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class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="ไซต์"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="เมนูหลัก" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">เมนูหลัก</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu 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id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="หน้าตา"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="หน้าตา" > <label id="vector-appearance-dropdown-label" for="vector-appearance-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">หน้าตา</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="//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%97%E0%B8%A3%E0%B8%87%E0%B8%A3%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%97%E0%B8%A3%E0%B8%87%E0%B8%A3%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%97%E0%B8%A3%E0%B8%87%E0%B8%A3%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%97%E0%B8%A3%E0%B8%87%E0%B8%A3%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"></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-ปริมาตร" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ปริมาตร"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>ปริมาตร</span> </div> </a> <ul id="toc-ปริมาตร-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-พื้นที่ผิว" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#พื้นที่ผิว"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>พื้นที่ผิว</span> </div> </a> <ul id="toc-พื้นที่ผิว-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="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">ทรงรี</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 54 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-54" 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">54 ภาษา</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%B3%D8%B7%D8%AD_%D9%86%D8%A7%D9%82%D8%B5%D9%8A" title="سطح ناقصي – อาหรับ" lang="ar" hreflang="ar" data-title="سطح ناقصي" 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/Elipsoide_de_revoluci%C3%B3n" title="Elipsoide de revolución – อัสตูเรียส" lang="ast" hreflang="ast" data-title="Elipsoide de revolución" 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/Ellipsoid" title="Ellipsoid – อาเซอร์ไบจาน" lang="az" hreflang="az" data-title="Ellipsoid" data-language-autonym="Azərbaycanca" data-language-local-name="อาเซอร์ไบจาน" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BB%D1%96%D0%BF%D1%81%D0%BE%D1%96%D0%B4" title="Эліпсоід – เบลารุส" lang="be" hreflang="be" data-title="Эліпсоід" data-language-autonym="Беларуская" data-language-local-name="เบลารุส" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Елипсоид – บัลแกเรีย" lang="bg" hreflang="bg" data-title="Елипсоид" data-language-autonym="Български" data-language-local-name="บัลแกเรีย" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/El%C2%B7lipsoide" title="El·lipsoide – คาตาลัน" lang="ca" hreflang="ca" data-title="El·lipsoide" data-language-autonym="Català" data-language-local-name="คาตาลัน" 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/Elipsoid" title="Elipsoid – เช็ก" lang="cs" hreflang="cs" data-title="Elipsoid" 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%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Эллипсоид – ชูวัช" lang="cv" hreflang="cv" data-title="Эллипсоид" 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/Elipsoid" title="Elipsoid – เวลส์" lang="cy" hreflang="cy" data-title="Elipsoid" 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/Ellipsoide" title="Ellipsoide – เดนมาร์ก" lang="da" hreflang="da" data-title="Ellipsoide" 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/Ellipsoid" title="Ellipsoid – เยอรมัน" lang="de" hreflang="de" data-title="Ellipsoid" 