilh-page"><a href="/w/index.php?title=%E7%8E%9B%E8%BE%BE%E7%93%A6&action=edit&redlink=1" class="new" title="玛达瓦（页面不存在）">玛达瓦</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama" class="extiw" title="en:Madhava of Sangamagrama"><span lang="en" dir="auto">Madhava of Sangamagrama</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><a href="/wiki/%E5%A8%81%E5%BB%89%C2%B7%E7%90%BC%E6%96%AF_(%E6%95%B0%E5%AD%A6%E5%AE%B6)" title="威廉·琼斯 (数学家)">威廉·琼斯</a></li> <li><a href="/wiki/%E7%B4%84%E7%BF%B0%C2%B7%E6%A2%85%E6%AC%BD" title="約翰·梅欽">約翰·梅欽</a></li> <li><a href="/wiki/%E7%BA%A6%E7%BF%B0%C2%B7%E4%BC%A6%E5%A5%87" title="约翰·伦奇">约翰·伦奇</a></li> <li><a href="/wiki/%E9%B2%81%E9%81%93%E5%A4%AB%C2%B7%E8%8C%83%E7%A7%91%E4%BC%8A%E4%BC%A6" title="鲁道夫·范科伊伦">鲁道夫·范科伊伦</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></ul></td> </tr><tr><th class="sidebar-heading" style="border-top:#aaa 1px solid;"> 歷史</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/%E5%9C%93%E5%91%A8%E7%8E%87%E8%A8%88%E7%AE%97%E5%B9%B4%E8%A1%A8" title="圓周率計算年表">年表</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="border-top:#aaa 1px solid;"> 文化</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/%E5%9C%93%E5%91%A8%E7%8E%87%E6%97%A5" title="圓周率日">節日</a></li></ul></td> </tr><tr><th class="sidebar-heading" style="border-top:#aaa 1px solid;"> 相關主題</th></tr><tr><td class="sidebar-content"> <ul><li><a href="/wiki/%E5%8C%96%E5%9C%93%E7%82%BA%E6%96%B9" title="化圓為方">化圓為方</a></li> <li><a href="/wiki/%E5%B7%B4%E5%A1%9E%E5%B0%94%E9%97%AE%E9%A2%98" title="巴塞尔问题">巴塞爾問題</a></li> <li><a href="/wiki/%E5%9C%86%E5%91%A8%E7%8E%87%E4%B8%AD%E8%BF%9E%E7%BB%AD%E7%9A%84%E5%85%AD%E4%B8%AA9" title="圆周率中连续的六个9">连续的六个9</a></li></ul></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 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class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/%E6%98%86%E5%B1%B1%E4%BA%AD%E6%9E%97%E5%85%AC%E5%9B%AD%E7%A5%96%E5%86%B2%E4%B9%8B%E5%83%8F.jpg/300px-%E6%98%86%E5%B1%B1%E4%BA%AD%E6%9E%97%E5%85%AC%E5%9B%AD%E7%A5%96%E5%86%B2%E4%B9%8B%E5%83%8F.jpg" decoding="async" width="300" height="169" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/%E6%98%86%E5%B1%B1%E4%BA%AD%E6%9E%97%E5%85%AC%E5%9B%AD%E7%A5%96%E5%86%B2%E4%B9%8B%E5%83%8F.jpg/450px-%E6%98%86%E5%B1%B1%E4%BA%AD%E6%9E%97%E5%85%AC%E5%9B%AD%E7%A5%96%E5%86%B2%E4%B9%8B%E5%83%8F.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/%E6%98%86%E5%B1%B1%E4%BA%AD%E6%9E%97%E5%85%AC%E5%9B%AD%E7%A5%96%E5%86%B2%E4%B9%8B%E5%83%8F.jpg/600px-%E6%98%86%E5%B1%B1%E4%BA%AD%E6%9E%97%E5%85%AC%E5%9B%AD%E7%A5%96%E5%86%B2%E4%B9%8B%E5%83%8F.jpg 2x" data-file-width="2000" data-file-height="1125" /></a><figcaption><a href="/wiki/%E6%98%86%E5%B1%B1%E5%B8%82" title="昆山市">昆山</a>亭林公园祖冲之像</figcaption></figure> <p><b>祖沖之</b>（429年—500年），<a href="/wiki/%E8%A1%A8%E5%AD%97" title="表字">字</a><b>文远</b>，<a href="/wiki/%E8%8C%83%E9%98%B3%E9%83%A1" title="范阳郡">范阳郡</a><a href="/wiki/%E9%80%8E%E5%8E%BF_(%E8%A5%BF%E6%B1%89)" title="逎县 (西汉)">逎县</a>（今<a href="/wiki/%E6%B2%B3%E5%8C%97%E7%9C%81" title="河北省">河北省</a><a href="/wiki/%E4%BF%9D%E5%AE%9A%E5%B8%82" title="保定市">保定市</a><a href="/wiki/%E6%B6%9E%E6%B0%B4%E5%8E%BF" title="涞水县">涞水县</a>）人，<a href="/wiki/%E5%88%98%E5%AE%8B" title="刘宋">刘宋</a>时代杰出的<a href="/wiki/%E6%95%B0%E5%AD%A6%E5%AE%B6" title="数学家">数学家</a>、<a href="/wiki/%E5%A4%A9%E6%96%87%E5%AD%A6%E5%AE%B6" title="天文学家">天文学家</a>，主要成就在<a href="/wiki/%E6%95%B0%E5%AD%A6" title="数学">数学</a>、<a href="/wiki/%E5%A4%A9%E6%96%87" class="mw-redirect" title="天文">天文</a><a href="/wiki/%E5%8E%86%E6%B3%95" title="历法">历法</a>和<a href="/wiki/%E6%9C%BA%E6%A2%B0" title="机械">机械</a>制造三个领域。祖冲之的儿子<a href="/wiki/%E7%A5%96%E6%9A%85%E4%B9%8B" title="祖暅之">祖暅之</a>也是数学家。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="生平"><span id=".E7.94.9F.E5.B9.B3"></span>生平</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=1" title="编辑章节：生平"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>祖家歷代都對天文历法素有研究，祖冲之从小就有机会接触<a href="/wiki/%E5%A4%A9%E6%96%87" class="mw-redirect" title="天文">天文</a>、<a href="/wiki/%E6%95%B0%E5%AD%A6" title="数学">数学</a>知识。祖冲之青年时，就得到博学多才的名譽，<a href="/wiki/%E5%AE%8B%E5%AD%9D%E6%AD%A6%E5%B8%9D" title="宋孝武帝">宋孝武帝</a>听说后，派他到华林学省做研究工作。461年，他在<a href="/wiki/%E5%8D%97%E5%BE%90%E5%B7%9E_(%E5%88%98%E5%AE%8B)" title="南徐州 (刘宋)">南徐州</a>刺史府裏擔任<a href="/wiki/%E4%BB%8E%E4%BA%8B" title="从事">从事</a>，先后任南徐州从事史、公府参军。公元464年他调至娄县（今<a href="/wiki/%E6%B1%9F%E8%8B%8F" class="mw-redirect" title="江苏">江苏</a><a href="/wiki/%E6%98%86%E5%B1%B1%E5%B8%82" title="昆山市">昆山</a>东北）任县令。在此期间他编制了《<a href="/wiki/%E5%A4%A7%E6%98%8E%E6%9B%86_(%E7%A5%96%E6%B2%96%E4%B9%8B)" title="大明曆 (祖沖之)">大明曆</a>》，计算了<a href="/wiki/%E5%9C%86%E5%91%A8%E7%8E%87" class="mw-redirect" title="圆周率">圆周率</a>。