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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_cs.wikipedia.org&uselang=cs" class=""><span>Podpořte Wikipedii</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=Speci%C3%A1ln%C3%AD:Vytvo%C5%99it_%C3%BA%C4%8Det&returnto=Patn%C3%A1cti%C3%BAheln%C3%ADk" title="Doporučujeme vytvořit si účet a přihlásit se, ovšem není to povinné" class=""><span>Vytvoření účtu</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=Speci%C3%A1ln%C3%AD:P%C5%99ihl%C3%A1sit&returnto=Patn%C3%A1cti%C3%BAheln%C3%ADk" 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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Přihlášení</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"> Stránky pro odhlášené editory <a href="/wiki/N%C3%A1pov%C4%9Bda:%C3%9Avod" aria-label="Více informací o editování"><span>dozvědět se více</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/Speci%C3%A1ln%C3%AD:Moje_p%C5%99%C3%ADsp%C4%9Bvky" title="Seznam editací provedených z této IP adresy [y]" accesskey="y"><span>Příspěvky</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Moje_diskuse" title="Diskuse o editacích provedených z této IP adresy [n]" accesskey="n"><span>Diskuse</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="Projekt"> <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="Obsah" 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">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrýt</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">(úvod)</div> </a> </li> <li id="toc-Parametry" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Parametry"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Parametry</span> </div> </a> <ul id="toc-Parametry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Konstrukce_patnáctiúhelníku" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Konstrukce_patnáctiúhelníku"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Konstrukce patnáctiúhelníku</span> </div> </a> <ul id="toc-Konstrukce_patnáctiúhelníku-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externí_odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-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="Obsah" 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="Přepnout obsah" > <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">Přepnout obsah</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">Patnáctiúhelník</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="Přejděte k článku v jiném jazyce. Je dostupný v 40 jazycích" > <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-40" 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">40 jazyků</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%AE%D9%85%D8%B3_%D8%B9%D8%B4%D8%B1%D9%8A_%D8%A7%D9%84%D8%A3%D8%B6%D9%84%D8%A7%D8%B9" title="خمس عشري الأضلاع – arabština" lang="ar" hreflang="ar" data-title="خمس عشري الأضلاع" data-language-autonym="العربية" data-language-local-name="arabština" 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/Pentadec%C3%A1gonu" title="Pentadecágonu – asturština" lang="ast" hreflang="ast" data-title="Pentadecágonu" data-language-autonym="Asturianu" data-language-local-name="asturština" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%B5%D1%82%D0%BD%D0%B0%D0%B4%D0%B5%D1%81%D0%B5%D1%82%D0%BE%D1%8A%D0%B3%D1%8A%D0%BB%D0%BD%D0%B8%D0%BA" title="Петнадесетоъгълник – bulharština" lang="bg" hreflang="bg" data-title="Петнадесетоъгълник" data-language-autonym="Български" data-language-local-name="bulharština" 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/Pentadec%C3%A0gon" title="Pentadecàgon – katalánština" lang="ca" hreflang="ca" data-title="Pentadecàgon" data-language-autonym="Català" data-language-local-name="katalánština" 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%BE%D8%A7%D8%B2%D8%AF%DB%95%D9%84%D8%A7" title="پازدەلا – kurdština (sorání)" lang="ckb" hreflang="ckb" data-title="پازدەلا" data-language-autonym="کوردی" data-language-local-name="kurdština (sorání)" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Pentadekagon" title="Pentadekagon – dánština" lang="da" hreflang="da" data-title="Pentadekagon" data-language-autonym="Dansk" data-language-local-name="dánština" 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/F%C3%BCnfzehneck" title="Fünfzehneck – němčina" lang="de" hreflang="de" data-title="Fünfzehneck" data-language-autonym="Deutsch" data-language-local-name="němčina" 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%94%CE%B5%CE%BA%CE%B1%CF%80%CE%B5%CE%BD%CF%84%CE%AC%CE%B3%CF%89%CE%BD%CE%BF" title="Δεκαπεντάγωνο – řečtina" lang="el" hreflang="el" data-title="Δεκαπεντάγωνο" data-language-autonym="Ελληνικά" data-language-local-name="řečtina" 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/Pentadec%C3%A0gon" title="Pentadecàgon – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Pentadecàgon" 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/Pentadecagon" title="Pentadecagon – angličtina" lang="en" hreflang="en" data-title="Pentadecagon" data-language-autonym="English" data-language-local-name="angličtina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Pentadec%C3%A1gono" title="Pentadecágono – španělština" lang="es" hreflang="es" data-title="Pentadecágono" data-language-autonym="Español" data-language-local-name="španělština" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Pentadekagono" title="Pentadekagono – baskičtina" lang="eu" hreflang="eu" data-title="Pentadekagono" data-language-autonym="Euskara" data-language-local-name="baskičtina" 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/%D9%BE%D8%A7%D9%86%D8%B2%D8%AF%D9%87%E2%80%8C%D8%B6%D9%84%D8%B9%DB%8C" title="پانزده‌ضلعی – perština" lang="fa" hreflang="fa" data-title="پانزده‌ضلعی" data-language-autonym="فارسی" data-language-local-name="perština" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Pentad%C3%A9cagone" title="Pentadécagone – francouzština" lang="fr" hreflang="fr" data-title="Pentadécagone" data-language-autonym="Français" data-language-local-name="francouzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Pentadec%C3%A1gono" title="Pentadecágono – galicijština" lang="gl" hreflang="gl" data-title="Pentadecágono" data-language-autonym="Galego" data-language-local-name="galicijština" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Tizen%C3%B6tsz%C3%B6g" title="Tizenötszög – maďarština" lang="hu" hreflang="hu" data-title="Tizenötszög" data-language-autonym="Magyar" data-language-local-name="maďarština" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Pentadekagon" title="Pentadekagon – indonéština" lang="id" hreflang="id" data-title="Pentadekagon" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Pentadecagono" title="Pentadecagono – italština" lang="it" hreflang="it" data-title="Pentadecagono" data-language-autonym="Italiano" data-language-local-name="italština" 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%81%E4%BA%94%E8%A7%92%E5%BD%A2" title="十五角形 – japonština" lang="ja" hreflang="ja" data-title="十五角形" data-language-autonym="日本語" data-language-local-name="japonština" 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%9E%E1%83%94%E1%83%9C%E1%83%A2%E1%83%90%E1%83%93%E1%83%94%E1%83%99%E1%83%90%E1%83%92%E1%83%9D%E1%83%9C%E1%83%98" title="პენტადეკაგონი – gruzínština" lang="ka" hreflang="ka" data-title="პენტადეკაგონი" data-language-autonym="ქართული" data-language-local-name="gruzínština" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8B%AD%EC%98%A4%EA%B0%81%ED%98%95" title="십오각형 – korejština" lang="ko" hreflang="ko" data-title="십오각형" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D0%B5%D1%82%D0%BD%D0%B0%D0%B5%D1%81%D0%B5%D1%82%D0%B0%D0%B3%D0%BE%D0%BB%D0%BD%D0%B8%D0%BA" title="Петнаесетаголник – makedonština" lang="mk" hreflang="mk" data-title="Петнаесетаголник" data-language-autonym="Македонски" data-language-local-name="makedonština" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pentadekagon" title="Pentadekagon – malajština" lang="ms" hreflang="ms" data-title="Pentadekagon" data-language-autonym="Bahasa