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%95%CE%BB%CE%BB%CE%B5%CE%B9%CF%88%CE%BF%CE%B5%CE%B9%CE%B4%CE%AE" title="Ελλειψοειδή – กรีก" lang="el" hreflang="el" data-title="Ελλειψοειδή" data-language-autonym="Ελληνικά" data-language-local-name="กรีก" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid – อังกฤษ" lang="en" hreflang="en" data-title="Ellipsoid" 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/Elipsoido" title="Elipsoido – เอสเปรันโต" lang="eo" hreflang="eo" data-title="Elipsoido" 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/Elipsoide" title="Elipsoide – สเปน" lang="es" hreflang="es" data-title="Elipsoide" 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/Ellipsoid" title="Ellipsoid – เอสโตเนีย" lang="et" hreflang="et" data-title="Ellipsoid" 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/Elipsoide" title="Elipsoide – บาสก์" lang="eu" hreflang="eu" data-title="Elipsoide" 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%A8%DB%8C%D8%B6%DB%8C%E2%80%8C%DA%AF%D9%88%D9%86" title="بیضی‌گون – เปอร์เซีย" lang="fa" hreflang="fa" data-title="بیضی‌گون" 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/Ellipsoidi" title="Ellipsoidi – ฟินแลนด์" lang="fi" hreflang="fi" data-title="Ellipsoidi" 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/Ellipso%C3%AFde" title="Ellipsoïde – ฝรั่งเศส" lang="fr" hreflang="fr" data-title="Ellipsoïde" data-language-autonym="Français" data-language-local-name="ฝรั่งเศส" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/%C3%89ileaps%C3%B3ideach" title="Éileapsóideach – ไอริช" lang="ga" hreflang="ga" data-title="Éileapsóideach" data-language-autonym="Gaeilge" data-language-local-name="ไอริช" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9C%D7%99%D7%A4%D7%A1%D7%95%D7%90%D7%99%D7%93" title="אליפסואיד – ฮิบรู" lang="he" hreflang="he" data-title="אליפסואיד" 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%A6%E0%A5%80%E0%A4%B0%E0%A5%8D%E0%A4%98%E0%A4%B5%E0%A5%83%E0%A4%A4%E0%A5%8D%E0%A4%A4%E0%A4%BE%E0%A4%AD" title="दीर्घवृत्ताभ – ฮินดี" lang="hi" hreflang="hi" data-title="दीर्घवृत्ताभ" data-language-autonym="हिन्दी" data-language-local-name="ฮินดี" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Ellipszoid" title="Ellipszoid – ฮังการี" lang="hu" hreflang="hu" data-title="Ellipszoid" data-language-autonym="Magyar" data-language-local-name="ฮังการี" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B7%D5%AC%D5%AB%D5%BA%D5%BD%D5%B8%D5%AB%D5%A4" title="Էլիպսոիդ – อาร์เมเนีย" lang="hy" hreflang="hy" data-title="Էլիպսոիդ" data-language-autonym="Հայերեն" data-language-local-name="อาร์เมเนีย" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Elipsoid" title="Elipsoid – อินโดนีเซีย" lang="id" hreflang="id" data-title="Elipsoid" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Sporvala" title="Sporvala – ไอซ์แลนด์" lang="is" hreflang="is" data-title="Sporvala" 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/Ellissoide" title="Ellissoide – อิตาลี" lang="it" hreflang="it" data-title="Ellissoide" 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/%E6%A5%95%E5%86%86%E4%BD%93" title="楕円体 – ญี่ปุ่น" lang="ja" hreflang="ja" data-title="楕円体" 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%94%E1%83%9A%E1%83%98%E1%83%A4%E1%83%A1%E1%83%9D%E1%83%98%E1%83%93%E1%83%98" title="ელიფსოიდი – จอร์เจีย" lang="ka" hreflang="ka" data-title="ელიფსოიდი" data-language-autonym="ქართული" data-language-local-name="จอร์เจีย" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Эллипсоид – คาซัค" lang="kk" hreflang="kk" data-title="Эллипсоид" data-language-autonym="Қазақша" data-language-local-name="คาซัค" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%83%80%EC%9B%90%EB%A9%B4" title="타원면 – เกาหลี" lang="ko" hreflang="ko" data-title="타원면" 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%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Эллипсоид – คีร์กีซ" lang="ky" hreflang="ky" data-title="Эллипсоид" 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/Ellipsoid" title="Ellipsoid – ลักเซมเบิร์ก" lang="lb" hreflang="lb" data-title="Ellipsoid" data-language-autonym="Lëtzebuergesch" data-language-local-name="ลักเซมเบิร์ก" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Elipso%C4%ABds" title="Elipsoīds – ลัตเวีย" lang="lv" hreflang="lv" data-title="Elipsoīds" data-language-autonym="Latviešu" data-language-local-name="ลัตเวีย" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Ellipso%C3%AFde" title="Ellipsoïde – ดัตช์" lang="nl" hreflang="nl" data-title="Ellipsoïde" 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/Ellipsoide" title="Ellipsoide – นอร์เวย์นีนอสก์" lang="nn" hreflang="nn" data-title="Ellipsoide" 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/Ellipsoide" title="Ellipsoide – นอร์เวย์บุคมอล" lang="nb" hreflang="nb" data-title="Ellipsoide" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Elipsoida" title="Elipsoida – โปแลนด์" lang="pl" hreflang="pl" data-title="Elipsoida" data-language-autonym="Polski" data-language-local-name="โปแลนด์" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Elipsoide" title="Elipsoide – โปรตุเกส" lang="pt" hreflang="pt" data-title="Elipsoide" data-language-autonym="Português" data-language-local-name="โปรตุเกส" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Elipsoid" title="Elipsoid – โรมาเนีย" lang="ro" hreflang="ro" data-title="Elipsoid" 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%AD%D0%BB%D0%BB%D0%B8%D0%BF%D1%81%D0%BE%D0%B8%D0%B4" title="Эллипсоид – รัสเซีย" lang="ru" hreflang="ru" data-title="Эллипсоид" data-language-autonym="Русский" data-language-local-name="รัสเซีย" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid – Simple English" lang="en-simple" hreflang="en-simple" data-title="Ellipsoid" 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/Elipsoid" title="Elipsoid – สโลวัก" lang="sk" hreflang="sk" data-title="Elipsoid" 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/Elipsoid" title="Elipsoid – สโลวีเนีย" lang="sl" hreflang="sl" data-title="Elipsoid" data-language-autonym="Slovenščina" data-language-local-name="สโลวีเนีย" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Elipsoidi" title="Elipsoidi – แอลเบเนีย" lang="sq" hreflang="sq" data-title="Elipsoidi" data-language-autonym="Shqip" data-language-local-name="แอลเบเนีย" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid – สวีเดน" lang="sv" hreflang="sv" data-title="Ellipsoid" data-language-autonym="Svenska" data-language-local-name="สวีเดน" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AF%80%E0%AE%B3%E0%AF%8D%E0%AE%B5%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%BF%E0%AE%A3%E0%AF%8D%E0%AE%AE%E0%AE%AE%E0%AF%8D" title="நீள்வட்டத்திண்மம் – ทมิฬ" lang="ta" hreflang="ta" data-title="நீள்வட்டத்திண்மம்" data-language-autonym="தமிழ்" data-language-local-name="ทมิฬ" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Elipsoit" title="Elipsoit – ตุรกี" lang="tr" hreflang="tr" data-title="Elipsoit" data-language-autonym="Türkçe" data-language-local-name="ตุรกี" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D0%BB%D1%96%D0%BF%D1%81%D0%BE%D1%97%D0%B4" title="Еліпсоїд – ยูเครน" lang="uk" hreflang="uk" data-title="Еліпсоїд" data-language-autonym="Українська" data-language-local-name="ยูเครน" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ellipsoid" title="Ellipsoid – อุซเบก" lang="uz" hreflang="uz" data-title="Ellipsoid" 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/Ellipsoid" title="Ellipsoid – เวียดนาม" lang="vi" hreflang="vi" data-title="Ellipsoid" 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-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%A4%AD%E7%90%83" title="椭球 – จีน" lang="zh" hreflang="zh" data-title="椭球" 