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รัศมี - วิกิพีเดีย
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href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_th.wikipedia.org&uselang=th" class=""><span>บริจาคให้วิกิพีเดีย</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=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AA%E0%B8%A3%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%9A%E0%B8%B1%E0%B8%8D%E0%B8%8A%E0%B8%B5%E0%B8%9C%E0%B8%B9%E0%B9%89%E0%B9%83%E0%B8%8A%E0%B9%89%E0%B9%83%E0%B8%AB%E0%B8%A1%E0%B9%88&returnto=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5" title="แนะนำให้คุณสร้างบัญชีและเข้าสู่ระบบ แต่ไม่บังคับ" class=""><span>สร้างบัญชี</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=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%A5%E0%B9%87%E0%B8%AD%E0%B8%81%E0%B8%AD%E0%B8%B4%E0%B8%99&returnto=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5" title="แนะนำให้คุณเข้าสู่ระบบ แต่ไม่บังคับ [o]" accesskey="o" class=""><span>เข้าสู่ระบบ</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="ตัวเลือกเพิ่มเติม" > <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="เครื่องมือส่วนตัว" > <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">เครื่องมือส่วนตัว</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="เมนูผู้ใช้" > <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="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_th.wikipedia.org&uselang=th"><span>บริจาคให้วิกิพีเดีย</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AA%E0%B8%A3%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%9A%E0%B8%B1%E0%B8%8D%E0%B8%8A%E0%B8%B5%E0%B8%9C%E0%B8%B9%E0%B9%89%E0%B9%83%E0%B8%8A%E0%B9%89%E0%B9%83%E0%B8%AB%E0%B8%A1%E0%B9%88&returnto=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5" title="แนะนำให้คุณสร้างบัญชีและเข้าสู่ระบบ แต่ไม่บังคับ"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>สร้างบัญชี</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%A5%E0%B9%87%E0%B8%AD%E0%B8%81%E0%B8%AD%E0%B8%B4%E0%B8%99&returnto=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5" title="แนะนำให้คุณเข้าสู่ระบบ แต่ไม่บังคับ [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>เข้าสู่ระบบ</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"> หน้าสำหรับผู้แก้ไขที่ออกจากระบบ <a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%98%E0%B8%B5%E0%B9%83%E0%B8%8A%E0%B9%89:%E0%B8%9A%E0%B8%97%E0%B8%99%E0%B8%B3" aria-label="เรียนรู้เพิ่มเกี่ยวกับการแก้ไข"><span>เรียนรู้เพิ่มเติม</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/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B9%80%E0%B8%A3%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%89%E0%B8%B1%E0%B8%99%E0%B9%80%E0%B8%82%E0%B8%B5%E0%B8%A2%E0%B8%99" title="รายการการแก้ไขจากเลขที่อยู่ไอพีนี้ [y]" accesskey="y"><span>ส่วนร่วม</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2%E0%B8%9E%E0%B8%B9%E0%B8%94%E0%B8%84%E0%B8%B8%E0%B8%A2%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B8%89%E0%B8%B1%E0%B8%99" title="อภิปรายเกี่ยวกับการแก้ไขจากเลขที่อยู่ไอพีนี้ [n]" accesskey="n"><span>คุย</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"><!-- CentralNotice --></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="ไซต์"> <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="สารบัญ" 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">สารบัญ</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ย้ายเมนูไปที่แถบด้านข้าง</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ซ่อน</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">บทนำ</div> </a> </li> <li id="toc-รัศมีจากพื้นที่" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#รัศมีจากพื้นที่"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>รัศมีจากพื้นที่</span> </div> </a> <ul id="toc-รัศมีจากพื้นที่-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-รัศมีจากจุดสามจุด" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#รัศมีจากจุดสามจุด"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>รัศมีจากจุดสามจุด</span> </div> </a> <ul id="toc-รัศมีจากจุดสามจุด-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-สูตรสำหรับรูปหลายเหลี่ยมปกติ" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#สูตรสำหรับรูปหลายเหลี่ยมปกติ"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>สูตรสำหรับรูปหลายเหลี่ยมปกติ</span> </div> </a> <button aria-controls="toc-สูตรสำหรับรูปหลายเหลี่ยมปกติ-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>Toggle สูตรสำหรับรูปหลายเหลี่ยมปกติ subsection</span> </button> <ul id="toc-สูตรสำหรับรูปหลายเหลี่ยมปกติ-sublist" class="vector-toc-list"> <li id="toc-รัศมีจากด้านข้าง" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#รัศมีจากด้านข้าง"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>รัศมีจากด้านข้าง</span> </div> </a> <ul id="toc-รัศมีจากด้านข้าง-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-สูตรสำหรับไฮเพอร์คิวบ์_(hypercubes)" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#สูตรสำหรับไฮเพอร์คิวบ์_(hypercubes)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>สูตรสำหรับไฮเพอร์คิวบ์ (hypercubes)</span> </div> </a> <button aria-controls="toc-สูตรสำหรับไฮเพอร์คิวบ์_(hypercubes)-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>Toggle สูตรสำหรับไฮเพอร์คิวบ์ (hypercubes) subsection</span> </button> <ul id="toc-สูตรสำหรับไฮเพอร์คิวบ์_(hypercubes)-sublist" class="vector-toc-list"> <li id="toc-รัศมีจากด้านข้าง_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#รัศมีจากด้านข้าง_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>รัศมีจากด้านข้าง</span> </div> </a> <ul id="toc-รัศมีจากด้านข้าง_2-sublist" class="vector-toc-list"> </ul> </li> </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="สารบัญ" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">รัศมี</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="ไปที่บทความในภาษาอื่น ซึ่งมีใน 102 ภาษา" > <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-102" 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">102 ภาษา</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Radius" title="Radius – แอฟริกานส์" lang="af" hreflang="af" data-title="Radius" data-language-autonym="Afrikaans" data-language-local-name="แอฟริกานส์" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Radius_(Kreis)" title="Radius (Kreis) – เยอรมันสวิส" lang="gsw" hreflang="gsw" data-title="Radius (Kreis)" data-language-autonym="Alemannisch" data-language-local-name="เยอรมันสวิส" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%AC%E1%8B%B5%E1%8B%A8%E1%88%B5" title="ሬድየስ – อัมฮารา" lang="am" hreflang="am" data-title="ሬድየስ" data-language-autonym="አማርኛ" data-language-local-name="อัมฮารา" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Radio_(cheometr%C3%ADa)" title="Radio (cheometría) – อารากอน" lang="an" hreflang="an" data-title="Radio (cheometría)" data-language-autonym="Aragonés" data-language-local-name="อารากอน" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B5%D9%81_%D8%A7%D9%84%D9%82%D8%B7%D8%B1" title="نصف القطر – อาหรับ" lang="ar" hreflang="ar" data-title="نصف القطر" data-language-autonym="العربية" data-language-local-name="อาหรับ" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Radiu_(xeometr%C3%ADa)" title="Radiu (xeometría) – อัสตูเรียส" lang="ast" hreflang="ast" data-title="Radiu (xeometría)" data-language-autonym="Asturianu" data-language-local-name="อัสตูเรียส" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Radius" title="Radius – อาเซอร์ไบจาน" lang="az" hreflang="az" data-title="Radius" data-language-autonym="Azərbaycanca" data-language-local-name="อาเซอร์ไบจาน" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус – บัชคีร์" lang="ba" hreflang="ba" data-title="Радиус" data-language-autonym="Башҡортса" data-language-local-name="บัชคีร์" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D1%8B%D1%83%D1%81" title="Радыус – เบลารุส" lang="be" hreflang="be" data-title="Радыус" data-language-autonym="Беларуская" data-language-local-name="เบลารุส" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D1%8B%D1%8E%D1%81" title="Радыюс – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Радыюс" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус – บัลแกเรีย" lang="bg" hreflang="bg" data-title="Радиус" data-language-autonym="Български" data-language-local-name="บัลแกเรีย" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B8%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%A7" title="ব্যাসার্ধ – บังกลา" lang="bn" hreflang="bn" data-title="ব্যাসার্ধ" data-language-autonym="বাংলা" data-language-local-name="บังกลา" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Skin_(geometriezh)" title="Skin (geometriezh) – เบรตัน" lang="br" hreflang="br" data-title="Skin (geometriezh)" data-language-autonym="Brezhoneg" data-language-local-name="เบรตัน" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Polupre%C4%8Dnik" title="Poluprečnik – บอสเนีย" lang="bs" hreflang="bs" data-title="Poluprečnik" data-language-autonym="Bosanski" data-language-local-name="บอสเนีย" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Radi_(geometria)" title="Radi (geometria) – คาตาลัน" lang="ca" hreflang="ca" data-title="Radi (geometria)" data-language-autonym="Català" data-language-local-name="คาตาลัน" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%86%DB%8C%D9%88%DB%95%D8%AA%DB%8C%D8%B1%DB%95" title="نیوەتیرە – เคิร์ดตอนกลาง" lang="ckb" hreflang="ckb" data-title="نیوەتیرە" data-language-autonym="کوردی" data-language-local-name="เคิร์ดตอนกลาง" 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/Polom%C4%9Br" title="Poloměr – เช็ก" lang="cs" hreflang="cs" data-title="Poloměr" data-language-autonym="Čeština" data-language-local-name="เช็ก" 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%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус – ชูวัช" lang="cv" hreflang="cv" data-title="Радиус" data-language-autonym="Чӑвашла" data-language-local-name="ชูวัช" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Radiws" title="Radiws – เวลส์" lang="cy" hreflang="cy" data-title="Radiws" data-language-autonym="Cymraeg" data-language-local-name="เวลส์" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Radius" title="Radius – เดนมาร์ก" lang="da" hreflang="da" data-title="Radius" data-language-autonym="Dansk" data-language-local-name="เดนมาร์ก" 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/Radius" title="Radius – เยอรมัน" lang="de" hreflang="de" data-title="Radius" data-language-autonym="Deutsch" data-language-local-name="เยอรมัน" 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%91%CE%BA%CF%84%CE%AF%CE%BD%CE%B1_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Ακτίνα (γεωμετρία) – กรีก" lang="el" hreflang="el" data-title="Ακτίνα (γεωμετρία)" data-language-autonym="Ελληνικά" data-language-local-name="กรีก" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/R%C3%A2%C7%B5_(giumetr%C3%ACa)" title="Râǵ (giumetrìa) – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Râǵ (giumetrìa)" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Radius" title="Radius – อังกฤษ" lang="en" hreflang="en" data-title="Radius" data-language-autonym="English" data-language-local-name="อังกฤษ" 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/Radiuso" title="Radiuso – เอสเปรันโต" lang="eo" hreflang="eo" data-title="Radiuso" data-language-autonym="Esperanto" data-language-local-name="เอสเปรันโต" 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/Radio_(geometr%C3%ADa)" title="Radio (geometría) – สเปน" lang="es" hreflang="es" data-title="Radio (geometría)" data-language-autonym="Español" data-language-local-name="สเปน" 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/Raadius" title="Raadius – เอสโตเนีย" lang="et" hreflang="et" data-title="Raadius" data-language-autonym="Eesti" data-language-local-name="เอสโตเนีย" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Erradio_(geometria)" title="Erradio (geometria) – บาสก์" lang="eu" hreflang="eu" data-title="Erradio (geometria)" data-language-autonym="Euskara" data-language-local-name="บาสก์" 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%B4%D8%B9%D8%A7%D8%B9" title="شعاع – เปอร์เซีย" lang="fa" hreflang="fa" data-title="شعاع" data-language-autonym="فارسی" data-language-local-name="เปอร์เซีย" 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/S%C3%A4de_(geometria)" title="Säde (geometria) – ฟินแลนด์" lang="fi" hreflang="fi" data-title="Säde (geometria)" data-language-autonym="Suomi" data-language-local-name="ฟินแลนด์" 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/Rayon_(g%C3%A9om%C3%A9trie)" title="Rayon (géométrie) – ฝรั่งเศส" lang="fr" hreflang="fr" data-title="Rayon (géométrie)" data-language-autonym="Français" data-language-local-name="ฝรั่งเศส" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr badge-Q70894304 mw-list-item" title=""><a href="https://frr.wikipedia.org/wiki/Raadius" title="Raadius – ฟริเซียนเหนือ" lang="frr" hreflang="frr" data-title="Raadius" data-language-autonym="Nordfriisk" data-language-local-name="ฟริเซียนเหนือ" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Reidius" title="Reidius – เกลิกสกอต" lang="gd" hreflang="gd" data-title="Reidius" data-language-autonym="Gàidhlig" data-language-local-name="เกลิกสกอต" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Raio_(xeometr%C3%ADa)" title="Raio (xeometría) – กาลิเซีย" lang="gl" hreflang="gl" data-title="Raio (xeometría)" data-language-autonym="Galego" data-language-local-name="กาลิเซีย" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%A4%E0%AB%8D%E0%AA%B0%E0%AA%BF%E0%AA%9C%E0%AB%8D%E0%AA%AF%E0%AA%BE" title="ત્રિજ્યા – คุชราต" lang="gu" hreflang="gu" data-title="ત્રિજ્યા" data-language-autonym="ગુજરાતી" data-language-local-name="คุชราต" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A8%D7%93%D7%99%D7%95%D7%A1" title="רדיוס – ฮิบรู" lang="he" hreflang="he" data-title="רדיוס" data-language-autonym="עברית" data-language-local-name="ฮิบรู" 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%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="त्रिज्या – ฮินดี" lang="hi" hreflang="hi" data-title="त्रिज्या" data-language-autonym="हिन्दी" data-language-local-name="ฮินดี" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%87%D5%A1%D5%BC%D5%A1%D5%BE%D5%AB%D5%B2" title="Շառավիղ – อาร์เมเนีย" lang="hy" hreflang="hy" data-title="Շառավիղ" data-language-autonym="Հայերեն" data-language-local-name="อาร์เมเนีย" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Radio_(geometria)" title="Radio (geometria) – อินเตอร์ลิงกัว" lang="ia" hreflang="ia" data-title="Radio (geometria)" data-language-autonym="Interlingua" data-language-local-name="อินเตอร์ลิงกัว" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Jari-jari" title="Jari-jari – อินโดนีเซีย" lang="id" hreflang="id" data-title="Jari-jari" data-language-autonym="Bahasa Indonesia" data-language-local-name="อินโดนีเซีย" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%93%D3%80%D0%B0%D0%B9%D0%B8%D1%81%D1%82" title="ГӀайист – อินกุช" lang="inh" hreflang="inh" data-title="ГӀайист" data-language-autonym="ГӀалгӀай" data-language-local-name="อินกุช" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Geisli_(r%C3%BAmfr%C3%A6%C3%B0i)" title="Geisli (rúmfræði) – ไอซ์แลนด์" lang="is" hreflang="is" data-title="Geisli (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="ไอซ์แลนด์" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Raggio_(geometria)" title="Raggio (geometria) – อิตาลี" lang="it" hreflang="it" data-title="Raggio (geometria)" data-language-autonym="Italiano" data-language-local-name="อิตาลี" 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/%E5%8D%8A%E5%BE%84" title="半径 – ญี่ปุ่น" lang="ja" hreflang="ja" data-title="半径" data-language-autonym="日本語" data-language-local-name="ญี่ปุ่น" 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%A0%E1%83%90%E1%83%93%E1%83%98%E1%83%A3%E1%83%A1%E1%83%98" title="რადიუსი – จอร์เจีย" lang="ka" hreflang="ka" data-title="რადიუსი" data-language-autonym="ქართული" data-language-local-name="จอร์เจีย" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Aqqa%E1%B9%9B" title="Aqqaṛ – กาไบล" lang="kab" hreflang="kab" data-title="Aqqaṛ" data-language-autonym="Taqbaylit" data-language-local-name="กาไบล" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус – คาซัค" lang="kk" hreflang="kk" data-title="Радиус" data-language-autonym="Қазақша" data-language-local-name="คาซัค" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%80%E1%9E%B6%E1%9F%86" title="កាំ – เขมร" lang="km" hreflang="km" data-title="កាំ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="เขมร" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%98%EC%A7%80%EB%A6%84" title="반지름 – เกาหลี" lang="ko" hreflang="ko" data-title="반지름" data-language-autonym="한국어" data-language-local-name="เกาหลี" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81_(%D0%B0%D0%B9%D0%BB%D0%B0%D0%BD%D0%B0%D0%BD%D1%8B%D0%BD)" title="Радиус (айлананын) – คีร์กีซ" lang="ky" hreflang="ky" data-title="Радиус (айлананын)" data-language-autonym="Кыргызча" data-language-local-name="คีร์กีซ" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Radius" title="Radius – ลักเซมเบิร์ก" lang="lb" hreflang="lb" data-title="Radius" data-language-autonym="Lëtzebuergesch" data-language-local-name="ลักเซมเบิร์ก" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Apskritimo_spindulys" title="Apskritimo spindulys – ลิทัวเนีย" lang="lt" hreflang="lt" data-title="Apskritimo spindulys" data-language-autonym="Lietuvių" data-language-local-name="ลิทัวเนีย" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/R%C4%81diuss" title="Rādiuss – ลัตเวีย" lang="lv" hreflang="lv" data-title="Rādiuss" data-language-autonym="Latviešu" data-language-local-name="ลัตเวีย" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Tana_(je%C3%B4metria)" title="Tana (jeômetria) – มาลากาซี" lang="mg" hreflang="mg" data-title="Tana (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="มาลากาซี" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%83%D0%BF%D1%80%D0%B5%D1%87%D0%BD%D0%B8%D0%BA" title="Полупречник – มาซิโดเนีย" lang="mk" hreflang="mk" data-title="Полупречник" data-language-autonym="Македонски" data-language-local-name="มาซิโดเนีย" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%86%E0%B4%B0%E0%B4%82" title="ആരം – มาลายาลัม" lang="ml" hreflang="ml" data-title="ആരം" data-language-autonym="മലയാളം" data-language-local-name="มาลายาลัม" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус – มองโกเลีย" lang="mn" hreflang="mn" data-title="Радиус" data-language-autonym="Монгол" data-language-local-name="มองโกเลีย" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="त्रिज्या – มราฐี" lang="mr" hreflang="mr" data-title="त्रिज्या" data-language-autonym="मराठी" data-language-local-name="มราฐี" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Jejari" title="Jejari – มาเลย์" lang="ms" hreflang="ms" data-title="Jejari" data-language-autonym="Bahasa Melayu" data-language-local-name="มาเลย์" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%81%E1%80%BB%E1%80%84%E1%80%BA%E1%80%B8%E1%80%9D%E1%80%80%E1%80%BA" title="အချင်းဝက် – พม่า" lang="my" hreflang="my" data-title="အချင်းဝက်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="พม่า" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%85%E0%A4%B0%E0%A5%8D%E0%A4%A7%E0%A4%B5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%B8" title="अर्धव्यास – เนปาล" lang="ne" hreflang="ne" data-title="अर्धव्यास" data-language-autonym="नेपाली" data-language-local-name="เนปาล" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Straal_(wiskunde)" title="Straal (wiskunde) – ดัตช์" lang="nl" hreflang="nl" data-title="Straal (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="ดัตช์" 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/Radius" title="Radius – นอร์เวย์นีนอสก์" lang="nn" hreflang="nn" data-title="Radius" data-language-autonym="Norsk nynorsk" data-language-local-name="นอร์เวย์นีนอสก์" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Radius" title="Radius – นอร์เวย์บุคมอล" lang="nb" hreflang="nb" data-title="Radius" data-language-autonym="Norsk bokmål" data-language-local-name="นอร์เวย์บุคมอล" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Rai_(geometria)" title="Rai (geometria) – อ็อกซิตัน" lang="oc" hreflang="oc" data-title="Rai (geometria)" data-language-autonym="Occitan" data-language-local-name="อ็อกซิตัน" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Raadiyesii" title="Raadiyesii – โอโรโม" lang="om" hreflang="om" data-title="Raadiyesii" data-language-autonym="Oromoo" data-language-local-name="โอโรโม" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B0%E0%A9%87%E0%A8%A1%E0%A9%80%E0%A8%85%E0%A8%B8" title="ਰੇਡੀਅਸ – ปัญจาบ" lang="pa" hreflang="pa" data-title="ਰੇਡੀਅਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="ปัญจาบ" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Promie%C5%84_(geometria)" title="Promień (geometria) – โปแลนด์" lang="pl" hreflang="pl" data-title="Promień (geometria)" data-language-autonym="Polski" data-language-local-name="โปแลนด์" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B1%D8%AF%D8%A7%D8%B3" title="رداس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="رداس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Raio_(geometria)" title="Raio (geometria) – โปรตุเกส" lang="pt" hreflang="pt" data-title="Raio (geometria)" data-language-autonym="Português" data-language-local-name="โปรตุเกส" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Illwa" title="Illwa – เคชวา" lang="qu" hreflang="qu" data-title="Illwa" data-language-autonym="Runa Simi" data-language-local-name="เคชวา" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Raz%C4%83" title="Rază – โรมาเนีย" lang="ro" hreflang="ro" data-title="Rază" data-language-autonym="Română" data-language-local-name="โรมาเนีย" 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%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус – รัสเซีย" lang="ru" hreflang="ru" data-title="Радиус" data-language-autonym="Русский" data-language-local-name="รัสเซีย" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sc mw-list-item"><a href="https://sc.wikipedia.org/wiki/Raju_(geometria)" title="Raju (geometria) – ซาร์เดญา" lang="sc" hreflang="sc" data-title="Raju (geometria)" data-language-autonym="Sardu" data-language-local-name="ซาร์เดญา" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Radius" title="Radius – สกอตส์" lang="sco" hreflang="sco" data-title="Radius" data-language-autonym="Scots" data-language-local-name="สกอตส์" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Radijus" title="Radijus – เซอร์โบ-โครเอเชีย" lang="sh" hreflang="sh" data-title="Radijus" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="เซอร์โบ-โครเอเชีย" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%85%E0%B6%BB%E0%B6%BA" title="අරය – สิงหล" lang="si" hreflang="si" data-title="අරය" data-language-autonym="සිංහල" data-language-local-name="สิงหล" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Radius" title="Radius – Simple English" lang="en-simple" hreflang="en-simple" data-title="Radius" 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/Polomer_(kru%C5%BEnica)" title="Polomer (kružnica) – สโลวัก" lang="sk" hreflang="sk" data-title="Polomer (kružnica)" data-language-autonym="Slovenčina" data-language-local-name="สโลวัก" 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/Polmer" title="Polmer – สโลวีเนีย" lang="sl" hreflang="sl" data-title="Polmer" data-language-autonym="Slovenščina" data-language-local-name="สโลวีเนีย" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Taramunyongo" title="Taramunyongo – โชนา" lang="sn" hreflang="sn" data-title="Taramunyongo" data-language-autonym="ChiShona" data-language-local-name="โชนา" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Gacan_(Joomitiri)" title="Gacan (Joomitiri) – โซมาลี" lang="so" hreflang="so" data-title="Gacan (Joomitiri)" data-language-autonym="Soomaaliga" data-language-local-name="โซมาลี" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Rrezja" title="Rrezja – แอลเบเนีย" lang="sq" hreflang="sq" data-title="Rrezja" data-language-autonym="Shqip" data-language-local-name="แอลเบเนีย" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%83%D0%BF%D1%80%D0%B5%D1%87%D0%BD%D0%B8%D0%BA" title="Полупречник – เซอร์เบีย" lang="sr" hreflang="sr" data-title="Полупречник" data-language-autonym="Српски / srpski" data-language-local-name="เซอร์เบีย" 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/Radie" title="Radie – สวีเดน" lang="sv" hreflang="sv" data-title="Radie" data-language-autonym="Svenska" data-language-local-name="สวีเดน" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Nusukipenyo" title="Nusukipenyo – สวาฮีลี" lang="sw" hreflang="sw" data-title="Nusukipenyo" data-language-autonym="Kiswahili" data-language-local-name="สวาฮีลี" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Pr%C5%8Dmiy%C5%84_(geometryj%C5%8F)" title="Prōmiyń (geometryjŏ) – ไซลีเซีย" lang="szl" hreflang="szl" data-title="Prōmiyń (geometryjŏ)" data-language-autonym="Ślůnski" data-language-local-name="ไซลีเซีย" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%86%E0%AE%B0%E0%AE%AE%E0%AF%8D,_%E0%AE%B5%E0%AE%9F%E0%AE%BF%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="ஆரம், வடிவியல் – ทมิฬ" lang="ta" hreflang="ta" data-title="ஆரம், வடிவியல்" data-language-autonym="தமிழ்" data-language-local-name="ทมิฬ" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%B5%E0%B1%8D%E0%B0%AF%E0%B0%BE%E0%B0%B8%E0%B0%BE%E0%B0%B0%E0%B1%8D%E0%B0%A5%E0%B0%AE%E0%B1%81" title="వ్యాసార్థము – เตลูกู" lang="te" hreflang="te" data-title="వ్యాసార్థము" data-language-autonym="తెలుగు" data-language-local-name="เตลูกู" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Radius" title="Radius – ตากาล็อก" lang="tl" hreflang="tl" data-title="Radius" data-language-autonym="Tagalog" data-language-local-name="ตากาล็อก" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Yar%C4%B1%C3%A7ap" title="Yarıçap – ตุรกี" lang="tr" hreflang="tr" data-title="Yarıçap" data-language-autonym="Türkçe" data-language-local-name="ตุรกี" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D0%B8%D1%83%D1%81" title="Радиус – ตาตาร์" lang="tt" hreflang="tt" data-title="Радиус" data-language-autonym="Татарча / tatarça" data-language-local-name="ตาตาร์" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B4%D1%96%D1%83%D1%81" title="Радіус – ยูเครน" lang="uk" hreflang="uk" data-title="Радіус" data-language-autonym="Українська" data-language-local-name="ยูเครน" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B1%D8%AF%D8%A7%D8%B3" title="رداس – อูรดู" lang="ur" hreflang="ur" data-title="رداس" data-language-autonym="اردو" data-language-local-name="อูรดู" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Radius" title="Radius – อุซเบก" lang="uz" hreflang="uz" data-title="Radius" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="อุซเบก" 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/B%C3%A1n_k%C3%ADnh" title="Bán kính – เวียดนาม" lang="vi" hreflang="vi" data-title="Bán kính" data-language-autonym="Tiếng Việt" data-language-local-name="เวียดนาม" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8D%8A%E5%BE%84" title="半径 – จีนอู๋" lang="wuu" hreflang="wuu" data-title="半径" data-language-autonym="吴语" data-language-local-name="จีนอู๋" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A8%D7%90%D7%93%D7%99%D7%95%D7%A1" title="ראדיוס – ยิดดิช" lang="yi" hreflang="yi" data-title="ראדיוס" data-language-autonym="ייִדיש" data-language-local-name="ยิดดิช" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/%C3%8Cd%C3%A1m%C3%A9j%C3%AC_%C3%B2b%C3%ACr%C3%ACk%C3%ACti%C3%AC" title="Ìdáméjì òbìrìkìtiì – โยรูบา" lang="yo" hreflang="yo" data-title="Ìdáméjì òbìrìkìtiì" data-language-autonym="Yorùbá" data-language-local-name="โยรูบา" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8D%8A%E5%BE%84" title="半径 – จีน" lang="zh" hreflang="zh" data-title="半径" data-language-autonym="中文" data-language-local-name="จีน" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Po%C3%A0%E2%81%BF-k%C3%A8ng" title="Poàⁿ-kèng – จีนมินหนาน" lang="nan" hreflang="nan" data-title="Poàⁿ-kèng" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="จีนมินหนาน" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8D%8A%E5%BE%91" title="半徑 – กวางตุ้ง" lang="yue" hreflang="yue" data-title="半徑" data-language-autonym="粵語" data-language-local-name="กวางตุ้ง" 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/Q173817#sitelinks-wikipedia" title="แก้ไขลิงก์ข้ามภาษา" class="wbc-editpage">แก้ไขลิงก์</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="เนมสเปซ"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5" title="ดูหน้าเนื้อหา [c]" accesskey="c"><span>บทความ</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B9%E0%B8%94%E0%B8%84%E0%B8%B8%E0%B8%A2:%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5" rel="discussion" title="อภิปรายเกี่ยวกับหน้าเนื้อหา [t]" accesskey="t"><span>อภิปราย</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="เปลี่ยนรูปแบบภาษา" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">ไทย</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="ดู"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5"><span>อ่าน</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=edit" title="แก้ไขรหัสต้นฉบับของหน้านี้ [e]" accesskey="e"><span>แก้ไข</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=history" title="แก้ไขเก่าของหน้านี้ [h]" accesskey="h"><span>ดูประวัติ</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="หน้าเครื่องมือ"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="เครื่องมือ" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button 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data-event-name="pinnable-header.vector-page-tools.unpin">ซ่อน</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="ตัวเลือกเพิ่มเติม" > <div class="vector-menu-heading"> การกระทำ </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5"><span>อ่าน</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=edit" title="แก้ไขรหัสต้นฉบับของหน้านี้ [e]" accesskey="e"><span>แก้ไข</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=history"><span>ดูประวัติ</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> ทั่วไป </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%9A%E0%B8%97%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B9%82%E0%B8%A2%E0%B8%87%E0%B8%A1%E0%B8%B2/%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5" title="รายการหน้าวิกิทุกหน้าที่ลิงก์มาที่นี่ [j]" accesskey="j"><span>หน้าที่ลิงก์มา</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9B%E0%B8%A3%E0%B8%B1%E0%B8%9A%E0%B8%9B%E0%B8%A3%E0%B8%B8%E0%B8%87%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B9%82%E0%B8%A2%E0%B8%87%E0%B8%A1%E0%B8%B2/%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5" rel="nofollow" title="รายการเปลี่ยนแปลงล่าสุดในหน้าที่ลิงก์จากหน้านี้ [k]" accesskey="k"><span>การเปลี่ยนแปลงที่เกี่ยวโยง</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/%E0%B8%A7%E0%B8%B4%E0%B8%81%E0%B8%B4%E0%B8%9E%E0%B8%B5%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2:%E0%B8%AD%E0%B8%B1%E0%B8%9B%E0%B9%82%E0%B8%AB%E0%B8%A5%E0%B8%94" title="อัปโหลดไฟล์ [u]" accesskey="u"><span>อัปโหลดไฟล์</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AB%E0%B8%99%E0%B9%89%E0%B8%B2%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9" title="รายการหน้าพิเศษทั้งหมด [q]" accesskey="q"><span>หน้าพิเศษ</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&oldid=11810508" title="ลิงก์ถาวรมารุ่นนี้ของหน้านี้"><span>ลิงก์ถาวร</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=info" title="ข้อมูลเพิ่มเติมเกี่ยวกับหน้านี้"><span>สารสนเทศหน้า</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AD%E0%B9%89%E0%B8%B2%E0%B8%87%E0%B8%AD%E0%B8%B4%E0%B8%87&page=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&id=11810508&wpFormIdentifier=titleform" title="สารสนเทศเกี่ยวกับวิธีการอ้างอิงหน้านี้"><span>อ้างอิงบทความนี้</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:UrlShortener&url=https%3A%2F%2Fth.wikipedia.org%2Fwiki%2F%25E0%25B8%25A3%25E0%25B8%25B1%25E0%25B8%25A8%25E0%25B8%25A1%25E0%25B8%25B5"><span>รับยูอาร์แอลแบบสั้น</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:QrCode&url=https%3A%2F%2Fth.wikipedia.org%2Fwiki%2F%25E0%25B8%25A3%25E0%25B8%25B1%25E0%25B8%25A8%25E0%25B8%25A1%25E0%25B8%25B5"><span>ดาวน์โหลดคิวอาร์โค้ด</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> พิมพ์/ส่งออก </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:%E0%B8%AB%E0%B8%99%E0%B8%B1%E0%B8%87%E0%B8%AA%E0%B8%B7%E0%B8%AD&bookcmd=book_creator&referer=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5"><span>สร้างหนังสือ</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B4%E0%B9%80%E0%B8%A8%E0%B8%A9:DownloadAsPdf&page=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=show-download-screen"><span>ดาวน์โหลดเป็น PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&printable=yes" title="รุ่นที่พร้อมพิมพ์ของหน้านี้ [p]" accesskey="p"><span>รุ่นพร้อมพิมพ์</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"> ในโครงการอื่น </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/Radius" hreflang="en"><span>วิกิมีเดียคอมมอนส์</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/Q173817" title="ลิงก์ไปยังสิ่งนี้ในคลังซึ่งเชื่อมโยงข้อมูลต่าง ๆ เข้าด้วยกัน [g]" accesskey="g"><span>สิ่งนี้ในวิกิสนเทศ</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="หน้าเครื่องมือ"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="หน้าตา"> <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">หน้าตา</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">ย้ายเมนูไปที่แถบด้านข้าง</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ซ่อน</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">จากวิกิพีเดีย สารานุกรมเสรี</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="th" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r9751016">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}</style><div role="note" class="hatnote navigation-not-searchable">"radius" เปลี่ยนทางมาที่นี่ บทความนี้เกี่ยวกับเราขาคณิต สำหรับกระดูกมนุษย์ ดูที่ <a href="/wiki/%E0%B8%81%E0%B8%A3%E0%B8%B0%E0%B8%94%E0%B8%B9%E0%B8%81%E0%B9%80%E0%B8%A3%E0%B9%80%E0%B8%94%E0%B8%B5%E0%B8%A2%E0%B8%AA" title="กระดูกเรเดียส">กระดูกเรเดียส</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:CIRCLE_1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/CIRCLE_1.svg/220px-CIRCLE_1.svg.png" decoding="async" width="220" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/CIRCLE_1.svg/330px-CIRCLE_1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/CIRCLE_1.svg/440px-CIRCLE_1.svg.png 2x" data-file-width="612" data-file-height="618" /></a><figcaption>รูปวงกลมที่แสดงถึงรัศมี เส้นผ่านศูนย์กลาง จุดศูนย์กลาง และเส้นรอบวง</figcaption></figure> <p><b>รัศมี</b> (<a href="/wiki/%E0%B8%A0%E0%B8%B2%E0%B8%A9%E0%B8%B2%E0%B8%AD%E0%B8%B1%E0%B8%87%E0%B8%81%E0%B8%A4%E0%B8%A9" title="ภาษาอังกฤษ">อังกฤษ</a>: radius พหูพจน์: radii) ของ<a href="/wiki/%E0%B8%A3%E0%B8%B9%E0%B8%9B%E0%B8%A7%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%A1" title="รูปวงกลม">รูปวงกลม</a>หรือ<a href="/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%A1" title="ทรงกลม">ทรงกลม</a> คือ<a href="/wiki/%E0%B8%AA%E0%B9%88%E0%B8%A7%E0%B8%99%E0%B8%82%E0%B8%AD%E0%B8%87%E0%B9%80%E0%B8%AA%E0%B9%89%E0%B8%99%E0%B8%95%E0%B8%A3%E0%B8%87" title="ส่วนของเส้นตรง">ส่วนของเส้นตรง</a>ใดๆ ที่เชื่อมต่อระหว่าง<a href="/w/index.php?title=%E0%B8%88%E0%B8%B8%E0%B8%94%E0%B8%A8%E0%B8%B9%E0%B8%99%E0%B8%A2%E0%B9%8C%E0%B8%81%E0%B8%A5%E0%B8%B2%E0%B8%87&action=edit&redlink=1" class="new" title="จุดศูนย์กลาง (ไม่มีหน้านี้)">จุดศูนย์กลาง</a> ไปยัง<a href="/wiki/%E0%B9%80%E0%B8%AA%E0%B9%89%E0%B8%99%E0%B8%A3%E0%B8%AD%E0%B8%9A%E0%B8%A7%E0%B8%87" title="เส้นรอบวง">เส้นรอบวง</a>หรือพื้นผิวของทรงกลม อีกนัยหนึ่งหมายถึง<a href="/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%A2%E0%B8%B2%E0%B8%A7" title="ความยาว">ความยาว</a>ของส่วนของเส้นตรงนั้น รัศมีเป็นส่วนครึ่งหนึ่งของ<a href="/wiki/%E0%B9%80%E0%B8%AA%E0%B9%89%E0%B8%99%E0%B8%9C%E0%B9%88%E0%B8%B2%E0%B8%99%E0%B8%A8%E0%B8%B9%E0%B8%99%E0%B8%A2%E0%B9%8C%E0%B8%81%E0%B8%A5%E0%B8%B2%E0%B8%87" title="เส้นผ่านศูนย์กลาง">เส้นผ่านศูนย์กลาง</a> ในทางวิทยาศาสตร์และวิศวกรรมศาสตร์ มีการใช้คำว่า <a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B9%82%E0%B8%84%E0%B9%89%E0%B8%87&action=edit&redlink=1" class="new" title="รัศมีความโค้ง (ไม่มีหน้านี้)">รัศมีความโค้ง</a> (radius of curvature) แทนความหมายที่คล้ายกับรัศมี </p><p>ในกรณีทั่วไปที่ไม่ใช่สำหรับรูปวงกลมหรือทรงกลม อาทิ <a href="/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%81%E0%B8%A3%E0%B8%B0%E0%B8%9A%E0%B8%AD%E0%B8%81" title="ทรงกระบอก">ทรงกระบอก</a> <a href="/wiki/%E0%B8%A3%E0%B8%B9%E0%B8%9B%E0%B8%AB%E0%B8%A5%E0%B8%B2%E0%B8%A2%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A1" title="รูปหลายเหลี่ยม">รูปหลายเหลี่ยม</a> <a href="/wiki/%E0%B8%81%E0%B8%A3%E0%B8%B2%E0%B8%9F" class="mw-disambig" title="กราฟ">กราฟ</a> หรือชิ้นส่วนจักรกลต่างๆ รัศมีสามารถหมายถึง<a href="/wiki/%E0%B8%A3%E0%B8%B0%E0%B8%A2%E0%B8%B0%E0%B8%97%E0%B8%B2%E0%B8%87" title="ระยะทาง">ระยะทาง</a>ที่วัดจาก<a href="/wiki/%E0%B8%88%E0%B8%B8%E0%B8%94%E0%B8%81%E0%B8%B6%E0%B9%88%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%B2%E0%B8%87" title="จุดกึ่งกลาง">จุดกึ่งกลาง</a>หรือ<a href="/w/index.php?title=%E0%B9%81%E0%B8%81%E0%B8%99%E0%B8%AA%E0%B8%A1%E0%B8%A1%E0%B8%B2%E0%B8%95%E0%B8%A3&action=edit&redlink=1" class="new" title="แกนสมมาตร (ไม่มีหน้านี้)">แกนสมมาตร</a>ไปยังจุดอื่นที่อยู่ภายนอก ซึ่งในกรณีนี้รัศมีอาจมีความยาวมากกว่าครึ่งหนึ่งของเส้นผ่านศูนย์กลางก็ได้ </p><p>ความสัมพันธ์ระหว่างรัศมี <i>r</i> กับเส้นรอบวง <i>c</i> ของรูปวงกลมคือ </p> <dl><dd><dl><dd><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 r={\frac {c}{2\pi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mrow> <mn>2</mn> <mi>π<!-- π --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {c}{2\pi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0629e741fc986f41a34efcbd5bb413a85a0bb81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.478ex; height:4.676ex;" alt="{\displaystyle r={\frac {c}{2\pi }}}"></span></dd></dl></dd></dl> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="รัศมีจากพื้นที่"><span id=".E0.B8.A3.E0.B8.B1.E0.B8.A8.E0.B8.A1.E0.B8.B5.E0.B8.88.E0.B8.B2.E0.B8.81.E0.B8.9E.E0.B8.B7.E0.B9.89.E0.B8.99.E0.B8.97.E0.B8.B5.E0.B9.88"></span>รัศมีจากพื้นที่</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=edit&section=1" title="แก้ไขส่วน: รัศมีจากพื้นที่"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>รัศมีของวงกลมที่มีพื้นที่เป็น <i>A</i> คือ </p> <dl><dd><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 r={\sqrt {\frac {A}{\pi }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mi>A</mi> <mi>π<!-- π --></mi> </mfrac> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\sqrt {\frac {A}{\pi }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f2db8947fd41608098e3654a7444aaa6bf1b932" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.697ex; height:6.343ex;" alt="{\displaystyle r={\sqrt {\frac {A}{\pi }}}.}"></span></dd></dl> <p>รัศมีเป็นครึ่งหนึ่งของเส้นผ่าศูนย์กลาง </p> <div class="mw-heading mw-heading2"><h2 id="รัศมีจากจุดสามจุด"><span id=".E0.B8.A3.E0.B8.B1.E0.B8.A8.E0.B8.A1.E0.B8.B5.E0.B8.88.E0.B8.B2.E0.B8.81.E0.B8.88.E0.B8.B8.E0.B8.94.E0.B8.AA.E0.B8.B2.E0.B8.A1.E0.B8.88.E0.B8.B8.E0.B8.94"></span>รัศมีจากจุดสามจุด</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=edit&section=2" title="แก้ไขส่วน: รัศมีจากจุดสามจุด"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>ความยาวรัศมีของรูปวงกลมที่ผ่านจุดสามจุดใดๆ <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 P_{1},P_{2},P_{3}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{1},P_{2},P_{3}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6496aa54a239e79ccaabd1618355ad058c6bdcc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:10.094ex; height:2.509ex;" alt="{\displaystyle P_{1},P_{2},P_{3}\,\!