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class="vector-toc-text">Bevezető</div> </a> </li> <li id="toc-Gyakorlati_jelentősége" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gyakorlati_jelentősége"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Gyakorlati jelentősége</span> </div> </a> <ul id="toc-Gyakorlati_jelentősége-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kiszámítása" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kiszámítása"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Kiszámítása</span> </div> </a> <button aria-controls="toc-Kiszámítása-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>A(z) Kiszámítása alszakasz kinyitása/becsukása</span> </button> <ul id="toc-Kiszámítása-sublist" class="vector-toc-list"> <li id="toc-Kör" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kör"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Kör</span> </div> </a> <ul id="toc-Kör-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bonyolultabb_alakzatok" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bonyolultabb_alakzatok"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Bonyolultabb alakzatok</span> </div> </a> <ul id="toc-Bonyolultabb_alakzatok-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Kapcsolódó_szócikkek" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kapcsolódó_szócikkek"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Kapcsolódó szócikkek</span> </div> </a> <ul id="toc-Kapcsolódó_szócikkek-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="Tartalomjegyzék" 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="Tartalomjegyzék kinyitása/becsukása" > <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">Tartalomjegyzék kinyitása/becsukása</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">Kerület (geometria)</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="Ugrás egy más nyelvű szócikkre. Elérhető 80 nyelven" > <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-80" 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">80 nyelv</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Perimeter" title="Perimeter – angol" lang="en" hreflang="en" data-title="Perimeter" data-language-autonym="English" data-language-local-name="angol" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Omtrek" title="Omtrek – afrikaans" lang="af" hreflang="af" data-title="Omtrek" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%98%E1%8C%A0%E1%8A%90_%E1%8B%99%E1%88%AA%E1%8B%AB" title="መጠነ ዙሪያ – amhara" lang="am" hreflang="am" data-title="መጠነ ዙሪያ" data-language-autonym="አማርኛ" data-language-local-name="amhara" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AD%D9%8A%D8%B7_(%D9%87%D9%86%D8%AF%D8%B3%D8%A9_%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A9)" title="محيط (هندسة رياضية) – arab" lang="ar" hreflang="ar" data-title="محيط (هندسة رياضية)" data-language-autonym="العربية" data-language-local-name="arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AA%E0%A7%B0%E0%A6%BF%E0%A6%B8%E0%A7%80%E0%A6%AE%E0%A6%BE" title="পৰিসীমা – asszámi" lang="as" hreflang="as" data-title="পৰিসীমা" data-language-autonym="অসমীয়া" data-language-local-name="asszámi" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Per%C3%ADmetru" title="Perímetru – asztúr" lang="ast" hreflang="ast" data-title="Perímetru" data-language-autonym="Asturianu" data-language-local-name="asztúr" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Muyta" title="Muyta – ajmara" lang="ay" hreflang="ay" data-title="Muyta" data-language-autonym="Aymar aru" data-language-local-name="ajmara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Perimetr" title="Perimetr – azerbajdzsáni" lang="az" hreflang="az" data-title="Perimetr" data-language-autonym="Azərbaycanca" data-language-local-name="azerbajdzsáni" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D1%8B%D0%BC%D0%B5%D1%82%D1%80" title="Перыметр – belarusz" lang="be" hreflang="be" data-title="Перыметр" data-language-autonym="Беларуская" data-language-local-name="belarusz" 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%9F%D1%8D%D1%80%D1%8B%D0%BC%D1%8D%D1%82%D0%B0%D1%80" title="Пэрымэтар – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Пэрымэтар" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B8%D0%BC%D0%B5%D1%82%D1%8A%D1%80" title="Периметър – bolgár" lang="bg" hreflang="bg" data-title="Периметър" data-language-autonym="Български" data-language-local-name="bolgár" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%B8%E0%A7%80%E0%A6%AE%E0%A6%BE" title="পরিসীমা – bangla" lang="bn" hreflang="bn" data-title="পরিসীমা" data-language-autonym="বাংলা" data-language-local-name="bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Per%C3%ADmetre" title="Perímetre – katalán" lang="ca" hreflang="ca" data-title="Perímetre" data-language-autonym="Català" data-language-local-name="katalán" 