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-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%A9%A2%E7%90%83" title="橢球 – กวางตุ้ง" lang="yue" hreflang="yue" data-title="橢球" 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/Q190046#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%97%E0%B8%A3%E0%B8%87%E0%B8%A3%E0%B8%B5" title="ดูหน้าเนื้อหา [c]" accesskey="c"><span>บทความ</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E0%B8%9E%E0%B8%B9%E0%B8%94%E0%B8%84%E0%B8%B8%E0%B8%A2:%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%A3%E0%B8%B5&action=edit&redlink=1" rel="discussion" class="new" title="อภิปรายเกี่ยวกับหน้าเนื้อหา (ไม่มีหน้านี้) [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%97%E0%B8%A3%E0%B8%87%E0%B8%A3%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%97%E0%B8%A3%E0%B8%87%E0%B8%A3%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%97%E0%B8%A3%E0%B8%87%E0%B8%A3%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 cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">เครื่องมือ</span> </label> <div class="vector-dropdown-content"> <div 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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/Category:Ellipsoids" 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/Q190046" 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"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:Gnuplot_ellipsoid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Gnuplot_ellipsoid.svg/220px-Gnuplot_ellipsoid.svg.png" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Gnuplot_ellipsoid.svg/330px-Gnuplot_ellipsoid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Gnuplot_ellipsoid.svg/440px-Gnuplot_ellipsoid.svg.png 2x" data-file-width="600" data-file-height="480" /></a><figcaption>ทรงรี วาดในซอฟต์แวร์<a href="/wiki/%E0%B8%99%E0%B8%B4%E0%B8%A7%E0%B8%9E%E0%B8%A5%E0%B8%AD%E0%B8%95" title="นิวพลอต">นิวพลอต</a></figcaption></figure> <p><b>ทรงรี</b> คือผิวกำลังสองชนิดหนึ่ง ในสามมิติ เทียบได้กับวงรีในสองมิติ รูปสมการมาตรฐานของทรงรี บนแกน <i>x</i>-<i>y</i>-<i>z</i> ใน<a href="/wiki/%E0%B8%A3%E0%B8%B0%E0%B8%9A%E0%B8%9A%E0%B8%9E%E0%B8%B4%E0%B8%81%E0%B8%B1%E0%B8%94%E0%B8%84%E0%B8%B2%E0%B8%A3%E0%B9%8C%E0%B8%97%E0%B8%B5%E0%B9%80%E0%B8%8B%E0%B8%B5%E0%B8%A2%E0%B8%99" title="ระบบพิกัดคาร์ทีเซียน">ระบบพิกัดคาร์ทีเซียน</a> 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 {x^{2} \over a^{2}}+{y^{2} \over b^{2}}+{z^{2} \over c^{2}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {x^{2} \over a^{2}}+{y^{2} \over b^{2}}+{z^{2} \over c^{2}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/303573ace88047e7932c90d55d2c691d44ce2d39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:19.193ex; height:6.009ex;" alt="{\displaystyle {x^{2} \over a^{2}}+{y^{2} \over b^{2}}+{z^{2} \over c^{2}}=1}"></span></dd></dl> <p>โดย <i>a</i>, <i>b</i> และ <i>c</i> เป็นค่าคงที่ <a href="/wiki/%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99%E0%B8%88%E0%B8%A3%E0%B8%B4%E0%B8%87" title="จำนวนจริง">จำนวนจริง</a>บวก เป็นค่าที่กำหนดรูปร่างของทรงรี ในกรณีที่ค่าคงที่ 2 ตัวมีค่าเท่ากัน จะได้กรณีพิเศษคือ <a href="/wiki/%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%84%E0%B8%A5%E0%B9%89%E0%B8%B2%E0%B8%A2%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%81%E0%B8%A5%E0%B8%A1" title="ทรงคล้ายทรงกลม">ทรงคล้ายทรงกลม</a> กรณีที่ค่าทั้ง 3 ค่ามีค่เท่ากันจะได้เป็น <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> </p><p>ถ้าสมมุติให้ a ≥ b ≥ c แล้ว </p> <ul><li>a ≠ b ≠ c จะได้เป็น ทรงรีแกนไม่เท่า (<b>scalene</b> ellipsoid)</li> <li>c = 0 ได้เป็น วงรี</li> <li>c > a = b ได้รูป ทรงคล้ายทรงกลมแบนข้าง (<b>prolate</b> spheroid) รูปคล้ายลูกรักบี้</li> <li>c < a = b ได้รูป ทรงคล้ายทรงกลมแบนขั้ว (<b>oblate</b> spheroid)</li> <li>b = a = c ได้ <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></li></ul> <div