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href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=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=Kruh" 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=Kruh" title="Doporučujeme vám přihlásit se, ovšem není to povinné. 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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-Základní_vzorce" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Základní_vzorce"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Základní vzorce</span> </div> </a> <button aria-controls="toc-Základní_vzorce-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Přepnout podsekci Základní vzorce</span> </button> <ul id="toc-Základní_vzorce-sublist" class="vector-toc-list"> <li id="toc-Pro_poloměr" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pro_poloměr"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Pro poloměr</span> </div> </a> <ul id="toc-Pro_poloměr-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pro_průměr" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pro_průměr"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Pro průměr</span> </div> </a> <ul id="toc-Pro_průměr-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Odvození_vzorce_pro_plochu_pomocí_integrace" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Odvození_vzorce_pro_plochu_pomocí_integrace"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Odvození vzorce pro plochu pomocí integrace</span> </div> </a> <ul id="toc-Odvození_vzorce_pro_plochu_pomocí_integrace-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Další_pojmy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Další_pojmy"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Další pojmy</span> </div> </a> <ul id="toc-Další_pojmy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kvadratura_kruhu" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kvadratura_kruhu"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Kvadratura kruhu</span> </div> </a> <ul id="toc-Kvadratura_kruhu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Odkazy</span> </div> </a> <button aria-controls="toc-Odkazy-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Přepnout podsekci Odkazy</span> </button> <ul id="toc-Odkazy-sublist" class="vector-toc-list"> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</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-2"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Obsah" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Obsah" > <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">Kruh</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 60 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-60" 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">60 jazyků</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Cerclo" title="Cerclo – aragonština" lang="an" hreflang="an" data-title="Cerclo" data-language-autonym="Aragonés" data-language-local-name="aragonština" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%B1%D8%B5_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="قرص (رياضيات) – arabština" lang="ar" hreflang="ar" data-title="قرص (رياضيات)" 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/C%C3%ADrculu" title="Círculu – asturština" lang="ast" hreflang="ast" data-title="Círculu" data-language-autonym="Asturianu" data-language-local-name="asturština" 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/Dair%C9%99" title="Dairə – ázerbájdžánština" lang="az" hreflang="az" data-title="Dairə" data-language-autonym="Azərbaycanca" data-language-local-name="ázerbájdžánština" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%DA%86%D8%A6%D9%88%D8%B1%D9%87" title="چئوره – South Azerbaijani" lang="azb" hreflang="azb" data-title="چئوره" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9A%D1%80%D1%83%D0%B3" title="Круг – běloruština" lang="be" hreflang="be" data-title="Круг" data-language-autonym="Беларуская" data-language-local-name="běloruština" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D1%80%D1%83%D0%B3" title="Круг – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Круг" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Krug" title="Krug – bosenština" lang="bs" hreflang="bs" data-title="Krug" data-language-autonym="Bosanski" data-language-local-name="bosenština" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Cercle" title="Cercle – katalánština" lang="ca" hreflang="ca" data-title="Cercle" data-language-autonym="Català" data-language-local-name="katalánština" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cu mw-list-item"><a href="https://cu.wikipedia.org/wiki/%D0%9A%D1%80%D1%AB%D0%B3%D1%8A" title="Крѫгъ – staroslověnština" lang="cu" hreflang="cu" data-title="Крѫгъ" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="staroslověnština" class="interlanguage-link-target"><span>Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%C3%87%D0%B0%D0%B2%D1%80%D0%B0%D1%88%D0%BA%D0%B0" title="Çаврашка – čuvaština" lang="cv" hreflang="cv" data-title="Çаврашка" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Kreisscheibe" title="Kreisscheibe – němčina" lang="de" hreflang="de" data-title="Kreisscheibe" 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%AF%CF%83%CE%BA%CE%BF%CF%82_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Δίσκος (γεωμετρία) – řečtina" lang="el" hreflang="el" data-title="Δίσκος (γεωμετρία)" data-language-autonym="Ελληνικά" data-language-local-name="řečtina" 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/Disk_(mathematics)" title="Disk (mathematics) – angličtina" lang="en" hreflang="en" data-title="Disk (mathematics)" data-language-autonym="English" data-language-local-name="angličtina" 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/Disko_(matematiko)" title="Disko (matematiko) – esperanto" lang="eo" hreflang="eo" data-title="Disko (matematiko)" data-language-autonym="Esperanto" data-language-local-name="esperanto" 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/Disco_(topolog%C3%ADa)" title="Disco (topología) – španělština" lang="es" hreflang="es" data-title="Disco (topología)" data-language-autonym="Español" data-language-local-name="španělština" 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/Ring" title="Ring – estonština" lang="et" hreflang="et" data-title="Ring" data-language-autonym="Eesti" data-language-local-name="estonština" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%82%D8%B1%D8%B5_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C)" title="قرص (ریاضی) – perština" lang="fa" hreflang="fa" data-title="قرص (ریاضی)" data-language-autonym="فارسی" data-language-local-name="perština" 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/Kiekko_(matematiikka)" title="Kiekko (matematiikka) – finština" lang="fi" hreflang="fi" data-title="Kiekko (matematiikka)" data-language-autonym="Suomi" data-language-local-name="finština" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Ts%C3%B5%C3%B5r_(geomeetri%C3%A4)" title="Tsõõr (geomeetriä) – võruština" lang="vro" hreflang="vro" data-title="Tsõõr (geomeetriä)" data-language-autonym="Võro" data-language-local-name="võruština" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Disque_(g%C3%A9om%C3%A9trie)" title="Disque (géométrie) – francouzština" lang="fr" hreflang="fr" data-title="Disque (géométrie)" 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/C%C3%ADrculo" title="Círculo – galicijština" lang="gl" hreflang="gl" data-title="Círculo" data-language-autonym="Galego" data-language-local-name="galicijština" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he badge-Q70894304 mw-list-item" title=""><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%99%D7%92%D7%95%D7%9C" title="עיגול – hebrejština" lang="he" hreflang="he" data-title="עיגול" data-language-autonym="עברית" data-language-local-name="hebrejština" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Krug" title="Krug – chorvatština" lang="hr" hreflang="hr" data-title="Krug" data-language-autonym="Hrvatski" data-language-local-name="chorvatština" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Wou_(mekanik)" title="Wou (mekanik) – haitština" lang="ht" hreflang="ht" data-title="Wou (mekanik)" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitština" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%87%D6%80%D5%BB%D5%A1%D5%B6_(%D5%A5%D6%80%D5%AF%D6%80%D5%A1%D5%B9%D5%A1%D6%83%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6)" title="Շրջան (երկրաչափություն) – arménština" lang="hy" hreflang="hy" data-title="Շրջան (երկրաչափություն)" data-language-autonym="Հայերեն" data-language-local-name="arménština" 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/Cakram_(matematika)" title="Cakram (matematika) – indonéština" lang="id" hreflang="id" data-title="Cakram (matematika)" 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-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Disko_(geometrio)" title="Disko (geometrio) – ido" lang="io" hreflang="io" data-title="Disko (geometrio)" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Cerchio" title="Cerchio – italština" lang="it" hreflang="it" data-title="Cerchio" 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%86%86%E6%9D%BF" title="円板 – japonština" lang="ja" hreflang="ja" data-title="円板" 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%AC%E1%83%A0%E1%83%94" title="წრე – gruzínština" lang="ka" hreflang="ka" data-title="წრე" 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%9B%90%ED%8C%90" title="원판 – korejština" lang="ko" hreflang="ko" data-title="원판" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Skritulys" title="Skritulys – litevština" lang="lt" hreflang="lt" data-title="Skritulys" data-language-autonym="Lietuvių" data-language-local-name="litevština" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Ri%C5%86%C4%B7is" title="Riņķis – lotyština" lang="lv" hreflang="lv" data-title="Riņķis" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mdf mw-list-item"><a href="https://mdf.wikipedia.org/wiki/%D0%A8%D0%B0%D1%80%D0%BA%D1%81%D1%81%D1%8C" title="Шаркссь – mokšanština" lang="mdf" hreflang="mdf" data-title="Шаркссь" data-language-autonym="Мокшень" data-language-local-name="mokšanština" class="interlanguage-link-target"><span>Мокшень</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Kapila_(je%C3%B4metria)" title="Kapila (jeômetria) – malgaština" lang="mg" hreflang="mg" data-title="Kapila (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="malgaština" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%A2%D1%8B%D1%80%D1%82%D1%8B%D1%88_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5)" title="Тыртыш (математике) – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Тыртыш (математике)" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D1%80%D1%83%D0%B3" title="Круг – makedonština" lang="mk" hreflang="mk" data-title="Круг" data-language-autonym="Македонски" data-language-local-name="makedonština" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A1%E0%B4%BF%E0%B4%B8%E0%B5%8D%E0%B4%95%E0%B5%8D_(%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%B6%E0%B4%BE%E0%B4%B8%E0%B5%8D%E0%B4%A4%E0%B5%8D%E0%B4%B0%E0%B4%82)" title="ഡിസ്ക് (ഗണിതശാസ്ത്രം) – malajálamština" lang="ml" hreflang="ml" data-title="ഡിസ്ക് (ഗണിതശാസ്ത്രം)" data-language-autonym="മലയാളം" data-language-local-name="malajálamština" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%9A%D0%B8%D1%80%D1%8C%D0%BA%D1%81" title="Кирькс – erzjanština" lang="myv" hreflang="myv" data-title="Кирькс" data-language-autonym="Эрзянь" data-language-local-name="erzjanština" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Schijf_(wiskunde)" title="Schijf (wiskunde) – nizozemština" lang="nl" hreflang="nl" data-title="Schijf (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="nizozemština" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Disk_(matematikk)" title="Disk (matematikk) – norština (bokmål)" lang="nb" hreflang="nb" data-title="Disk (matematikk)" 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 mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ko%C5%82o" title="Koło – polština" lang="pl" hreflang="pl" data-title="Koło" data-language-autonym="Polski" data-language-local-name="polština" 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/C%C3%ADrculo" title="Círculo – portugalština" lang="pt" hreflang="pt" data-title="Círculo" 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/Disc_(geometrie)" title="Disc (geometrie) – rumunština" lang="ro" hreflang="ro" data-title="Disc (geometrie)" 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%9A%D1%80%D1%83%D0%B3" title="Круг – ruština" lang="ru" hreflang="ru" data-title="Круг" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A2%D3%A9%D0%B3%D2%AF%D1%80%D2%AF%D0%BA" title="Төгүрүк – jakutština" lang="sah" hreflang="sah" data-title="Төгүрүк" data-language-autonym="Саха тыла" data-language-local-name="jakutština" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Krug" title="Krug – srbochorvatština" lang="sh" hreflang="sh" data-title="Krug" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="srbochorvatština" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Kruh" title="Kruh – slovenština" lang="sk" hreflang="sk" data-title="Kruh" data-language-autonym="Slovenčina" data-language-local-name="slovenština" 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/Krog" title="Krog – slovinština" lang="sl" hreflang="sl" data-title="Krog" data-language-autonym="Slovenščina" data-language-local-name="slovinština" 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/Qarku_(matematik%C3%AB)" title="Qarku (matematikë) – albánština" lang="sq" hreflang="sq" data-title="Qarku (matematikë)" data-language-autonym="Shqip" data-language-local-name="albánština" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D1%80%D1%83%D0%B3" title="Круг – srbština" lang="sr" hreflang="sr" data-title="Круг" 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/Cirkelskiva" title="Cirkelskiva – švédština" lang="sv" hreflang="sv" data-title="Cirkelskiva" data-language-autonym="Svenska" data-language-local-name="švédština" 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%B5%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AF%81_(%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="வட்டு (கணிதம்) – tamilština" lang="ta" hreflang="ta" data-title="வட்டு (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="tamilština" 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/Daire" title="Daire – turečtina" lang="tr" hreflang="tr" data-title="Daire" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A2%D2%AF%D0%B3%D3%99%D1%80%D3%99%D0%BA" title="Түгәрәк – tatarština" lang="tt" hreflang="tt" data-title="Түгәрәк" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarština" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D1%80%D1%83%D0%B3" title="Круг – ukrajinština" lang="uk" hreflang="uk" data-title="Круг" data-language-autonym="Українська" data-language-local-name="ukrajinština" 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/Doira_(shakl)" title="Doira (shakl) – uzbečtina" lang="uz" hreflang="uz" data-title="Doira (shakl)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbečtina" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%C3%ACnh_tr%C3%B2n" title="Hình tròn – vietnamština" lang="vi" hreflang="vi" data-title="Hình tròn" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamština" 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/%E5%9C%86%E7%9B%98" title="圆盘 – čínština" lang="zh" hreflang="zh" data-title="圆盘" data-language-autonym="中文" data-language-local-name="čínština" class="interlanguage-link-target"><span>中文</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/Q238231#sitelinks-wikipedia" title="Editovat mezijazykové odkazy" class="wbc-editpage">Upravit odkazy</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="Jmenné prostory"> <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/Kruh" title="Zobrazit obsahovou stránku [c]" accesskey="c"><span>Článek</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskuse:Kruh" rel="discussion" title="Diskuse ke stránce [t]" accesskey="t"><span>Diskuse</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="Změnit variantu