劉宋末年，祖冲之回到建康任谒者仆射，此后直到劉宋灭亡一段时间后，他花了较大精力来研究机械制造。494年到498年之间，他在<a href="/wiki/%E5%8D%97%E9%BD%90" title="南齐">南齐</a>朝廷担任<a href="/wiki/%E9%95%BF%E6%B0%B4%E6%A0%A1%E5%B0%89" title="长水校尉">长水校尉</a>一职，受四品俸禄。 </p> <div class="mw-heading mw-heading2"><h2 id="数学贡献"><span id=".E6.95.B0.E5.AD.A6.E8.B4.A1.E7.8C.AE"></span>数学贡献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=2" title="编辑章节：数学贡献"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在数学上，祖冲之研究过《<a href="/wiki/%E4%B9%9D%E7%AB%A0%E7%AE%97%E6%9C%AF" title="九章算术">九章算术</a>》和<a href="/wiki/%E5%88%98%E5%BE%BD" title="刘徽">刘徽</a>所做的注解，给刘徽的《<a href="/wiki/%E9%87%8D%E5%B7%AE" class="mw-redirect" title="重差">重差</a>》作过注解。他还著有《<a href="/wiki/%E7%BC%80%E6%9C%AF" title="缀术">缀术</a>》一书，汇集了祖冲之父子的数学研究成果。这本书内容深奥，以至“学官莫能究其深奥，故废而不理”。《缀术》在<a href="/wiki/%E5%94%90%E4%BB%A3" class="mw-redirect" title="唐代">唐代</a>被收入《<a href="/wiki/%E7%AE%97%E7%BB%8F%E5%8D%81%E4%B9%A6" title="算经十书">算经十书</a>》，成为唐代国子监算学课本，当时学习《缀术》需要四年的时间，可见《缀术》的艰深。《缀术》曾经传至<a href="/wiki/%E6%9C%9D%E9%AE%AE_(%E5%9C%B0%E5%8D%80)" title="朝鮮 (地區)">朝鲜</a>和<a href="/wiki/%E6%97%A5%E6%9C%AC" title="日本">日本</a>，但到<a href="/wiki/%E5%8C%97%E5%AE%8B" title="北宋">北宋</a>时这部书就已轶失。人们只能通过其他文献了解祖冲之的部分工作：在《<a href="/wiki/%E9%9A%8B%E4%B9%A6" title="隋书">隋书</a>·律曆志》中留有小段祖冲之关于圆周率工作的记载；唐代<a href="/wiki/%E6%9D%8E%E6%B7%B3%E9%A2%A8" title="李淳風">李淳风</a>在《九章算术》注文中记载了祖冲之和儿子祖暅求球体积的方法。祖冲之还研究过“开差幂”和“开差立”问题，涉及<a href="/wiki/%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8B" title="二次方程">二次方程</a>和<a href="/wiki/%E4%B8%89%E6%AC%A1%E6%96%B9%E7%A8%8B" title="三次方程">三次方程</a>的求根问题。遗留下来的祖冲之的数学贡献主要有他对<a href="/wiki/%E5%9C%86%E5%91%A8%E7%8E%87" class="mw-redirect" title="圆周率">圆周率</a>的计算结果和球体体积的计算公式。 </p> <div class="mw-heading mw-heading3"><h3 id="计算圆周率"><span id=".E8.AE.A1.E7.AE.97.E5.9C.86.E5.91.A8.E7.8E.87"></span>计算圆周率</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=3" title="编辑章节：计算圆周率"><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：<a href="/wiki/%E5%AF%86%E7%8E%87" title="密率">密率</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r85100532"><div role="note" class="hatnote navigation-not-searchable">参见：<a href="/wiki/%E5%9C%86%E5%91%A8%E7%8E%87" class="mw-redirect" title="圆周率">圆周率</a></div> <p>据《<a href="/wiki/%E9%9A%8B%E4%B9%A6" title="隋书">隋书</a>·律曆志》<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>记载，祖沖之以「以直徑一億為一丈，圓周盈數三丈一尺四寸一分五厘九毫二秒七忽，朒數三丈一尺四寸一分五厘九毫二秒六忽，正數在盈朒二限之間。密率，圓徑一百一十三，圓周三百五十五。約率，圓徑七，週二十二。」，以此为直径求<a href="/wiki/%E5%9C%86%E5%91%A8%E7%8E%87" class="mw-redirect" title="圆周率">圆周率</a>，求得盈数（即过剩的近似值）为<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3.1415927}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3.1415927</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3.1415927}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba1d6a43dcc4e13d09b74e2ec05298f49c4800b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.946ex; height:2.176ex;" alt="{\displaystyle 3.1415927}"></span>；朒数（即不足的近似值）为<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3.1415926}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3.1415926</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3.1415926}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/91c7a22c6d6bb66fc57dcc181ecf96e8d35836a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.946ex; height:2.176ex;" alt="{\displaystyle 3.1415926}"></span>，圆周率的真值介于盈朒两数之间。《隋书》没有具体说明祖冲之是用什么方法计算出盈朒两数的。一般认为，祖冲之采用的是<a href="/wiki/%E5%89%B2%E5%9C%86%E6%9C%AF_(%E5%88%98%E5%BE%BD)#祖率" title="割圆术 (刘徽)">刘徽割圆术</a>分割到24576边形，又用<a href="/wiki/%E5%89%B2%E5%9C%86%E6%9C%AF_(%E5%88%98%E5%BE%BD)#刘徽圆周率不等式" title="割圆术 (刘徽)">刘徽圆周率不等式</a>得祖冲之著名的圆周率不等式： <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3.1415926<\pi <3.1415927}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3.1415926</mn> <mo><</mo> <mi>π</mi> <mo><</mo> <mn>3.1415927</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3.1415926<\pi <3.1415927}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2aca8712bcbd7836f7e1db9811a1e93ef71110aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:27.422ex; height:2.176ex;" alt="{\displaystyle 3.1415926<\pi <3.1415927}"></span>。祖冲之的这一结果精确到小数点后第7位，直到一千多年后才由15世纪的<a href="/wiki/%E9%98%BF%E6%8B%89%E4%BC%AF%E5%8D%8A%E5%B2%9B" title="阿拉伯半岛">阿拉伯</a>数学家<a href="/wiki/%E5%8D%A1%E8%A5%BF" title="卡西">阿尔·卡西</a>以17位有效数字打破此记录<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>。 </p><p>按照当时计算使用分数的习惯，祖冲之还采用了两个分数值的<a href="/wiki/%E5%9C%86%E5%91%A8%E7%8E%87" class="mw-redirect" title="圆周率">圆周率</a>：“约率”<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {22}{7}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>22</mn> <mn>7</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {22}{7}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cb5d075d03ff7edd66274d09cb1e2dd0aee7bc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.48ex; height:3.676ex;" alt="{\displaystyle {\tfrac {22}{7}}}"></span>（或称之为“疏率”<span id="noteTag-cite_ref-sup"><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>註 1<span class="cite-bracket">]</span></a></sup></span>）以及“密率”<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {355}{113}}=3.141592920354}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>355</mn> <mn>113</mn> </mfrac> </mstyle> </mrow> <mo>=</mo> <mn>3.141592920354</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\tfrac {355}{113}}=3.141592920354}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cefaaca1ef5dccf6755f8b77567b863e95e7a7c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:22.159ex; height:3.676ex;" alt="{\displaystyle {\tfrac {355}{113}}=3.141592920354}"></span>。在分母<16600的所有整分数中，密率的比值最接近圆周率<span id="noteTag-cite_ref-sup"><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>註 2<span class="cite-bracket">]</span></a></sup></span>。祖冲之可能利用<a href="/wiki/%E4%BD%95%E6%89%BF%E5%A4%A9_(%E5%8D%97%E6%9C%9D)" title="何承天 (南朝)">何承天</a>的<a href="/wiki/%E8%B0%83%E6%97%A5%E6%B3%95#圆周率约率和密率" title="调日法">调日法</a>求得圆周率的约率和密率<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>。数学家<a href="/wiki/%E5%8D%8E%E7%BD%97%E5%BA%9A" title="华罗庚">华罗庚</a>曾认为密率的求得，说明祖冲之可能已经掌握了<a href="/wiki/%E8%BF%9E%E5%88%86%E6%95%B0" title="连分数">连分数</a>的概念。 </p><p>根據日本數學史家<a href="/wiki/%E4%B8%89%E4%B8%8A%E4%B9%89%E5%A4%AB" title="三上义夫">三上义夫</a>，雖<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi ={\tfrac {22}{7}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>22</mn> <mn>7</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi ={\tfrac {22}{7}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/311968a01fe08d5066a875f8333b00f9defe4c2d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:6.911ex; height:3.676ex;" alt="{\displaystyle \pi ={\tfrac {22}{7}}}"></span>是<a href="/wiki/%E5%8F%A4%E5%B8%8C%E8%85%8A" title="古希腊">古希腊</a>数学家<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>早已取得的数值，但<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi ={\tfrac {355}{113}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>355</mn> <mn>113</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi ={\tfrac {355}{113}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c9a0e5903d016b357e3ac69f1cdca82c58a39dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:7.733ex; height:3.676ex;" alt="{\displaystyle \pi ={\tfrac {355}{113}}}"></span>这个分数在<a href="/wiki/%E6%AC%A7%E6%B4%B2" title="欧洲">欧洲</a>直到1586年才由<a href="/wiki/%E8%8D%B7%E5%85%B0" title="荷兰">荷兰</a><a href="/wiki/%E5%BD%BC%E5%BE%97%C2%B7%E5%AE%89%E6%89%98%E5%B0%BC%E6%96%AF%E5%AE%97%C2%B7%E6%AD%90%E6%B2%83%E7%89%B9%E7%93%A6%E7%89%B9" class="mw-redirect" title="彼得·安托尼斯宗·歐沃特瓦特">彼得·安托尼斯宗·歐沃特瓦特</a>重新求出並廣泛流傳。鑑於此，<a href="/wiki/%E4%B8%89%E4%B8%8A%E4%B9%89%E5%A4%AB" title="三上义夫">三上义夫</a>提议把<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 355 \over 113}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mn>355</mn> </mstyle> <mn>113</mn> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle 355 \over 113}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/240ee068a90d33910c40c2c583b5829dd62fd31a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.323ex; height:5.176ex;" alt="{\displaystyle 355 \over 113}"></span>称为“祖率”<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading3"><h3 id="计算球体体积"><span id=".E8.AE.A1.E7.AE.97.E7.90.83.E4.BD.93.E4.BD.93.E7.A7.AF"></span>计算球体体积</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=4" title="编辑章节：计算球体体积"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>祖冲之还和儿子祖暅之一起，用巧妙的方法解决了球体体积的计算问题。 </p><p>《九章算术》中认为，球体的外切圆柱体积与球体体积之比等于正方形与其内切圆面积之比，刘徽在他为《九章算术》作的注释中指出，原书的说法是不正确的，只有“<a href="/wiki/%E7%89%9F%E5%90%88%E6%96%B9%E7%9B%96" title="牟合方盖">牟合方盖</a>”（垂直相交的两个圆柱体的共同部分的体积）与球体积之比，才正好等于正方形与其内切圆的面积之比。但刘徽没有给出“牟合方盖”的体积公式，所以也就得不出球体的体积公式。 </p><p>祖冲之父子采用“幂势既同，则积不容异。”（即“等高处横截面积常相等的两个立体，其体积也必然相等”）这一原理，求出了“牟合方盖”的体积，而球体体积等于<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi \over 4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> <mn>4</mn> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi \over 4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6a0b09884a506293568263efe49ac399804925b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:2.168ex; height:4.676ex;" alt="{\displaystyle \pi \over 4}"></span>乘以“牟合方盖”体积，从而最终算出球体积为<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi d^{3} \over 6}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> <mn>6</mn> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi d^{3} \over 6}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a98e076fc1e52ba23a47daa17e6f92bd374eb1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.44ex; height:5.676ex;" alt="{\displaystyle \pi d^{3} \over 6}"></span>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span>为球直径）。 </p><p>祖冲之父子所采用的“幂势既同，则积不容异”这一原理，在<a href="/wiki/%E6%AC%A7%E6%B4%B2" title="欧洲">欧洲</a>由<a href="/wiki/%E6%84%8F%E5%A4%A7%E5%88%A9" title="意大利">意大利</a>数学家<a href="/wiki/%E5%8D%A1%E7%93%A6%E5%88%97%E9%87%8C" class="mw-redirect" title="卡瓦列里">卡瓦列里</a>于17世纪重新发现，所以西文文献一般称该原理为<a href="/wiki/%E5%8D%A1%E7%93%A6%E5%88%97%E9%87%8C%E5%8E%9F%E7%90%86" class="mw-redirect" title="卡瓦列里原理">卡瓦列里原理</a>。也称为“<a href="/wiki/%E7%A5%96%E6%9A%85%E5%8E%9F%E7%90%86" title="祖暅原理">祖暅原理</a>”。 </p> <div class="mw-heading mw-heading2"><h2 id="天文历法贡献"><span id=".E5.A4.A9.E6.96.87.E5.8E.86.E6.B3.95.E8.B4.A1.E7.8C.AE"></span>天文历法贡献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=5" title="编辑章节：天文历法贡献"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:%E7%A5%96%E5%86%B2%E4%B9%8B%E8%B7%AF%2B%E5%93%88%E9%9B%B7%E8%B7%AF,_%E4%B8%8A%E6%B5%B7%E5%B8%82%E5%8C%97%E8%94%A1%E9%95%87.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/%E7%A5%96%E5%86%B2%E4%B9%8B%E8%B7%AF%2B%E5%93%88%E9%9B%B7%E8%B7%AF%2C_%E4%B8%8A%E6%B5%B7%E5%B8%82%E5%8C%97%E8%94%A1%E9%95%87.jpg/220px-%E7%A5%96%E5%86%B2%E4%B9%8B%E8%B7%AF%2B%E5%93%88%E9%9B%B7%E8%B7%AF%2C_%E4%B8%8A%E6%B5%B7%E5%B8%82%E5%8C%97%E8%94%A1%E9%95%87.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/%E7%A5%96%E5%86%B2%E4%B9%8B%E8%B7%AF%2B%E5%93%88%E9%9B%B7%E8%B7%AF%2C_%E4%B8%8A%E6%B5%B7%E5%B8%82%E5%8C%97%E8%94%A1%E9%95%87.jpg/330px-%E7%A5%96%E5%86%B2%E4%B9%8B%E8%B7%AF%2B%E5%93%88%E9%9B%B7%E8%B7%AF%2C_%E4%B8%8A%E6%B5%B7%E5%B8%82%E5%8C%97%E8%94%A1%E9%95%87.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/%E7%A5%96%E5%86%B2%E4%B9%8B%E8%B7%AF%2B%E5%93%88%E9%9B%B7%E8%B7%AF%2C_%E4%B8%8A%E6%B5%B7%E5%B8%82%E5%8C%97%E8%94%A1%E9%95%87.jpg/440px-%E7%A5%96%E5%86%B2%E4%B9%8B%E8%B7%AF%2B%E5%93%88%E9%9B%B7%E8%B7%AF%2C_%E4%B8%8A%E6%B5%B7%E5%B8%82%E5%8C%97%E8%94%A1%E9%95%87.jpg 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption>紀念中國數學家祖沖之和英國天文學家<a href="/wiki/%E6%84%9B%E5%BE%B7%E8%92%99%C2%B7%E5%93%88%E9%9B%B7" title="愛德蒙·哈雷">愛德蒙·哈雷</a>的兩條路名，在上海<a href="/wiki/%E6%B5%A6%E4%B8%9C%E6%96%B0%E5%8C%BA" title="浦东新区">浦东新区</a><a href="/wiki/%E5%BC%A0%E6%B1%9F%E9%95%87" title="张江镇">张江镇</a></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Ji33,_4-2,_Zu_Chongzhi,_1955.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Ji33%2C_4-2%2C_Zu_Chongzhi%2C_1955.jpg/220px-Ji33%2C_4-2%2C_Zu_Chongzhi%2C_1955.jpg" decoding="async" width="220" height="324" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Ji33%2C_4-2%2C_Zu_Chongzhi%2C_1955.jpg/330px-Ji33%2C_4-2%2C_Zu_Chongzhi%2C_1955.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/34/Ji33%2C_4-2%2C_Zu_Chongzhi%2C_1955.jpg/440px-Ji33%2C_4-2%2C_Zu_Chongzhi%2C_1955.jpg 2x" data-file-width="2525" data-file-height="3722" /></a><figcaption>纪念邮票：祖冲之像</figcaption></figure> <p>祖冲之在天文历法方面的成就，大都包含在他所编制的《<a href="/wiki/%E5%A4%A7%E6%98%8E%E6%9B%86_(%E7%A5%96%E6%B2%96%E4%B9%8B)" title="大明曆 (祖沖之)">大明曆</a>》及为《大明曆》所写的《驳议》中。 </p><p>在祖冲之之前，人们使用的历法是天文学家<a href="/wiki/%E4%BD%95%E6%89%BF%E5%A4%A9_(%E5%8D%97%E6%9C%9D)" title="何承天 (南朝)">何承天</a>编制的《<a href="/wiki/%E5%85%83%E5%98%89%E6%9B%86" title="元嘉曆">元嘉曆</a>》。祖冲之经过多年的观测和推算，发现《元嘉曆》存在很大的差误。于是祖冲之着手制定新的历法，<a href="/wiki/%E5%AE%8B%E5%AD%9D%E6%AD%A6%E5%B8%9D" title="宋孝武帝">宋孝武帝</a><a href="/wiki/%E5%A4%A7%E6%98%8E_(%E5%88%98%E5%AE%8B)" title="大明 (刘宋)">大明</a>六年（公元462年）他编制成了《大明曆》。大明曆在祖冲之生前始终没能采用，直到<a href="/wiki/%E6%A2%81%E6%AD%A6%E5%B8%9D" title="梁武帝">梁武帝</a><a href="/wiki/%E5%A4%A9%E7%9B%91" title="天监">天监</a>九年（公元510年）才正式颁布施行。《大明曆》的主要成就如下： </p> <ul><li>区分了<a href="/wiki/%E5%9B%9E%E5%BD%92%E5%B9%B4" title="回归年">回归年</a>和<a href="/wiki/%E6%81%92%E6%98%9F%E5%B9%B4" title="恒星年">恒星年</a>，首次把<a href="/wiki/%E5%B2%81%E5%B7%AE" class="mw-redirect" title="岁差">岁差</a>引进历法，测得岁差为45年11月差一度（今测二分點约为70.713年沿黃道西行差一度）<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>。岁差的引入是中国历法史上的重大进步。