}"></span> ที่ไม่อยู่บนเส้นตรงเดียวกัน คำนวณได้จาก </p> <dl><dd><dl><dd><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 r={\frac {|P_{1}-P_{3}|}{2\sin \theta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−<!-- − --></mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {|P_{1}-P_{3}|}{2\sin \theta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4bb7a8cf7955d05cee5de1a2b82bbce501feb9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:14.21ex; height:5.843ex;" alt="{\displaystyle r={\frac {|P_{1}-P_{3}|}{2\sin \theta }}}"></span></dd></dl></dd></dl> <p>โดยที่ <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 \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ<!-- θ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> คือขนาดของมุม <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 \angle P_{1}P_{2}P_{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∠<!-- ∠ --></mi> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \angle P_{1}P_{2}P_{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38408ea9d8a8aacccd4c22b6e729152db7d58cf2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.318ex; height:2.509ex;" alt="{\displaystyle \angle P_{1}P_{2}P_{3}}"></span> </p><p>สูตรต่อไปนี้ใช้กฎของไซน์ </p><p>ถ้าจุดสามจุดกำหนดให้มีพิกัด <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 (x_{1},y_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{1},y_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fc74086e56542bd28b46a84faaee3cebdd4a899" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.421ex; height:2.843ex;" alt="{\displaystyle (x_{1},y_{1})}"></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 (x_{2},y_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{2},y_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d52d44e16a796acee486af49af05f678566d181a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.421ex; height:2.843ex;" alt="{\displaystyle (x_{2},y_{2})}"></span> และ <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 (x_{3},y_{3})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{3},y_{3})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3f4325abeb2792b97969c8ebcf2b65a1e17d3c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.421ex; height:2.843ex;" alt="{\displaystyle (x_{3},y_{3})}"></span>, ดังนั้นจะสามารถใช้สูตรดังต่อไปนี้: </p> <dl><dd><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 r={\frac {\sqrt {\left(\left({\it {x_{2}}}-{\it {x_{1}}}\right)^{2}+\left({\it {y_{2}}}-{\it {y_{1}}}\right)^{2}\right)\left(\left({\it {x_{2}}}-{\it {x_{3}}}\right)^{2}+\left({\it {y_{2}}}-{\it {y_{3}}}\right)^{2}\right)\left(\left({\it {x_{3}}}-{\it {x_{1}}}\right)^{2}+\left({\it {y_{3}}}-{\it {y_{1}}}\right)^{2}\right)}}{2\left|{\it {x_{1}}}\,{\it {y_{2}}}+{\it {x_{2}}}\,{\it {y_{3}}}+{\it {x_{3}}}\,{\it {y_{1}}}-{\it {x_{1}}}\,{\it {y_{3}}}-{\it {x_{2}}}\,{\it {y_{1}}}-{\it {x_{3}}}\,{\it {y_{2}}}\right|}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mrow> <mo>(</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">2</mn> </mrow> </msub> </mrow> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">1</mn> </mrow> </msub> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">2</mn> </mrow> </msub> </mrow> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">1</mn> </mrow> </msub> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">2</mn> </mrow> </msub> </mrow> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">3</mn> </mrow> </msub> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">2</mn> </mrow> </msub> </mrow> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">3</mn> </mrow> </msub> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">3</mn> </mrow> </msub> </mrow> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">1</mn> </mrow> </msub> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">3</mn> </mrow> </msub> </mrow> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">1</mn> </mrow> </msub> </mrow> </mrow> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </msqrt> <mrow> <mn>2</mn> <mrow> <mo>|</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">1</mn> </mrow> </msub> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">2</mn> </mrow> </msub> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">2</mn> </mrow> </msub> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">3</mn> </mrow> </msub> </mrow> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">3</mn> </mrow> </msub> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">1</mn> </mrow> </msub> </mrow> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">1</mn> </mrow> </msub> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">3</mn> </mrow> </msub> </mrow> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">2</mn> </mrow> </msub> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">1</mn> </mrow> </msub> </mrow> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">3</mn> </mrow> </msub> </mrow> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi class="MJX-tex-mathit" mathvariant="italic">y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn class="MJX-tex-mathit" mathvariant="italic">2</mn> </mrow> </msub> </mrow> </mrow> </mrow> <mo>|</mo> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {\sqrt {\left(\left({\it {x_{2}}}-{\it {x_{1}}}\right)^{2}+\left({\it {y_{2}}}-{\it {y_{1}}}\right)^{2}\right)\left(\left({\it {x_{2}}}-{\it {x_{3}}}\right)^{2}+\left({\it {y_{2}}}-{\it {y_{3}}}\right)^{2}\right)\left(\left({\it {x_{3}}}-{\it {x_{1}}}\right)^{2}+\left({\it {y_{3}}}-{\it {y_{1}}}\right)^{2}\right)}}{2\left|{\it {x_{1}}}\,{\it {y_{2}}}+{\it {x_{2}}}\,{\it {y_{3}}}+{\it {x_{3}}}\,{\it {y_{1}}}-{\it {x_{1}}}\,{\it {y_{3}}}-{\it {x_{2}}}\,{\it {y_{1}}}-{\it {x_{3}}}\,{\it {y_{2}}}\right|}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b3d3042e5fa738edd4ce8cee28adf29abb5f35c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:85.273ex; height:9.843ex;" alt="{\displaystyle r={\frac {\sqrt {\left(\left({\it {x_{2}}}-{\it {x_{1}}}\right)^{2}+\left({\it {y_{2}}}-{\it {y_{1}}}\right)^{2}\right)\left(\left({\it {x_{2}}}-{\it {x_{3}}}\right)^{2}+\left({\it {y_{2}}}-{\it {y_{3}}}\right)^{2}\right)\left(\left({\it {x_{3}}}-{\it {x_{1}}}\right)^{2}+\left({\it {y_{3}}}-{\it {y_{1}}}\right)^{2}\right)}}{2\left|{\it {x_{1}}}\,{\it {y_{2}}}+{\it {x_{2}}}\,{\it {y_{3}}}+{\it {x_{3}}}\,{\it {y_{1}}}-{\it {x_{1}}}\,{\it {y_{3}}}-{\it {x_{2}}}\,{\it {y_{1}}}-{\it {x_{3}}}\,{\it {y_{2}}}\right|}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="สูตรสำหรับรูปหลายเหลี่ยมปกติ"><span id=".E0.B8.AA.E0.B8.B9.E0.B8.95.E0.B8.A3.E0.B8.AA.E0.B8.B3.E0.B8.AB.E0.B8.A3.E0.B8.B1.E0.B8.9A.E0.B8.A3.E0.B8.B9.E0.B8.9B.E0.B8.AB.E0.B8.A5.E0.B8.B2.E0.B8.A2.E0.B9.80.E0.B8.AB.E0.B8.A5.E0.B8.B5.E0.B9.88.E0.B8.A2.E0.B8.A1.E0.B8.9B.E0.B8.81.E0.B8.95.E0.B8.B4"></span>สูตรสำหรับรูปหลายเหลี่ยมปกติ</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=edit&section=3" title="แก้ไขส่วน: สูตรสำหรับรูปหลายเหลี่ยมปกติ"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>สูตรเหล่านี้ถือว่าเป็นรูปหลายเหลี่ยมปกติกับด้าน <i>n</i> ด้าน </p> <div class="mw-heading mw-heading3"><h3 id="รัศมีจากด้านข้าง"><span id=".E0.B8.A3.E0.B8.B1.E0.B8.A8.E0.B8.A1.E0.B8.B5.E0.B8.88.E0.B8.B2.E0.B8.81.E0.B8.94.E0.B9.89.E0.B8.B2.E0.B8.99.E0.B8.82.E0.B9.89.E0.B8.B2.E0.B8.87"></span>รัศมีจากด้านข้าง</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=edit&section=4" title="แก้ไขส่วน: รัศมีจากด้านข้าง"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>รัศมีสามารถคำนวณได้จากด้าน s โดย: </p> <dl><dd><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 r=R_{n}\,s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=R_{n}\,s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6dfda67bc650c5be6d63d9be7d7616557260eba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.607ex; height:2.509ex;" alt="{\displaystyle r=R_{n}\,s}"></span>    เมื่อ   <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 R_{n}={\frac {1}{2\sin {\frac {\pi }{n}}}}\quad \quad {\begin{array}{r|ccr|c}n&R_{n}&&n&R_{n}\\\hline 2&0.50000000&&10&1.6180340-\\3&0.5773503-&&11&1.7747328-\\4&0.7071068-&&12&1.9318517-\\5&0.8506508+&&13&2.0892907+\\6&1.00000000&&14&2.2469796+\\7&1.1523824+&&15&2.4048672-\\8&1.3065630-&&16&2.5629154+\\9&1.4619022+&&17&2.7210956-\end{array}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>sin</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π<!-- π --></mi> <mi>n</mi> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mspace width="1em" /> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right center center right center" rowspacing="4pt" columnspacing="1em" rowlines="solid none" columnlines="solid none none solid"> <mtr> <mtd> <mi>n</mi> </mtd> <mtd> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mtd> <mtd /> <mtd> <mi>n</mi> </mtd> <mtd> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mn>0.50000000</mn> </mtd> <mtd /> <mtd> <mn>10</mn> </mtd> <mtd> <mn>1.6180340</mn> <mo>−<!-- − --></mo> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>0.5773503</mn> <mo>−<!-- − --></mo> </mtd> <mtd /> <mtd> <mn>11</mn> </mtd> <mtd> <mn>1.7747328</mn> <mo>−<!-- − --></mo> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> <mtd> <mn>0.7071068</mn> <mo>−<!-- − --></mo> </mtd> <mtd /> <mtd> <mn>12</mn> </mtd> <mtd> <mn>1.9318517</mn> <mo>−<!-- − --></mo> </mtd> </mtr> <mtr> <mtd> <mn>5</mn> </mtd> <mtd> <mn>0.8506508</mn> <mo>+</mo> </mtd> <mtd /> <mtd> <mn>13</mn> </mtd> <mtd> <mn>2.0892907</mn> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mn>6</mn> </mtd> <mtd> <mn>1.00000000</mn> </mtd> <mtd /> <mtd> <mn>14</mn> </mtd> <mtd> <mn>2.2469796</mn> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mn>7</mn> </mtd> <mtd> <mn>1.1523824</mn> <mo>+</mo> </mtd> <mtd /> <mtd> <mn>15</mn> </mtd> <mtd> <mn>2.4048672</mn> <mo>−<!-- − --></mo> </mtd> </mtr> <mtr> <mtd> <mn>8</mn> </mtd> <mtd> <mn>1.3065630</mn> <mo>−<!-- − --></mo> </mtd> <mtd /> <mtd> <mn>16</mn> </mtd> <mtd> <mn>2.5629154</mn> <mo>+</mo> </mtd> </mtr> <mtr> <mtd> <mn>9</mn> </mtd> <mtd> <mn>1.4619022</mn> <mo>+</mo> </mtd> <mtd /> <mtd> <mn>17</mn> </mtd> <mtd> <mn>2.7210956</mn> <mo>−<!-- − --></mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{n}={\frac {1}{2\sin {\frac {\pi }{n}}}}\quad \quad {\begin{array}{r|ccr|c}n&R_{n}&&n&R_{n}\\\hline 2&0.50000000&&10&1.6180340-\\3&0.5773503-&&11&1.7747328-\\4&0.7071068-&&12&1.9318517-\\5&0.8506508+&&13&2.0892907+\\6&1.00000000&&14&2.2469796+\\7&1.1523824+&&15&2.4048672-\\8&1.3065630-&&16&2.5629154+\\9&1.4619022+&&17&2.7210956-\end{array}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc7cc72e08f07fd0b386392dec631f474e1a0f72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -14.338ex; width:57.306ex; height:29.843ex;" alt="{\displaystyle R_{n}={\frac {1}{2\sin {\frac {\pi }{n}}}}\quad \quad {\begin{array}{r|ccr|c}n&R_{n}&&n&R_{n}\\\hline 2&0.50000000&&10&1.6180340-\\3&0.5773503-&&11&1.7747328-\\4&0.7071068-&&12&1.9318517-\\5&0.8506508+&&13&2.0892907+\\6&1.00000000&&14&2.2469796+\\7&1.1523824+&&15&2.4048672-\\8&1.3065630-&&16&2.5629154+\\9&1.4619022+&&17&2.7210956-\end{array}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="สูตรสำหรับไฮเพอร์คิวบ์_(hypercubes)"><span id=".E0.B8.AA.E0.B8.B9.E0.B8.95.E0.B8.A3.E0.B8.AA.E0.B8.B3.E0.B8.AB.E0.B8.A3.E0.B8.B1.E0.B8.9A.E0.B9.84.E0.B8.AE.E0.B9.80.E0.B8.9E.E0.B8.AD.E0.B8.A3.E0.B9.8C.E0.B8.84.E0.B8.B4.E0.B8.A7.E0.B8.9A.E0.B9.8C_.28hypercubes.29"></span>สูตรสำหรับไฮเพอร์คิวบ์ (hypercubes)</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=edit&section=5" title="แก้ไขส่วน: สูตรสำหรับไฮเพอร์คิวบ์ (hypercubes)"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="รัศมีจากด้านข้าง_2"><span id=".E0.B8.A3.E0.B8.B1.E0.B8.A8.E0.B8.A1.E0.B8.B5.E0.B8.88.E0.B8.B2.E0.B8.81.E0.B8.94.E0.B9.89.E0.B8.B2.E0.B8.99.E0.B8.82.E0.B9.89.E0.B8.B2.E0.B8.87_2"></span>รัศมีจากด้านข้าง</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%A3%E0%B8%B1%E0%B8%A8%E0%B8%A1%E0%B8%B5&action=edit&section=6" title="แก้ไขส่วน: รัศมีจากด้านข้าง"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>รัศมีของไฮเพอร์คิวบ์ d มิติที่มีด้าน s คือ </p> <dl><dd><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 r={\frac {s}{2}}{\sqrt {d}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>s</mi> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>d</mi> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {s}{2}}{\sqrt {d}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/176da9e23c0b9fdab7190f97a62d26ddfad7b9b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.944ex; height:4.676ex;" alt="{\displaystyle r={\frac {s}{2}}{\sqrt {d}}.}"></span></dd></dl> <style data-mw-deduplicate="TemplateStyles:r9895811">.mw-parser-output .asbox{position:relative;overflow:hidden}.mw-parser-output .asbox 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