jazyka" > <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">čeština</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="Zobrazení"> <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/Kruh"><span>Číst</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kruh&veaction=edit" title="Editovat tuto stránku [v]" accesskey="v"><span>Editovat</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kruh&action=edit" title="Editovat zdrojový kód této stránky [e]" accesskey="e"><span>Editovat zdroj</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kruh&action=history" title="Starší verze této stránky. [h]" accesskey="h"><span>Zobrazit historii</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Nástroje ke stránce"> <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="Nástroje" > <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">Nástroje</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Nástroje</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skrýt</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Další možnosti" > <div class="vector-menu-heading"> Akce </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Kruh"><span>Číst</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kruh&veaction=edit" title="Editovat tuto stránku [v]" accesskey="v"><span>Editovat</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kruh&action=edit" title="Editovat zdrojový kód této stránky [e]" accesskey="e"><span>Editovat zdroj</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kruh&action=history"><span>Zobrazit historii</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Obecné </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Co_odkazuje_na/Kruh" title="Seznam všech wikistránek, které sem odkazují [j]" accesskey="j"><span>Odkazuje sem</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Souvisej%C3%ADc%C3%AD_zm%C4%9Bny/Kruh" rel="nofollow" title="Nedávné změny stránek, na které je odkazováno [k]" accesskey="k"><span>Související změny</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=cs" title="Nahrát obrázky či jiná multimédia [u]" accesskey="u"><span>Načíst soubor</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Kruh&oldid=24598615" title="Trvalý odkaz na současnou verzi této stránky"><span>Trvalý odkaz</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Kruh&action=info" title="Více informací o této stránce"><span>Informace o stránce</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Citovat&page=Kruh&id=24598615&wpFormIdentifier=titleform" title="Informace o tom, jak citovat tuto stránku"><span>Citovat stránku</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:UrlShortener&url=https%3A%2F%2Fcs.wikipedia.org%2Fwiki%2FKruh"><span>Získat zkrácené URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:QrCode&url=https%3A%2F%2Fcs.wikipedia.org%2Fwiki%2FKruh"><span>Stáhnout QR kód</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Tisk/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Kniha&bookcmd=book_creator&referer=Kruh"><span>Vytvořit knihu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:DownloadAsPdf&page=Kruh&action=show-download-screen"><span>Stáhnout jako PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Kruh&printable=yes" title="Tato stránka v podobě vhodné k tisku [p]" accesskey="p"><span>Verze k tisku</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Na jiných projektech </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:Discs" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://cs.wikiquote.org/wiki/Kruh" hreflang="cs"><span>Wikicitáty</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/Q238231" title="Odkaz na propojenou položku datového úložiště [g]" accesskey="g"><span>Položka Wikidat</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="Nástroje ke stránce"> <div 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" typeof="mw:File/Thumb"><a href="/wiki/Soubor:Kruh-2.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Kruh-2.svg/250px-Kruh-2.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Kruh-2.svg/330px-Kruh-2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Kruh-2.svg/500px-Kruh-2.svg.png 2x" data-file-width="691" data-file-height="691" /></a><figcaption> Kruh</figcaption></figure> <div class="uvodni-upozorneni hatnote noprint">Další významy jsou uvedeny na stránce <a href="/wiki/Kruh_(rozcestn%C3%ADk)" class="mw-disambig" title="Kruh (rozcestník)">Kruh (rozcestník)</a>.</div> <p><b>Kruh</b> je rovinný geometrický útvar, omezený <a href="/wiki/Kru%C5%BEnice" title="Kružnice">kružnicí</a>. Kruh je určen svým středem <i>S</i> a poloměrem <i>r</i>: Je to množina všech bodů roviny, které mají od středu vzdálenost menší nebo rovnou poloměru. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Základní_vzorce"><span id="Z.C3.A1kladn.C3.AD_vzorce"></span>Základní vzorce</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=1" title="Editace sekce: Základní vzorce" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kruh&action=edit&section=1" title="Editovat zdrojový kód sekce Základní vzorce"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Soubor:Area_of_a_circle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Area_of_a_circle.svg/500px-Area_of_a_circle.svg.png" decoding="async" width="350" height="149" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Area_of_a_circle.svg/960px-Area_of_a_circle.svg.png 1.5x" data-file-width="1175" data-file-height="500" /></a><figcaption>Grafické vyjádření vzorce pro obsah kruhu. Pokud se kruh rozdělí