Melayu" data-language-local-name="malajština" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Vijftienhoek" title="Vijftienhoek – nizozemština" lang="nl" hreflang="nl" data-title="Vijftienhoek" data-language-autonym="Nederlands" data-language-local-name="nizozemština" 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/Pentadekagon" title="Pentadekagon – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Pentadekagon" data-language-autonym="Norsk nynorsk" data-language-local-name="norština (nynorsk)" 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/Pentadekagon" title="Pentadekagon – norština (bokmål)" lang="nb" hreflang="nb" data-title="Pentadekagon" data-language-autonym="Norsk bokmål" data-language-local-name="norština (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl badge-Q70893996 mw-list-item" title=""><a href="https://pl.wikipedia.org/wiki/Pi%C4%99tnastok%C4%85t" title="Piętnastokąt – polština" lang="pl" hreflang="pl" data-title="Piętnastokąt" data-language-autonym="Polski" data-language-local-name="polština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt badge-Q70893996 mw-list-item" title=""><a href="https://pt.wikipedia.org/wiki/Pentadec%C3%A1gono" title="Pentadecágono – portugalština" lang="pt" hreflang="pt" data-title="Pentadecágono" data-language-autonym="Português" data-language-local-name="portugalština" 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/Pentadecagon" title="Pentadecagon – rumunština" lang="ro" hreflang="ro" data-title="Pentadecagon" data-language-autonym="Română" data-language-local-name="rumunština" 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%9F%D1%8F%D1%82%D0%BD%D0%B0%D0%B4%D1%86%D0%B0%D1%82%D0%B8%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D0%B8%D0%BA" title="Пятнадцатиугольник – ruština" lang="ru" hreflang="ru" data-title="Пятнадцатиугольник" data-language-autonym="Русский" data-language-local-name="ruština" 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/Pentadecagon" title="Pentadecagon – Simple English" lang="en-simple" hreflang="en-simple" data-title="Pentadecagon" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Petnajstkotnik" title="Petnajstkotnik – slovinština" lang="sl" hreflang="sl" data-title="Petnajstkotnik" data-language-autonym="Slovenščina" data-language-local-name="slovinština" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9F%D0%B5%D1%82%D0%BD%D0%B0%D0%B5%D1%81%D1%82%D0%BE%D1%83%D0%B3%D0%B0%D0%BE" title="Петнаестоугао – srbština" lang="sr" hreflang="sr" data-title="Петнаестоугао" data-language-autonym="Српски / srpski" data-language-local-name="srbština" 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/Pentadekagon" title="Pentadekagon – švédština" lang="sv" hreflang="sv" data-title="Pentadekagon" data-language-autonym="Svenska" data-language-local-name="švédština" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B9%E0%B8%9B%E0%B8%AA%E0%B8%B4%E0%B8%9A%E0%B8%AB%E0%B9%89%E0%B8%B2%E0%B9%80%E0%B8%AB%E0%B8%A5%E0%B8%B5%E0%B9%88%E0%B8%A2%E0%B8%A1" title="รูปสิบห้าเหลี่ยม – thajština" lang="th" hreflang="th" data-title="รูปสิบห้าเหลี่ยม" data-language-autonym="ไทย" data-language-local-name="thajština" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Onbe%C5%9Fgen" title="Onbeşgen – turečtina" lang="tr" hreflang="tr" data-title="Onbeşgen" data-language-autonym="Türkçe" data-language-local-name="turečtina" 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%9F%27%D1%8F%D1%82%D0%BD%D0%B0%D0%B4%D1%86%D1%8F%D1%82%D0%B8%D0%BA%D1%83%D1%82%D0%BD%D0%B8%D0%BA" title="П'ятнадцятикутник – ukrajinština" lang="uk" hreflang="uk" data-title="П'ятнадцятикутник" data-language-autonym="Українська" data-language-local-name="ukrajinština" 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/%D9%BE%D9%86%D8%AF%D8%B1%DB%81_%D8%A7%D8%B6%D9%84%D8%A7%D8%B9" title="پندرہ اضلاع – urdština" lang="ur" hreflang="ur" data-title="پندرہ اضلاع" data-language-autonym="اردو" data-language-local-name="urdština" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8D%81%E4%BA%94%E8%BE%B9%E5%BD%A2" title="十五边形 – čínština" lang="zh" hreflang="zh" data-title="十五边形" data-language-autonym="中文" data-language-local-name="čínština" 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/%E5%8D%81%E4%BA%94%E9%82%8A%E5%BD%A2" 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id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Vzhled"> <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">Vzhled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skrýt</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">Z Wikipedie, otevřené encyklopedie</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="cs" dir="ltr"><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Soubor:Pentadecagon.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Pentadecagon.svg/220px-Pentadecagon.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Pentadecagon.svg/330px-Pentadecagon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Pentadecagon.svg/440px-Pentadecagon.svg.png 2x" data-file-width="744" data-file-height="744" /></a><figcaption>pravidelný patnáctiúhelník.</figcaption></figure> <p><b>Patnáctiúhelník</b> je rovinný geometrický útvar, <a href="/wiki/Mnoho%C3%BAheln%C3%ADk" title="Mnohoúhelník">mnohoúhelník</a> s patnácti <a href="/wiki/Vrchol_(geometrie)" title="Vrchol (geometrie)">vrcholy</a> a patnácti <a href="/wiki/Strana_(geometrie)" title="Strana (geometrie)">stranami</a>. </p><p>Součet velikostí vnitřních <a href="/wiki/%C3%9Ahel" title="Úhel">úhlů</a> <a href="/wiki/Konvexnost" class="mw-redirect mw-disambig" title="Konvexnost">konvexního</a> patnáctiúhelníku je přesně 2340° (13π). </p><p>Pravidelný patnáctiúhelník lze složit z patnácti <a href="/wiki/Shodnost" class="mw-redirect" title="Shodnost">shodných</a> <a href="/wiki/Rovnoramenn%C3%BD_troj%C3%BAheln%C3%ADk" title="Rovnoramenný trojúhelník">rovnoramenných trojúhelníků</a>, jejichž úhly při základně mají velikost <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 {13\pi }{30}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>13</mn> <mi>π</mi> </mrow> <mn>30</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {13\pi }{30}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e419c70be62d6dc11affdf00b776fbe5d7a2efb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:4.493ex; height:5.176ex;" alt="{\displaystyle {\frac {13\pi }{30}}}"></span> a při vrcholu <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 {2\pi }{15}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mn>15</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {2\pi }{15}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5c8006f360db6129dc43338ce97df2b18f31aee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:3.331ex; height:5.176ex;" alt="{\displaystyle {\frac {2\pi }{15}}}"></span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Parametry">Parametry</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Patn%C3%A1cti%C3%BAheln%C3%ADk&veaction=edit&section=1" title="Editace sekce: Parametry" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Patn%C3%A1cti%C3%BAheln%C3%ADk&action=edit&section=1" title="Editovat zdrojový kód sekce Parametry"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pro pravidelný patnáctiúhelník platí vzorce: </p> <ul><li><i><a href="/wiki/Obvod_(geometrie)" title="Obvod (geometrie)">Obvod</a></i>: <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 o=15\cdot a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>o</mi> <mo>=</mo> <mn>15</mn> <mo>⋅</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle o=15\cdot a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/850e6c550845ef6a781db9082391fcbdd6ab3fe0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.46ex; height:2.176ex;" alt="{\displaystyle o=15\cdot a}"></span></li> <li><i><a href="/wiki/Obsah" title="Obsah">obsah</a></i>: <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 S={\frac {15}{4}}a^{2}\cot {\frac {\pi }{15}}={\frac {15a^{2}}{8}}\left({\sqrt {3}}+{\sqrt {15}}+{\sqrt {2}}{\sqrt {5+{\sqrt {5}}}}\right)\simeq 17.6424a^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>15</mn> <mn>4</mn> </mfrac> </mrow> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>cot</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>15</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>15</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mn>8</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>15</mn> </msqrt> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> </msqrt> </mrow> </mrow> <mo>)</mo> </mrow> <mo>≃</mo> <mn>17.6424</mn> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S={\frac {15}{4}}a^{2}\cot {\frac {\pi }{15}}={\frac {15a^{2}}{8}}\left({\sqrt {3}}+{\sqrt {15}}+{\sqrt {2}}{\sqrt {5+{\sqrt {5}}}}\right)\simeq 17.6424a^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/405971e4a8d66552d542fa820e5978669c95227f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:67.997ex; height:6.343ex;" alt="{\displaystyle S={\frac {15}{4}}a^{2}\cot {\frac {\pi }{15}}={\frac {15a^{2}}{8}}\left({\sqrt {3}}+{\sqrt {15}}+{\sqrt {2}}{\sqrt {5+{\sqrt {5}}}}\right)\simeq 17.6424a^{2}}"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Konstrukce_patnáctiúhelníku"><span id="Konstrukce_patn.C3.A1cti.C3.BAheln.C3.ADku"></span>Konstrukce patnáctiúhelníku</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Patn%C3%A1cti%C3%BAheln%C3%ADk&veaction=edit&section=2" title="Editace sekce: Konstrukce patnáctiúhelníku" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Patn%C3%A1cti%C3%BAheln%C3%ADk&action=edit&section=2" title="Editovat zdrojový kód sekce Konstrukce patnáctiúhelníku"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Konstrukce pravidelného patnáctiúhelníku <a href="/wiki/Eukleidovsk%C3%A1_konstrukce" title="Eukleidovská konstrukce">pomocí kružítka a pravítka</a> v 36 krocích: </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/Soubor:PentadecagonConstructionAni.gif" class="mw-file-description" title="Konstrukce pravidelného patnáctiúhelníku"><img alt="Konstrukce pravidelného patnáctiúhelníku" src="//upload.wikimedia.org/wikipedia/commons/6/63/PentadecagonConstructionAni.gif" decoding="async" width="407" height="529" class="mw-file-element" data-file-width="407" data-file-height="529" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Patn%C3%A1cti%C3%BAheln%C3%ADk&veaction=edit&section=3" title="Editace sekce: Související články" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Patn%C3%A1cti%C3%BAheln%C3%ADk&action=edit&section=3" title="Editovat zdrojový kód sekce Související články"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Mnoho%C3%BAheln%C3%ADk" title="Mnohoúhelník">Polygon</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Patn%C3%A1cti%C3%BAheln%C3%ADk&veaction=edit&section=4" title="Editace sekce: Externí odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Patn%C3%A1cti%C3%BAheln%C3%ADk&action=edit&section=4" title="Editovat zdrojový kód sekce Externí odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="wd"><span class="sisterproject sisterproject-commons"><span class="sisterproject_image"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons"><img alt="Logo Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></span> <span class="sisterproject_text">Obrázky, zvuky či videa k tématu <span class="sisterproject_text_target"><a href="https://commons.wikimedia.org/wiki/Category:15-gons" class="extiw" title="c:Category:15-gons">patnáctiúhelník</a></span> na <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a></span></span></span><i> </i></li> <li><span class="sisterproject sisterproject-wiktionary"><span class="sisterproject_image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Wiktionary-logo-cs.svg/16px-Wiktionary-logo-cs.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Wiktionary-logo-cs.svg/24px-Wiktionary-logo-cs.