class="mw-heading mw-heading2"><h2 id="ปริมาตร"><span id=".E0.B8.9B.E0.B8.A3.E0.B8.B4.E0.B8.A1.E0.B8.B2.E0.B8.95.E0.B8.A3"></span>ปริมาตร</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%A3%E0%B8%B5&action=edit&section=1" title="แก้ไขส่วน: ปริมาตร"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>หีบ<a href="/wiki/%E0%B8%9B%E0%B8%A3%E0%B8%B4%E0%B8%A1%E0%B8%B2%E0%B8%95%E0%B8%A3" title="ปริมาตร">ปริมาตร</a>ของทรงรี มีค่าเท่ากับ <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 {4}{3}}\pi abc}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> <mi>π</mi> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {4}{3}}\pi abc}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e6bab0d7b6f5d52c794e589223f04011463277e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.565ex; height:5.176ex;" alt="{\displaystyle {\frac {4}{3}}\pi abc}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="พื้นที่ผิว"><span id=".E0.B8.9E.E0.B8.B7.E0.B9.89.E0.B8.99.E0.B8.97.E0.B8.B5.E0.B9.88.E0.B8.9C.E0.B8.B4.E0.B8.A7"></span>พื้นที่ผิว</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E0%B8%97%E0%B8%A3%E0%B8%87%E0%B8%A3%E0%B8%B5&action=edit&section=2" title="แก้ไขส่วน: พื้นที่ผิว"><span>แก้</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E0%B8%9E%E0%B8%B7%E0%B9%89%E0%B8%99%E0%B8%97%E0%B8%B5%E0%B9%88" title="พื้นที่">พื้นที่</a>ผิวของทรงรี มีค่าเท่ากับ </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 2\pi \left(c^{2}+{\frac {bc^{2}}{\sqrt {a^{2}-c^{2}}}}F(\theta ,m)+b{\sqrt {a^{2}-c^{2}}}E(\theta ,m)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>b</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mi>F</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mi>E</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2\pi \left(c^{2}+{\frac {bc^{2}}{\sqrt {a^{2}-c^{2}}}}F(\theta ,m)+b{\sqrt {a^{2}-c^{2}}}E(\theta ,m)\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d29d2d06a3b9c0e2457396401beae9fa0d610567" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:50.622ex; height:7.509ex;" alt="{\displaystyle 2\pi \left(c^{2}+{\frac {bc^{2}}{\sqrt {a^{2}-c^{2}}}}F(\theta ,m)+b{\sqrt {a^{2}-c^{2}}}E(\theta ,m)\right)}"></span></dd></dl> <p>โดยที่ </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 m={\frac {a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2})}}\qquad \theta =\arcsin {\left(e\right)}\qquad e={\sqrt {1-{\frac {c^{2}}{a^{2}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mi>θ</mi> <mo>=</mo> <mi>arcsin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> </mrow> <mspace width="2em" /> <mi>e</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2})}}\qquad \theta =\arcsin {\left(e\right)}\qquad e={\sqrt {1-{\frac {c^{2}}{a^{2}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/885c891f60cacb354525a6c75f18b5dcaa7a032e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:53.372ex; height:7.509ex;" alt="{\displaystyle m={\frac {a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2})}}\qquad \theta =\arcsin {\left(e\right)}\qquad e={\sqrt {1-{\frac {c^{2}}{a^{2}}}}}}"></span></dd></dl> <p>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 \,F(\theta ,m)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>F</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,F(\theta ,m)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d171b2a5c72c0bcd0dd9bda5236d123ad136ad6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.489ex; height:2.843ex;" alt="{\displaystyle \,F(\theta ,m)\,}"></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 \,E(\theta ,m)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>E</mi> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>m</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,E(\theta ,m)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1871289fbc295b72903a10c39c625c3babb42555" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.524ex; height:2.843ex;" alt="{\displaystyle \,E(\theta ,m)\,}"></span> คือ <a href="/w/index.php?title=%E0%B8%9B%E0%B8%A3%E0%B8%B4%E0%B8%9E%E0%B8%B1%E0%B8%99%E0%B8%98%E0%B9%8C%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B8%A7%E0%B8%87%E0%B8%A3%E0%B8%B5&action=edit&redlink=1" class="new" title="ปริพันธ์เชิงวงรี (ไม่มีหน้านี้)">ปริพันธ์เชิงวงรี</a> ไม่สมบูรณ์ชนิดที่หนึ่ง และ ชนิดที่สอง </p><p>สูตรหาพื้นที่: </p> <ul><li>กรณีรูปแบน: <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 =2\pi \left(ab\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mi>b</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =2\pi \left(ab\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d85e01ad132ba7278e9cceda8500bb7bdfe65fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.372ex; height:2.843ex;" alt="{\displaystyle =2\pi \left(ab\right)}"></span></li> <li>กรณีรูปแบนข้าง: <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 =2\pi \left(c^{2}+ac{\frac {\arcsin {\left(e\right)}}{e}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>a</mi> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>arcsin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mi>e</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =2\pi \left(c^{2}+ac{\frac {\arcsin {\left(e\right)}}{e}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7960f9d4298e75e2bae76e2cc8b8bdd1f5d781a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.972ex; height:6.343ex;" alt="{\displaystyle =2\pi \left(c^{2}+ac{\frac {\arcsin {\left(e\right)}}{e}}\right)}"></span></li> <li>กรณีรูปแบนขั้ว: <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 =2\pi \left(a^{2}+c^{2}{\frac {\operatorname {arctanh} {\left(e\right)}}{e}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>arctanh</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mi>e</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =2\pi \left(a^{2}+c^{2}{\frac {\operatorname {arctanh} {\left(e\right)}}{e}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c89c56fe91687483a6798b9e15777617cee61f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.816ex; height:6.343ex;" alt="{\displaystyle =2\pi \left(a^{2}+c^{2}{\frac {\operatorname {arctanh} {\left(e\right)}}{e}}\right)}"></span></li></ul> <p>สูตรหาพื้นที่โดยประมาณ: </p> <ul><li>กรณีแกนไม่เท่า: <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 \approx 4\pi \left({\frac {a^{p}b^{p}+a^{p}c^{p}+b^{p}c^{p}}{3}}\right)^{1/p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≈</mo> <mn>4</mn> <mi>π</mi> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> <mn>3</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>p</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \approx 4\pi \left({\frac {a^{p}b^{p}+a^{p}c^{p}+b^{p}c^{p}}{3}}\right)^{1/p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/854bbeb50f27e9bf78e96b8e8d28740239a2a03a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.412ex; height:6.676ex;" alt="{\displaystyle \approx 4\pi \left({\frac {a^{p}b^{p}+a^{p}c^{p}+b^{p}c^{p}}{3}}\right)^{1/p}}"></span></li></ul> <p>โดยที่ p ≈ 1.6075 ให้ค่าความผิดพลาดสัมพัทธ์ ไม่เกิน 1.061% (สูตรของ <a href="/w/index.php?title=%E0%B8%99%E0%B8%B8%E0%B8%94_%E0%B8%97%E0%B8%AD%E0%B8%A1%E0%B9%80%E0%B8%8B%E0%B8%99&action=edit&redlink=1" class="new" title="นุด ทอมเซน (ไม่มีหน้านี้)">นุด ทอมเซน</a>) ; ค่า p = 8/5 = 1.6 เป็นค่าที่ดีที่สุดสำหรับทรงรี ที่คล้ายทรงกลม โดยมีค่าความผิดพลาดสัมพัทธ์ไม่เกิน 1.178% (สูตรของ <a href="/w/index.php?title=%E0%B9%80%E0%B8%94%E0%B8%A7%E0%B8%B4%E0%B8%94_%E0%B9%81%E0%B8%84%E0%B8%99%E0%B9%80%E0%B8%97%E0%B8%A3%E0%B8%A5&action=edit&redlink=1" class="new" title="เดวิด แคนเทรล (ไม่มีหน้านี้)">เดวิด แคนเทรล</a>) </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">เข้าถึงจาก "<a dir="ltr" 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