na velké množství tenkých <a href="/wiki/Kruhov%C3%A1_v%C3%BDse%C4%8D" title="Kruhová výseč">výsečí</a> a střídavě se složí tyto výseče k sobě, lze si představit, že vznikne obdélník. Jedna strana obdélníku je poloměr <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}" /></span>, druhá strana je polovina obvodu kruhu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7447766f482372c761858f993f1432bd3671b0dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.381ex; height:1.676ex;" alt="{\displaystyle \pi r}" /></span>, tím pádem obsah obdélníku vychází <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=\pi r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=\pi r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/277553f82c02cc6166f5993782ba17a8ff60edc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.033ex; height:2.676ex;" alt="{\displaystyle S=\pi r^{2}}" /></span>.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Pro_poloměr"><span id="Pro_polom.C4.9Br"></span>Pro poloměr</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=2" title="Editace sekce: Pro poloměr" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kruh&action=edit&section=2" title="Editovat zdrojový kód sekce Pro poloměr"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Obvod <i>o</i> kruhu je určen vzorcem: </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 o=2\pi r\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>o</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mi>r</mi> <mspace width="thinmathspace"></mspace> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle o=2\pi r\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea9aa3056b858d6ad8940e6aa78db071a24c4561" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.803ex; height:2.509ex;" alt="{\displaystyle o=2\pi r\,,}" /></span></dd></dl> <p>kde <a href="/wiki/P%C3%AD_(%C4%8D%C3%ADslo)" title="Pí (číslo)">π</a> označuje číslo pí, a jeho plocha <i>S</i> vzorcem: </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 S=\pi r^{2}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mspace width="thinmathspace"></mspace> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=\pi r^{2}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b6e3e95867ed19f47a4302f6c18c08102f29b90d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.067ex; height:2.676ex;" alt="{\displaystyle S=\pi r^{2}\,.}" /></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Pro_průměr"><span id="Pro_pr.C5.AFm.C4.9Br"></span>Pro průměr</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=3" title="Editace sekce: Pro průměr" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kruh&action=edit&section=3" title="Editovat zdrojový kód sekce Pro průměr"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pokud bychom uvažovali <a href="/wiki/Polom%C4%9Br" title="Poloměr">poloměr</a> (rádius) <i>r</i> jako polovinu <a href="/wiki/Pr%C5%AFm%C4%9Br_(geometrie)" title="Průměr (geometrie)">průměru</a> <i>d</i>, tedy dosadili: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r={\frac {d}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r={\frac {d}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02f7f4067a8bac8f92d43757deb0ceac1d3385ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:6.199ex; height:5.343ex;" alt="{\displaystyle r={\frac {d}{2}}}" /></span>, tak by vzorce vypadaly následovně: </p><p>pro obvod <i>o</i>: </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 o=2{\frac {\pi d}{2}}=\pi d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>o</mi> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>π</mi> <mi>d</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mi>π</mi> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle o=2{\frac {\pi d}{2}}=\pi d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fcc9ec55186de9f319d9603a46756e417c84db0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.419ex; height:5.343ex;" alt="{\displaystyle o=2{\frac {\pi d}{2}}=\pi d}" /></span></dd></dl> <p>a takto pro plochu <i>S</i>: </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 S=\pi \left({\frac {d}{2}}\right)^{2}=\pi {\frac {d^{2}}{2^{2}}}=\pi {\frac {d^{2}}{4}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mi>π</mi> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mn>4</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=\pi \left({\frac {d}{2}}\right)^{2}=\pi {\frac {d^{2}}{2^{2}}}=\pi {\frac {d^{2}}{4}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c19d6cb15691e66bc0fd92757da1103006064225" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.535ex; height:6.509ex;" alt="{\displaystyle S=\pi \left({\frac {d}{2}}\right)^{2}=\pi {\frac {d^{2}}{2^{2}}}=\pi {\frac {d^{2}}{4}}}" /></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Odvození_vzorce_pro_plochu_pomocí_integrace"><span id="Odvozen.C3.AD_vzorce_pro_plochu_pomoc.C3.AD_integrace"></span>Odvození vzorce pro plochu pomocí integrace</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=4" title="Editace sekce: Odvození vzorce pro plochu pomocí integrace" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kruh&action=edit&section=4" title="Editovat zdrojový kód sekce Odvození vzorce pro plochu pomocí integrace"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Obecný středový tvar rovnice kružnice se středem v počátku soustavy souřadné: </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}+y^{2}=r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+y^{2}=r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37dd4f282df84a83620f71dc52345122e0e3a514" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.64ex; height:3.009ex;" alt="{\displaystyle x^{2}+y^{2}=r^{2}}" /></span></dd></dl> <p>Rovnice části kružnice v I. kvadrantu: </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 y={\sqrt {r^{2}-x^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y={\sqrt {r^{2}-x^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77b2aac8c52e8d2f7748addae9947a1ac09e5a81" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.905ex; height:3.509ex;" alt="{\displaystyle y={\sqrt {r^{2}-x^{2}}}}" /></span></dd></dl> <p>Plocha kruhu se rovná čtyřnásobku plochy vymezené osami <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> a <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 y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" /></span> a částí kružnice v I. kvadrantu. Pomocí integrálního počtu tedy: </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 S=4\int _{0}^{r}{\sqrt {r^{2}-x^{2}}}\,\mathrm {d} x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mn>4</mn> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=4\int _{0}^{r}{\sqrt {r^{2}-x^{2}}}\,\mathrm {d} x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35459d41dccee8780059b365814177590b1f9c1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.633ex; height:5.843ex;" alt="{\displaystyle S=4\int _{0}^{r}{\sqrt {r^{2}-x^{2}}}\,\mathrm {d} x}" /></span></dd></dl> <p>Použijeme <a href="/wiki/Substitu%C4%8Dn%C3%AD_metoda_(integrov%C3%A1n%C3%AD)" title="Substituční metoda (integrování)">substituci</a>, <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=r\sin(\phi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mi>r</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=r\sin(\phi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a28d50554f4201c80f6c501051b6fdf24b0306" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.914ex; height:2.843ex;" alt="{\displaystyle x=r\sin(\phi )}" /></span>, a tedy <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 \mathrm {d} x=r\cos(\phi )\,\mathrm {d} \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>x</mi> <mo>=</mo> <mi>r</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {d} x=r\cos(\phi )\,\mathrm {d} \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b937d03c38315c4e4f03cdb8207f983c6710a543" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.527ex; height:2.843ex;" alt="{\displaystyle \mathrm {d} x=r\cos(\phi )\,\mathrm {d} \phi }" /></span>: </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 S=4\int _{0}^{\pi /2}{\sqrt {r^{2}-r^{2}\sin ^{2}(\phi )}}\,r\cos(\phi )\,\mathrm {d} \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mn>4</mn> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> </msqrt> </mrow> <mspace width="thinmathspace"></mspace> <mi>r</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=4\int _{0}^{\pi /2}{\sqrt {r^{2}-r^{2}\sin ^{2}(\phi )}}\,r\cos(\phi )\,\mathrm {d} \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ac087da27586a18ab087094a4fe907c525c59f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:39.872ex; height:6.343ex;" alt="{\displaystyle S=4\int _{0}^{\pi /2}{\sqrt {r^{2}-r^{2}\sin ^{2}(\phi )}}\,r\cos(\phi )\,\mathrm {d} \phi }" /></span></dd></dl> <p>Upravíme: </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 S=4\int _{0}^{\pi /2}r^{2}\cos ^{2}(\phi )\,\mathrm {d} \phi =4r^{2}\int _{0}^{\pi /2}\cos ^{2}(\phi )\,\mathrm {d} \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mn>4</mn> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msubsup> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ϕ</mi> <mo>=</mo> <mn>4</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msubsup> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace"></mspace> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=4\int _{0}^{\pi /2}r^{2}\cos ^{2}(\phi )\,\mathrm {d} \phi =4r^{2}\int _{0}^{\pi /2}\cos ^{2}(\phi )\,\mathrm {d} \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f0a19e83d0548fba640d822c9f8d1a4a7195010" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:47.577ex; height:6.343ex;" alt="{\displaystyle S=4\int _{0}^{\pi /2}r^{2}\cos ^{2}(\phi )\,\mathrm {d} \phi =4r^{2}\int _{0}^{\pi /2}\cos ^{2}(\phi )\,\mathrm {d} \phi }" /></span></dd></dl> <p>Integrujeme: </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 S=4r^{2}\left[{\frac {\phi }{2}}+{\frac {\sin(2\phi )}{4}}\right]_{0}^{\pi /2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mn>4</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mrow> <mo>[</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ϕ</mi> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mrow> <mn>4</mn> </mfrac> </mrow> </mrow> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=4r^{2}\left[{\frac {\phi }{2}}+{\frac {\sin(2\phi )}{4}}\right]_{0}^{\pi /2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cdf21eba2a7c7dc9d8d8310a106fc5b679535e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.247ex; height:6.843ex;" alt="{\displaystyle S=4r^{2}\left[{\frac {\phi }{2}}+{\frac {\sin(2\phi )}{4}}\right]_{0}^{\pi /2}}" /></span></dd></dl> <p>A po dosazení: </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 S=4r^{2}\left({\frac {\pi }{4}}+{\frac {\sin(\pi )}{4}}\right)=\pi r^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mn>4</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>π</mi> <mo