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/97/Wiktionary-logo-cs.svg/32px-Wiktionary-logo-cs.svg.png 2x" data-file-width="411" data-file-height="411" /></span></span></span> <span class="sisterproject_text"><span class="sisterproject_text_prefix">Slovníkové heslo </span><span class="sisterproject_text_target"><a href="https://cs.wiktionary.org/wiki/patn%C3%A1cti%C3%BAheln%C3%ADk" class="extiw" title="wikt:patnáctiúhelník">patnáctiúhelník</a></span><span class="sisterproject_text_suffix"> ve Wikislovníku</span></span></span></li></ul> <table class="plainlinks metadata noprint pahyl" cellpadding="2" style="background: transparent;"> <tbody><tr> <td><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/Soubor:Wiki_letter_w.svg" class="mw-file-description" title="Pahýl"><img alt="Pahýl" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a><figcaption>Pahýl</figcaption></figure> </td> <td><i>Tento článek je příliš stručný nebo <a href="/wiki/Wikipedie:Pah%C3%BDl" title="Wikipedie:Pahýl">postrádá důležité informace</a>.<br />Pomozte Wikipedii tím, že jej vhodně <a class="external text" href="https://cs.wikipedia.org/w/index.php?title=Patn%C3%A1cti%C3%BAheln%C3%ADk&action=edit">rozšíříte</a>. Nevkládejte však <a href="/wiki/Wikipedie:Autorsk%C3%A9_pr%C3%A1vo#Publikování_cizích_autorských_děl" title="Wikipedie:Autorské právo">bez oprávnění</a> cizí texty.</i> </td></tr></tbody></table> <div class="navbox noprint" title="Mnohoúhelníky"><table title="" class="navbox-navbox mw-collapsible autocollapse nowraplinks noprint" cellspacing="0" data-collapsetext="skrýt" data-expandtext="zobrazit"><style data-mw-deduplicate="TemplateStyles:r17064757">.mw-parser-output .navbox-title .mw-collapsible-toggle{font-weight:normal}</style><tbody><tr> <th class="navbox-title" colspan="2"> <span class="navbox-titletext"><a href="/wiki/Mnoho%C3%BAheln%C3%ADk" title="Mnohoúhelník">Mnohoúhelníky</a></span> </th> </tr><tr class="navbox-padding"><td></td></tr> <tr> <td class="navbox-list navbox-odd" colspan="2"> <div> <a href="/wiki/Troj%C3%BAheln%C3%ADk" title="Trojúhelník">Trojúhelník</a> • <a href="/wiki/%C4%8Cty%C5%99%C3%BAheln%C3%ADk" title="Čtyřúhelník">Čtyřúhelník</a> • <a href="/wiki/P%C4%9Bti%C3%BAheln%C3%ADk" title="Pětiúhelník">Pětiúhelník</a> • <a href="/wiki/%C5%A0esti%C3%BAheln%C3%ADk" title="Šestiúhelník">Šestiúhelník</a> • <a href="/wiki/Sedmi%C3%BAheln%C3%ADk" title="Sedmiúhelník">Sedmiúhelník</a> • <a href="/wiki/Osmi%C3%BAheln%C3%ADk" title="Osmiúhelník">Osmiúhelník</a> • <a href="/wiki/Dev%C3%ADti%C3%BAheln%C3%ADk" title="Devítiúhelník">Devítiúhelník</a> • <a href="/wiki/Deseti%C3%BAheln%C3%ADk" title="Desetiúhelník">Desetiúhelník</a> • <a href="/wiki/Jeden%C3%A1cti%C3%BAheln%C3%ADk" title="Jedenáctiúhelník">Jedenáctiúhelník</a> • <a href="/wiki/Dvan%C3%A1cti%C3%BAheln%C3%ADk" title="Dvanáctiúhelník">Dvanáctiúhelník</a> • <a href="/wiki/T%C5%99in%C3%A1cti%C3%BAheln%C3%ADk" title="Třináctiúhelník">Třináctiúhelník</a> • <a href="/wiki/%C4%8Ctrn%C3%A1cti%C3%BAheln%C3%ADk" title="Čtrnáctiúhelník">Čtrnáctiúhelník</a> • <a class="mw-selflink selflink">Patnáctiúhelník</a> • <a href="/wiki/%C5%A0estn%C3%A1cti%C3%BAheln%C3%ADk" title="Šestnáctiúhelník">Šestnáctiúhelník</a> • <a href="/wiki/Sedmn%C3%A1cti%C3%BAheln%C3%ADk" title="Sedmnáctiúhelník">Sedmnáctiúhelník</a> • <a href="/wiki/Osmn%C3%A1cti%C3%BAheln%C3%ADk" title="Osmnáctiúhelník">Osmnáctiúhelník</a> • <a href="/wiki/Devaten%C3%A1cti%C3%BAheln%C3%ADk" title="Devatenáctiúhelník">Devatenáctiúhelník</a> • <a href="/wiki/Dvaceti%C3%BAheln%C3%ADk" title="Dvacetiúhelník">Dvacetiúhelník</a> • <a href="/wiki/Jednadvaceti%C3%BAheln%C3%ADk" title="Jednadvacetiúhelník">Jednadvacetiúhelník</a> • <a href="/wiki/Dvaadvaceti%C3%BAheln%C3%ADk" title="Dvaadvacetiúhelník">Dvaadvacetiúhelník</a> • <a href="/w/index.php?title=%C4%8Cty%C5%99iadvaceti%C3%BAheln%C3%ADk&action=edit&redlink=1" class="new" title="Čtyřiadvacetiúhelník (stránka neexistuje)">Čtyřiadvacetiúhelník</a> • <a href="/wiki/T%C5%99iceti%C3%BAheln%C3%ADk" class="mw-redirect" title="Třicetiúhelník">Třicetiúhelník</a></div> </td> </tr></tbody></table> </div> <style 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