</li> <li>定一个回归年为365<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {15241 \over 62769}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>15241</mn> <mn>62769</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {15241 \over 62769}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/117d10c8496b30efa72277f6b15c86ce3b2e6ad7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:6.648ex; height:5.343ex;" alt="{\displaystyle {15241 \over 62769}}"></span>（=365.24281481日，今测为365.2421988日），直到<a href="/wiki/%E5%8D%97%E5%AE%8B" title="南宋">南宋</a><a href="/wiki/%E5%AE%8B%E5%AE%81%E5%AE%97" title="宋宁宗">宁宗</a><a href="/wiki/%E6%85%B6%E5%85%83_(%E5%B9%B4%E8%99%9F)" title="慶元 (年號)">庆元</a>五年（公元1199年）<a href="/wiki/%E6%9D%A8%E5%BF%A0%E8%BE%85" title="杨忠辅">杨忠辅</a>制<a href="/wiki/%E7%B5%B1%E5%A4%A9%E6%9B%86" title="統天曆">统天曆</a>以前，它一直是最精确的数据。</li> <li>采用391年置144闰的新<a href="/wiki/%E7%AB%A0_(%E6%9B%86%E6%B3%95)" title="章 (曆法)">闰周</a>，比以往历法采用的19年置7闰的闰周更加精密。</li> <li>定<a href="/wiki/%E4%BA%A4%E9%BB%9E%E6%9C%88" class="mw-redirect" title="交點月">交点月</a>日数为27<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {5598 \over 26377}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>5598</mn> <mn>26377</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {5598 \over 26377}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3bc8ff80111b810eeb58278a413ba0b4491af4ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:6.648ex; height:5.343ex;" alt="{\displaystyle {5598 \over 26377}}"></span>（=27.21223日，今测为27.212225日）。交点月日数的精确测得使得准确的日月食预报成为可能，祖冲之曾用大明曆推算了从元嘉十三年（公元436年）到大明三年（公元459年），23年间发生的4次月食时间，结果与实际完全符合。</li> <li>得出<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>每84年超辰一次的结论，即定<a href="/wiki/%E6%9C%A8%E6%98%9F" title="木星">木星</a>公转周期为11.858年（今测为11.862年）。</li> <li>给出了更精确的五星会合周期，其中<a href="/wiki/%E6%B0%B4%E6%98%9F" title="水星">水星</a>和木星的会合周期也接近现代的数值。</li> <li>提出了用<a href="/wiki/%E5%9C%AD%E8%A1%A8" title="圭表">圭表</a>测量正午太阳影长以定<a href="/wiki/%E5%86%AC%E8%87%B3" title="冬至">冬至</a>时刻的方法。</li></ul> <div class="mw-heading mw-heading2"><h2 id="机械制造贡献"><span id=".E6.9C.BA.E6.A2.B0.E5.88.B6.E9.80.A0.E8.B4.A1.E7.8C.AE"></span>机械制造贡献</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=6" title="编辑章节：机械制造贡献"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>祖冲之还曾设计制造过许多精巧的机械，在文献《<a href="/wiki/%E5%8D%97%E9%BD%90%E4%B9%A6" title="南齐书">南齐书</a>·祖冲之传》和《<a href="/wiki/%E5%8D%97%E5%8F%B2" title="南史">南史</a>·祖冲之传》中有所记载。他曾经设计制造过利用水力<span class="ilh-all" data-orig-title="舂米" data-lang-code="en" data-lang-name="英语" data-foreign-title="Rice pounder"><span class="ilh-page"><a href="/w/index.php?title=%E8%88%82%E7%B1%B3&action=edit&redlink=1" class="new" title="舂米（页面不存在）">舂米</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Rice_pounder" class="extiw" title="en:Rice pounder"><span lang="en" dir="auto">Rice pounder</span></a></span><span class="ilh-paren">）</span></span></span>、磨面的<a href="/wiki/%E6%B0%B4%E7%A2%93%E7%A3%A8" class="mw-redirect" title="水碓磨">水碓磨</a>；重新铸造了当时已经失传了的<a href="/wiki/%E6%8C%87%E5%8D%97%E8%BD%A6" title="指南车">指南车</a>，随便车子怎样转弯，车上的<a href="/wiki/%E9%93%9C" title="铜">铜</a>人总是指着南方；制造了"<a href="/wiki/%E5%8D%83%E9%87%8C%E8%88%B9" title="千里船">千里船</a>"，是一种<a href="/wiki/%E6%98%8E%E8%BD%AE%E8%88%B9" class="mw-redirect" title="明轮船">明轮船</a>，在新亭江（在今南京市西南）上试航过，一天可以航行一百多里。他还设计制造过计时仪器<a href="/wiki/%E6%BC%8F%E5%A3%BA" class="mw-redirect" title="漏壺">漏壶</a>和<a href="/wiki/%E6%AC%B9%E5%99%A8" title="欹器">欹器</a>。 </p> <div class="mw-heading mw-heading2"><h2 id="家庭"><span id=".E5.AE.B6.E5.BA.AD"></span>家庭</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=7" title="编辑章节：家庭"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="曾祖"><span id=".E6.9B.BE.E7.A5.96"></span>曾祖</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=8" title="编辑章节：曾祖"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E7%A5%96%E5%8F%B0%E4%B9%8B" title="祖台之">祖台之</a>，东晋侍中</li></ul> <div class="mw-heading mw-heading3"><h3 id="祖父"><span id=".E7.A5.96.E7.88.B6"></span>祖父</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=9" title="编辑章节：祖父"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>祖昌，刘宋大匠卿</li></ul> <div class="mw-heading mw-heading3"><h3 id="父亲"><span id=".E7.88.B6.E4.BA.B2"></span>父亲</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=10" title="编辑章节：父亲"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>祖朔之，南齐奉朝请</li></ul> <div class="mw-heading mw-heading3"><h3 id="儿子"><span id=".E5.84.BF.E5.AD.90"></span>儿子</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=11" title="编辑章节：儿子"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E7%A5%96%E6%9A%85%E4%B9%8B" title="祖暅之">祖暅之</a>，南梁太舟卿</li></ul> <div class="mw-heading mw-heading3"><h3 id="孙子"><span id=".E5.AD.99.E5.AD.90"></span>孙子</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=12" title="编辑章节：孙子"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=%E7%A5%96%E7%9A%93&action=edit&redlink=1" class="new" title="祖皓（页面不存在）">祖皓</a>，南梁广陵郡太守</li></ul> <div class="mw-heading mw-heading2"><h2 id="著作"><span id=".E8.91.97.E4.BD.9C"></span>著作</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=13" title="编辑章节：著作"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>《<a href="/wiki/%E9%9A%8B%E4%B9%A6" title="隋书">隋书</a>·经籍志》录有《长水校尉祖冲之集》五十一卷，但现已佚。 </p><p>散见于各种史籍记载的还有以下著作： </p> <ul><li>《<a href="https://zh.wikisource.org/wiki/%E5%85%A8%E9%BD%8A%E6%96%87/%E5%8D%B7%E5%8D%81%E5%85%AD#_安边论" class="extiw" title="s:全齊文/卷十六">安边论</a>》，已佚。</li> <li>《<a href="/wiki/%E8%BF%B0%E7%95%B0%E8%A8%98_(%E7%A5%96%E6%B2%96%E4%B9%8B)" title="述異記 (祖沖之)">述异记</a>》十卷，已佚。</li> <li>《<a href="/w/index.php?title=%E6%98%93%E8%80%81%E8%8E%8A%E4%B9%89%E9%87%8A&action=edit&redlink=1" class="new" title="易老莊义释（页面不存在）">易老莊义释</a>》，已佚。</li> <li>《<a href="/w/index.php?title=%E8%AE%BA%E8%AF%AD%E5%AD%9D%E7%BB%8F%E6%B3%A8&action=edit&redlink=1" class="new" title="论语孝经注（页面不存在）">论语孝经注</a>》，已佚。</li> <li>《<a href="/wiki/%E7%BC%80%E6%9C%AF" title="缀术">缀术</a>》六卷，已佚。</li> <li>《<a href="/w/index.php?title=%E4%B9%9D%E7%AB%A0%E8%BF%B0%E4%B9%89%E6%B3%A8&action=edit&redlink=1" class="new" title="九章述义注（页面不存在）">九章述义注</a>》九卷，已佚。</li> <li>《<a href="/w/index.php?title=%E9%87%8D%E5%B7%AE%E6%B3%A8&action=edit&redlink=1" class="new" title="重差注（页面不存在）">重差注</a>》一卷，已佚。</li> <li>《<a href="/wiki/%E5%A4%A7%E6%98%8E%E6%9B%86_(%E7%A5%96%E6%B2%96%E4%B9%8B)" title="大明曆 (祖沖之)">大明曆</a>》</li> <li>《<a href="https://zh.wikisource.org/wiki/%E5%85%A8%E9%BD%8A%E6%96%87/%E5%8D%B7%E5%8D%81%E5%85%AD#_上新历表" class="extiw" title="s:全齊文/卷十六">上大明曆表</a>》</li> <li>《<a href="https://zh.wikisource.org/wiki/%E5%85%A8%E9%BD%8A%E6%96%87/%E5%8D%B7%E5%8D%81%E5%85%AD#_辩戴法兴难新历" class="extiw" title="s:全齊文/卷十六">驳议</a>》</li> <li>《<a href="/w/index.php?title=%E5%BC%80%E7%AB%8B%E5%9C%86%E6%9C%AF&action=edit&redlink=1" class="new" title="开立圆术（页面不存在）">开立圆术</a>》</li></ul> <div class="mw-heading mw-heading2"><h2 id="紀念"><span id=".E7.B4.80.E5.BF.B5"></span>紀念</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=14" title="编辑章节：紀念"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>为纪念祖冲之： </p> <ul><li><a href="/wiki/%E6%9C%88%E7%90%83" title="月球">月球</a>背面的一座<a href="/wiki/%E7%8E%AF%E5%BD%A2%E5%B1%B1" class="mw-redirect" title="环形山">环形山</a>被命名为「<a href="/wiki/%E7%A5%96%E5%86%B2%E4%B9%8B%E7%8E%AF%E5%BD%A2%E5%B1%B1" title="祖冲之环形山">祖冲之环形山</a>」。</li> <li><a href="/wiki/%E5%B0%8F%E8%A1%8C%E6%98%9F1888" title="小行星1888">小行星1888</a>被命名为「祖冲之小行星」。</li> <li><a href="/wiki/%E4%B8%8A%E6%B5%B7" class="mw-redirect" title="上海">上海</a><a href="/wiki/%E6%B5%A6%E4%B8%9C" class="mw-redirect" title="浦东">浦东</a><a href="/wiki/%E5%BC%A0%E6%B1%9F%E9%AB%98%E7%A7%91%E6%8A%80%E5%9B%AD%E5%8C%BA" title="张江高科技园区">张江高科技园区</a>内有一条城市道路命名为「<a href="/wiki/%E7%A5%96%E5%86%B2%E4%B9%8B%E8%B7%AF" title="祖冲之路">祖冲之路</a>」。</li> <li><a href="/wiki/%E6%B7%B1%E5%9C%B3" class="mw-redirect" title="深圳">深圳</a><a href="/wiki/%E9%BE%8D%E5%B4%97%E5%8D%80" class="mw-redirect" title="龍崗區">龍崗區</a><a href="/wiki/%E5%9D%82%E7%94%B0%E8%A1%97%E9%81%93" title="坂田街道">坂田街道</a><a href="/wiki/%E5%8D%8E%E4%B8%BA" title="华为">华为</a>基地有一條道路命名為「<a href="/w/index.php?title=%E6%B2%96%E4%B9%8B%E5%A4%A7%E9%81%93&action=edit&redlink=1" class="new" title="沖之大道（页面不存在）">沖之大道</a>」</li> <li>上海<a href="/wiki/%E5%90%8C%E6%B5%8E%E5%A4%A7%E5%AD%A6" title="同济大学">同济大学</a><a href="/wiki/%E6%96%87%E8%BF%9C%E6%A5%BC" title="文远楼">文远楼</a>（祖冲之<a href="/wiki/%E8%A1%A8%E5%AD%97" title="表字">字</a>文远）</li> <li><a href="/wiki/%E8%8E%AB%E6%96%AF%E7%A7%91%E5%A4%A7%E5%AD%A6" class="mw-redirect" title="莫斯科大学">莫斯科大学</a>大礼堂前的走廊壁上，用彩色大理石镶嵌着祖冲之像。</li> <li>河北保定有一所以祖冲之命名的中学，有江泽民手书「河北<a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B%E4%B8%AD%E5%AD%A6&action=edit&redlink=1" class="new" title="祖冲之中学（页面不存在）">祖冲之中学</a>」石碑。</li></ul> <p>此外还有祖冲之邮票，祖冲之纪念银币等纪念品。 </p> <div class="mw-heading mw-heading2"><h2 id="参见"><span id=".E5.8F.82.E8.A7.81"></span>参见</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=15" title="编辑章节：参见"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="navigation" aria-label="Portals" class="noprint portal plainlist tright" style="margin:0.5em 0 0.5em 1em;border:solid #aaa 1px"> <ul style="display:table;box-sizing:border-box;padding:0.1em;max-width:175px;background:var(--background-color-base,#f9f9f9);font-size:85%;line-height:110%;font-weight:bold"> <li style="display:table-row"><span style="display:table-cell;padding:0.2em;vertical-align:middle;text-align:center"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Portal-puzzle.svg/32px-Portal-puzzle.svg.png" decoding="async" width="32" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Portal-puzzle.svg/48px-Portal-puzzle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Portal-puzzle.svg/64px-Portal-puzzle.svg.png 2x" data-file-width="32" data-file-height="28" /></span></span></span><span 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data-file-height="128" /></a></span></span><span style="display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle"><a href="/wiki/Portal:%E6%95%B0%E5%AD%A6" title="Portal:数学">数学主题</a></span></li> <li style="display:table-row"><span style="display:table-cell;padding:0.2em;vertical-align:middle;text-align:center"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/28px-Crab_Nebula.jpg" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/42px-Crab_Nebula.