stretchy="false">)</mo> </mrow> <mn>4</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=4r^{2}\left({\frac {\pi }{4}}+{\frac {\sin(\pi )}{4}}\right)=\pi r^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1505112fc51acdaf629e9c2061c8fbc9718f626" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.046ex; height:6.343ex;" alt="{\displaystyle S=4r^{2}\left({\frac {\pi }{4}}+{\frac {\sin(\pi )}{4}}\right)=\pi r^{2}}" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Další_pojmy"><span id="Dal.C5.A1.C3.AD_pojmy"></span>Další pojmy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=5" title="Editace sekce: Další pojmy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kruh&action=edit&section=5" title="Editovat zdrojový kód sekce Další pojmy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Část kruhu vymezená dvěma <a href="/wiki/Pr%C5%AFvodi%C4%8D" class="mw-redirect" title="Průvodič">průvodiči</a> je <b><a href="/wiki/Kruhov%C3%A1_v%C3%BDse%C4%8D" title="Kruhová výseč">kruhová výseč</a></b>, část kruhu omezená <a href="/wiki/Se%C4%8Dna" title="Sečna">sečnou</a> je <b><a href="/wiki/Kruhov%C3%A1_%C3%BAse%C4%8D" title="Kruhová úseč">kruhová úseč</a></b>. Plocha vymezená dvěma soustřednými kružnicemi o nestejném poloměru je <b><a href="/wiki/Mezikru%C5%BE%C3%AD" title="Mezikruží">mezikruží</a></b>. </p> <div class="mw-heading mw-heading2"><h2 id="Kvadratura_kruhu">Kvadratura kruhu</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=6" title="Editace sekce: Kvadratura kruhu" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kruh&action=edit&section=6" title="Editovat zdrojový kód sekce Kvadratura kruhu"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="uvodni-upozorneni hatnote"> Podrobnější informace naleznete v článku <a href="/wiki/Kvadratura_kruhu" title="Kvadratura kruhu">kvadratura kruhu</a>.</div> <p><a href="/wiki/Kvadratura_kruhu" title="Kvadratura kruhu">Kvadratura kruhu</a> je konstrukční úloha: sestrojit k danému kruhu <a href="/wiki/%C4%8Ctverec" title="Čtverec">čtverec</a> o stejném obsahu pouze pomocí <a href="/wiki/Konstrukce_pomoc%C3%AD_prav%C3%ADtka_a_kru%C5%BE%C3%ADtka" class="mw-redirect" title="Konstrukce pomocí pravítka a kružítka">pravítka a kružítka</a>. Tato úloha obecně nemá řešení, přibližná řešení byla ovšem známa už ve starověku. </p><p>Naproti tomu <a href="/w/index.php?title=Tarsk%C3%A9ho_probl%C3%A9m_kvadratury_kruhu&action=edit&redlink=1" class="new" title="Tarského problém kvadratury kruhu (stránka neexistuje)">Tarského problém kvadratury kruhu</a> je úloha rozdělit daný kruh na konečně mnoho kousků a složit z těchto kousků čtverec o stejném obsahu. S použitím <a href="/wiki/Axiom_v%C3%BDb%C4%9Bru" title="Axiom výběru">axiomu výběru</a> je tato úloha řešitelná, ovšem nikoliv prakticky. Kousky jsou <a href="/wiki/Nem%C4%9B%C5%99iteln%C3%A1_mno%C5%BEina" title="Neměřitelná množina">neměřitelné množiny</a>, které nelze realizovat hmotou složenou z <a href="/wiki/%C4%8C%C3%A1stice" title="Částice">částic</a>. Navíc řešení, které nalezl Laczkovich, vyžaduje <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 10^{50}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>50</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{50}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f32ecb7973f19a8ebafcdc5b850eb4c66611d72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.201ex; height:2.676ex;" alt="{\displaystyle 10^{50}}" /></span> kousků.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Třírozměrné tvary, jejichž <a href="/wiki/Rovinn%C3%BD_%C5%99ez" class="mw-redirect" title="Rovinný řez">průsečíky</a> s některými rovinami dávají kruhy, jsou <a href="/wiki/Koule" title="Koule">koule</a>, <a href="/wiki/Sf%C3%A9roid" title="Sféroid">sféroidy</a>, <a href="/wiki/V%C3%A1lec" title="Válec">válce</a> a <a href="/wiki/Ku%C5%BEel" title="Kužel">kužely</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Odkazy">Odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=7" title="Editace sekce: Odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kruh&action=edit&section=7" title="Editovat zdrojový kód sekce Odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Reference">Reference</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=8" title="Editace sekce: Reference" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kruh&action=edit&section=8" title="Editovat zdrojový kód sekce Reference"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><i>Pokroky matematiky, fyziky a astronomie</i>, roč. 35, č. 6</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=9" 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=Kruh&action=edit&section=9" 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/Kru%C5%BEnice" title="Kružnice">Kružnice</a></li> <li><a href="/wiki/Mezikru%C5%BE%C3%AD" title="Mezikruží">Mezikruží</a></li> <li><a href="/wiki/Kvadratura_kruhu" title="Kvadratura kruhu">Kvadratura kruhu</a></li> <li><a href="/wiki/Malfattiho_kruhy" title="Malfattiho kruhy">Malfattiho kruhy</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kruh&veaction=edit&section=10" 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=Kruh&action=edit&section=10" 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"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/20px-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/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></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:Discs" class="extiw" title="c:Category:Discs">kruh</a></span> na Wikimedia Commons</span></span></span><i> </i></li> <li><span class="sisterproject sisterproject-wikiquote"><span class="sisterproject_image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/13px-Wikiquote-logo.svg.png" decoding="async" width="13" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/20px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/27px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></span> <span class="sisterproject_text"><span class="sisterproject_text_prefix">Téma </span><span class="sisterproject_text_target"><a href="https://cs.wikiquote.org/wiki/Kruh" class="extiw" title="q:Kruh">Kruh</a></span><span class="sisterproject_text_suffix"> ve Wikicitátech</span></span></span></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/kruh" class="extiw" title="wikt:kruh">kruh</a></span><span class="sisterproject_text_suffix"> ve Wikislovníku</span></span></span></li> <li><span style="cursor:help;" data-lang="en" title="Jazyk cíle odkazu: angličtina">(anglicky)</span> <a rel="nofollow" class="external text" href="http://www.geometryatlas.com/categories/Circles">Vzorce pro kruh a kružnici</a> na Geometry Atlas.</li> <li><a rel="nofollow" class="external text" href="http://www.mathopenref.com/tocs/circlestoc.html">Interaktivní applety Java</a> Vlastnosti a jednoduché konstrukce kruhu a kružnice.</li></ul> <style data-mw-deduplicate="TemplateStyles:r23078045">.mw-parser-output .navbox2{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox2 .navbox2{margin-top:0}.mw-parser-output .navbox2+.navbox2{margin-top:-1px}.mw-parser-output .navbox2-inner,.mw-parser-output .navbox2-subgroup{width:100%}.mw-parser-output .navbox2-group,.mw-parser-output .navbox2-title,.mw-parser-output .navbox2-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output th.navbox2-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox2,.mw-parser-output .navbox2-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox2-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output tr+tr>.navbox2-abovebelow,.mw-parser-output tr+tr>.navbox2-group,.mw-parser-output tr+tr>.navbox2-image,.mw-parser-output tr+tr>.navbox2-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox2 th,.mw-parser-output .navbox2-title{background-color:#e0e0e0}.mw-parser-output .navbox2-abovebelow,.mw-parser-output th.navbox2-group,.mw-parser-output .navbox2-subgroup .navbox2-title{background-color:#e7e7e7}.mw-parser-output .navbox2-subgroup .navbox2-title{font-size:88%}.mw-parser-output .navbox2-subgroup .navbox2-group,.mw-parser-output .navbox2-subgroup .navbox2-abovebelow{background-color:#f0f0f0}.mw-parser-output .navbox2-even{background-color:#f7f7f7}.mw-parser-output .navbox2-odd{background-color:transparent}.mw-parser-output .navbox2 .hlist td dl,.mw-parser-output .navbox2 .hlist td ol,.mw-parser-output .navbox2 .hlist td ul,.mw-parser-output .navbox2 td.hlist dl,.mw-parser-output .navbox2 td.hlist ol,.mw-parser-output .navbox2 td.hlist ul{padding:0.125em 0}</style><div role="navigation" class="navbox2" aria-labelledby="Autoritní_data_frameless_&#124;text-top_&#124;10px_&#124;alt=Editovat_na_Wikidatech_&#124;link=https&#58;//www.wikidata.org/wiki/Q238231#identifiers&#124;Editovat_na_Wikidatech" style="padding:2px"><table class="nowraplinks hlist navbox2-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Autoritní_data_frameless_&#124;text-top_&#124;10px_&#124;alt=Editovat_na_Wikidatech_&#124;link=https&#58;//www.wikidata.org/wiki/Q238231#identifiers&#124;Editovat_na_Wikidatech" scope="row" class="navbox2-group" style="width:1%"><a href="/wiki/Autoritn%C3%AD_kontrola" title="Autoritní kontrola">Autoritní data</a> <span class="mw-valign-text-top" typeof="mw:File/Frameless"><a 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class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph156662">ph156662</a></span></span></li> <li><span class="nowrap"><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4406111-0">4406111-0</a></span></span></li></ul> </div></td></tr></tbody></table></div> <style data-mw-deduplicate="TemplateStyles:r16915398">.mw-parser-output div/**/#portallinks a{font-weight:bold}</style><div id="portallinks" class="catlinks"><a href="/wiki/Port%C3%A1l:Obsah" title="Portál:Obsah">Portály</a>: <a href="/wiki/Port%C3%A1l:Matematika" title="Portál:Matematika">Matematika</a> </div>    </div><noscript><img src="https://auth.wikimedia.org/loginwiki/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Citováno z „<a dir="ltr" href="https://cs.wikipedia.org/w/index.php?title=Kruh&oldid=24598615">https://cs.wikipedia.org/w/index.php?title=Kruh&oldid=24598615</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/N%C3%A1pov%C4%9Bda:Kategorie" title="Nápověda:Kategorie">Kategorie</a>: <ul><li><a href="/wiki/Kategorie:Obrazce" title="Kategorie:Obrazce">Obrazce</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skryté kategorie: <ul><li><a href="/wiki/Kategorie:Monitoring:%C4%8Cl%C3%A1nky_s_identifik%C3%A1torem_NKC" title="Kategorie:Monitoring:Články s identifikátorem NKC">Monitoring:Články s identifikátorem NKC</a></li><li><a href="/wiki/Kategorie:Monitoring:%C4%8Cl%C3%A1nky_s_identifik%C3%A1torem_GND" title="Kategorie:Monitoring:Články s identifikátorem GND">Monitoring:Články s identifikátorem GND</a></li></ul></div></div> </div> 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