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Crab_Nebula.jpg/56px-Crab_Nebula.jpg 2x" data-file-width="3864" data-file-height="3864" /></span></span></span><span style="display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle"><a href="/wiki/Portal:%E5%A4%A9%E6%96%87%E5%AD%A6" title="Portal:天文学">天文学主题</a></span></li> <li style="display:table-row"><span style="display:table-cell;padding:0.2em;vertical-align:middle;text-align:center"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/P_vip.svg/28px-P_vip.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/69/P_vip.svg/41px-P_vip.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/69/P_vip.svg/55px-P_vip.svg.png 2x" data-file-width="1911" data-file-height="1944" /></span></span></span><span style="display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle"><a href="/wiki/Portal:%E4%BA%BA%E7%89%A9" title="Portal:人物">人物主题</a></span></li></ul></div> <ul><li><a href="/wiki/%E7%A5%96%E6%9A%85%E4%B9%8B" title="祖暅之">祖暅之</a>、<a href="/wiki/%E7%A5%96%E6%9A%85%E5%8E%9F%E7%90%86" title="祖暅原理">祖暅原理</a></li> <li><a href="/wiki/%E5%9C%86%E5%91%A8%E7%8E%87" class="mw-redirect" title="圆周率">圆周率</a>：<a href="/wiki/%E5%AF%86%E7%8E%87" title="密率">密率</a></li> <li>《<a href="/wiki/%E5%A4%A7%E6%98%8E%E6%9B%86_(%E7%A5%96%E6%B2%96%E4%B9%8B)" title="大明曆 (祖沖之)">大明曆</a>》</li></ul> <div class="mw-heading mw-heading2"><h2 id="注脚"><span id=".E6.B3.A8.E8.84.9A"></span>注脚</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=16" title="编辑章节：注脚"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="references-NoteFoot"><ol class="references"> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">陈仁政在《说不尽的π》一书中提到，“疏率”是华罗庚在《数学是我国人民所擅长的学科》（1951年2月10日《人民日报》第3版）一文中使用的误称，其本人已在1962年的《从祖冲之的圆周率谈起》一书中予以纠正，然此误称依然流传于众多媒体<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>。</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"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {52163}{16604}}=3.1415923874}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>52163</mn> <mn>16604</mn> </mfrac> </mrow> <mo>=</mo> <mn>3.1415923874</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {52163}{16604}}=3.1415923874}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/218baa0d0e51463506c080eaa051449173a2e191" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:23.181ex; height:5.343ex;" alt="{\displaystyle {\frac {52163}{16604}}=3.1415923874}"></span>才比祖率略准。</span> </li> </ol></div> <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=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=17" 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 columns references-column-count references-column-count-2" style="-moz-column-count: 2; -webkit-column-count: 2; column-count: 2; 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"><a href="https://zh.wikisource.org/wiki/%E9%9A%8B%E6%9B%B8/%E5%8D%B716" class="extiw" title="s:隋書/卷16">隋書/卷16</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">吴文俊主编《中国数学史大系》副卷第一卷 480页 <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/7303052925" class="internal mw-magiclink-isbn">ISBN 7-303-05292-5</a>/O</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 book">陈仁政. 约率‘摇身一变’成‘疏率’. 说不尽的π. 北京: 科学出版社. 2005: 第18页. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9787030146359" title="Special:网络书源/9787030146359"><span title="国际标准书号">ISBN</span> 9787030146359</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E7%A5%96%E5%86%B2%E4%B9%8B&rft.atitle=%E7%BA%A6%E7%8E%87%E2%80%98%E6%91%87%E8%BA%AB%E4%B8%80%E5%8F%98%E2%80%99%E6%88%90%E2%80%98%E7%96%8F%E7%8E%87%E2%80%99&rft.au=%E9%99%88%E4%BB%81%E6%94%BF&rft.btitle=%E8%AF%B4%E4%B8%8D%E5%B0%BD%E7%9A%84%CF%80&rft.date=2005&rft.genre=bookitem&rft.isbn=9787030146359&rft.pages=%E7%AC%AC18%E9%A1%B5&rft.place=%E5%8C%97%E4%BA%AC&rft.pub=%E7%A7%91%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-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a href="/wiki/%E5%90%B4%E6%96%87%E4%BF%8A" title="吴文俊">吴文俊</a> 主编《中国数学史大系》第四卷 123页 ISBN 7-300-0425-8/O</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">“We are on this account strongly urged to express a desire that it should henceforth be called by the name of Tsu Ch'ong-chih's fractional value for π” Yoshio Mikami, Development of Mathematics in China and Japan p50 1913 Leipzig</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a href="/w/index.php?title=%E5%8A%89%E6%93%8D%E5%8D%97&action=edit&redlink=1" class="new" title="劉操南（页面不存在）">劉操南</a> 著《古代天文曆法釋證》310頁 <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/9787308067072" class="internal mw-magiclink-isbn">ISBN 978-7-308-06707-2</a></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="延伸阅读"><span id=".E5.BB.B6.E4.BC.B8.E9.98.85.E8.AF.BB"></span>延伸阅读</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E7%A5%96%E5%86%B2%E4%B9%8B&action=edit&section=18" title="编辑章节：延伸阅读"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><span class="mw-editsection-like plainlinks" style="float: right;"><span class="mw-editsection-bracket">[</span><a href="https://www.wikidata.org/wiki/Q227444" class="extiw" title="wikidata:Q227444"><span class="nomobile">在维基数据</span>编<span class="nomobile">辑</span></a><span class="mw-editsection-bracket">]</span></span> </p> <dl><dd><span class="noviewer" typeof="mw:File"><span title="维基文库"><img alt="维基文库中的相关文本：" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/15px-Wikisource-logo.svg.png" decoding="async" width="15" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/23px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/30px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span></span> 《<a href="https://zh.wikisource.org/wiki/%E5%8D%97%E9%BD%8A%E6%9B%B8/%E5%8D%B752#祖冲之" class="extiw" title="s:南齊書/卷52">南齊書·卷52</a>》，出自<a href="/wiki/%E8%90%A7%E5%AD%90%E6%98%BE" title="萧子显">萧子显</a>《<a href="/wiki/%E5%8D%97%E9%BD%90%E4%B9%A6" title="南齐书">南齊書</a>》</dd> <dd><span class="noviewer" typeof="mw:File"><span title="维基共享资源"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> 在<a href="/wiki/%E7%BB%B4%E5%9F%BA%E5%85%B1%E4%BA%AB%E8%B5%84%E6%BA%90" title="维基共享资源">维基共享资源</a><b><a href="https://commons.wikimedia.org/wiki/Category:Zu_Chongzhi" class="extiw" title="commons:Category:Zu Chongzhi">阅览影像</a></b></dd></dl> <ul><li><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/13px-Wikiquote-logo.svg.png" decoding="async" width="13" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/20px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/27px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span> <a href="/wiki/%E7%BB%B4%E5%9F%BA%E8%AF%AD%E5%BD%95" title="维基语录">维基语录</a>上<a href="https://zh.wikiquote.org/wiki/Special:Search/%E7%A5%96%E5%86%B2%E4%B9%8B" class="extiw" title="q:Special:Search/祖冲之">有关祖冲之的语录</a></li> <li>洪萬生：〈<a rel="nofollow" class="external text" href="http://highscope.ch.ntu.edu.tw/wordpress/?p=25185">如何閱讀祖沖之？</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210402020127/http://highscope.ch.ntu.edu.tw/wordpress/?p=25185">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> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20031222212111/http://www.prc.net.cn/items/zhrw/rwzj/zj/ke06.htm">祖冲之①</a> 曹增祥祖冲之传记。</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20031028100005/http://www.prc.net.cn/items/zhrw/rwzj/zj/ke06_2.htm">祖冲之②</a> 曹增祥祖冲之传记。</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20031206132402/http://www.ihns.ac.cn/members/zhbaichun/p2.htm">祖冲之设计制造的几种机械及其复原问题</a> 张柏春</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20040205044818/http://www.1230.org/Article_Show.asp?ArticleID=141">祖冲之</a> 其中有祖冲之成就的详细介绍。</li> <li><a rel="nofollow" class="external text" href="https://ctext.org/wiki.pl?if=gb&chapter=459026">南齐书·列传第三十三—文学</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210624204117/https://ctext.org/wiki.pl?if=gb&chapter=459026">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>）其中有《祖冲之传》。</li> <li><a rel="nofollow" class="external text" href="https://ctext.org/wiki.pl?if=gb&chapter=604394">南史·列传第六十二</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210624203055/https://ctext.org/wiki.pl?if=gb&chapter=604394">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>）其中有祖冲之传。</li> <li><a rel="nofollow" class="external text" href="http://www.guoxue.com/shibu/24shi/suisu/sui_016.htm">隋书·志第十一—律历上</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20210211123709/http://www.guoxue.com/shibu/24shi/suisu/sui_016.htm">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>）其中有祖冲之计算圆周率结果的简短记载。</li></ul> <div style="clear: 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