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/%DA%86%DB%8E%D9%88%DB%95" title="چێوە – közép-ázsiai kurd" lang="ckb" hreflang="ckb" data-title="چێوە" data-language-autonym="کوردی" data-language-local-name="közép-ázsiai kurd" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Perimetru" title="Perimetru – korzikai" lang="co" hreflang="co" data-title="Perimetru" data-language-autonym="Corsu" data-language-local-name="korzikai" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Obvod_(geometrie)" title="Obvod (geometrie) – cseh" lang="cs" hreflang="cs" data-title="Obvod (geometrie)" data-language-autonym="Čeština" data-language-local-name="cseh" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Perimedr" title="Perimedr – walesi" lang="cy" hreflang="cy" data-title="Perimedr" data-language-autonym="Cymraeg" data-language-local-name="walesi" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Omkreds" title="Omkreds – dán" lang="da" hreflang="da" data-title="Omkreds" data-language-autonym="Dansk" data-language-local-name="dán" 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/Umfang_(Geometrie)" title="Umfang (Geometrie) – német" lang="de" hreflang="de" data-title="Umfang (Geometrie)" data-language-autonym="Deutsch" data-language-local-name="német" 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%A0%CE%B5%CF%81%CE%AF%CE%BC%CE%B5%CF%84%CF%81%CE%BF%CF%82" title="Περίμετρος – görög" lang="el" hreflang="el" data-title="Περίμετρος" data-language-autonym="Ελληνικά" data-language-local-name="görög" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Perimetro" title="Perimetro – eszperantó" lang="eo" hreflang="eo" data-title="Perimetro" data-language-autonym="Esperanto" data-language-local-name="eszperantó" 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/Per%C3%ADmetro" title="Perímetro – spanyol" lang="es" hreflang="es" data-title="Perímetro" data-language-autonym="Español" data-language-local-name="spanyol" 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/%C3%9Cmberm%C3%B5%C3%B5t" title="Ümbermõõt – észt" lang="et" hreflang="et" data-title="Ümbermõõt" data-language-autonym="Eesti" data-language-local-name="észt" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Perimetro" title="Perimetro – baszk" lang="eu" hreflang="eu" data-title="Perimetro" data-language-autonym="Euskara" data-language-local-name="baszk" 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%85%D8%AD%DB%8C%D8%B7_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="محیط (هندسه) – perzsa" lang="fa" hreflang="fa" data-title="محیط (هندسه)" data-language-autonym="فارسی" data-language-local-name="perzsa" 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/Piiri_(geometria)" title="Piiri (geometria) – finn" lang="fi" hreflang="fi" data-title="Piiri (geometria)" data-language-autonym="Suomi" data-language-local-name="finn" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr badge-Q17437798 badge-goodarticle mw-list-item" title="jó szócikk"><a href="https://fr.wikipedia.org/wiki/P%C3%A9rim%C3%A8tre" title="Périmètre – francia" lang="fr" hreflang="fr" data-title="Périmètre" data-language-autonym="Français" data-language-local-name="francia" 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/Per%C3%ADmetro" title="Perímetro – gallego" lang="gl" hreflang="gl" data-title="Perímetro" data-language-autonym="Galego" data-language-local-name="gallego" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%99%D7%A7%D7%A3" title="היקף – héber" lang="he" hreflang="he" data-title="היקף" data-language-autonym="עברית" data-language-local-name="héber" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%AE%E0%A4%BE%E0%A4%AA" title="परिमाप – hindi" lang="hi" hreflang="hi" data-title="परिमाप" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Opseg" title="Opseg – horvát" lang="hr" hreflang="hr" data-title="Opseg" data-language-autonym="Hrvatski" data-language-local-name="horvát" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8A%D5%A1%D6%80%D5%A1%D5%A3%D5%AB%D5%AE" title="Պարագիծ – örmény" lang="hy" hreflang="hy" data-title="Պարագիծ" data-language-autonym="Հայերեն" data-language-local-name="örmény" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Perimetro" title="Perimetro – interlingva" lang="ia" hreflang="ia" data-title="Perimetro" data-language-autonym="Interlingua" data-language-local-name="interlingva" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Keliling" title="Keliling – indonéz" lang="id" hreflang="id" data-title="Keliling" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéz" 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/Perimetro" title="Perimetro – idó" lang="io" hreflang="io" data-title="Perimetro" data-language-autonym="Ido" data-language-local-name="idó" 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/Perimetro" title="Perimetro – olasz" lang="it" hreflang="it" data-title="Perimetro" data-language-autonym="Italiano" data-language-local-name="olasz" 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%91%A8%E9%95%B7" title="周長 – japán" lang="ja" hreflang="ja" data-title="周長" data-language-autonym="日本語" data-language-local-name="japán" 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%A0%E1%83%98%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98" title="პერიმეტრი – grúz" lang="ka" hreflang="ka" data-title="პერიმეტრი" data-language-autonym="ქართული" data-language-local-name="grúz" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tamezza_(tusnakt)" title="Tamezza (tusnakt) – kabije" lang="kab" hreflang="kab" data-title="Tamezza (tusnakt)" data-language-autonym="Taqbaylit" data-language-local-name="kabije" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B8%D0%BC%D0%B5%D1%82%D1%80" title="Периметр – kazah" lang="kk" hreflang="kk" data-title="Периметр" data-language-autonym="Қазақша" data-language-local-name="kazah" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%94%E1%9E%9A%E1%9E%B7%E1%9E%98%E1%9E%B6%E1%9E%8F%E1%9F%92%E1%9E%9A" title="បរិមាត្រ – khmer" lang="km" hreflang="km" data-title="បរិមាត្រ" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%91%98%EB%A0%88" title="둘레 – koreai" lang="ko" hreflang="ko" data-title="둘레" data-language-autonym="한국어" data-language-local-name="koreai" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D0%B9%D0%BB%D0%B0%D0%BD%D0%B0%D0%BD%D1%8B%D0%BD_%D1%83%D0%B7%D1%83%D0%BD%D0%B4%D1%83%D0%B3%D1%83" title="Айлананын узундугу – kirgiz" lang="ky" hreflang="ky" data-title="Айлананын узундугу" data-language-autonym="Кыргызча" data-language-local-name="kirgiz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Per%C3%ACmeter" title="Perìmeter – lombard" lang="lmo" hreflang="lmo" data-title="Perìmeter" data-language-autonym="Lombard" data-language-local-name="lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Perimetras" title="Perimetras – litván" lang="lt" hreflang="lt" data-title="Perimetras" data-language-autonym="Lietuvių" data-language-local-name="litván" 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/Perimetrs" title="Perimetrs – lett" lang="lv" hreflang="lv" data-title="Perimetrs" data-language-autonym="Latviešu" data-language-local-name="lett" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9E%D0%B1%D0%B5%D0%BC_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Обем (геометрија) – macedón" lang="mk" hreflang="mk" data-title="Обем (геометрија)" data-language-autonym="Македонски" data-language-local-name="macedón" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%AE%E0%A4%BF%E0%A4%A4%E0%A5%80" title="परिमिती – maráthi" lang="mr" hreflang="mr" data-title="परिमिती" data-language-autonym="मराठी" data-language-local-name="maráthi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Perimeter" title="Perimeter – maláj" lang="ms" hreflang="ms" data-title="Perimeter" data-language-autonym="Bahasa Melayu" data-language-local-name="maláj" 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/Omtrek" title="Omtrek – holland" lang="nl" hreflang="nl" data-title="Omtrek" data-language-autonym="Nederlands" data-language-local-name="holland" 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/Omkrins" title="Omkrins – norvég (nynorsk)" lang="nn" hreflang="nn" data-title="Omkrins" data-language-autonym="Norsk nynorsk" data-language-local-name="norvég (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/Omkrets" title="Omkrets – norvég (bokmål)" lang="nb" hreflang="nb" data-title="Omkrets" data-language-autonym="Norsk bokmål" data-language-local-name="norvég (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Perim%C3%A8tre" title="Perimètre – okszitán" lang="oc" hreflang="oc" data-title="Perimètre" data-language-autonym="Occitan" data-language-local-name="okszitán" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Obw%C3%B3d_(geometria)" title="Obwód (geometria) – lengyel" lang="pl" hreflang="pl" data-title="Obwód (geometria)" data-language-autonym="Polski" data-language-local-name="lengyel" 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/Per%C3%ADmetro" title="Perímetro – portugál" lang="pt" hreflang="pt" data-title="Perímetro" data-language-autonym="Português" data-language-local-name="portugál" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Iruru_muyu" title="Iruru muyu – kecsua" lang="qu" hreflang="qu" data-title="Iruru muyu" data-language-autonym="Runa Simi" data-language-local-name="kecsua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Perimetru" title="Perimetru – román" lang="ro" hreflang="ro" data-title="Perimetru" data-language-autonym="Română" data-language-local-name="román" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rsk mw-list-item"><a href="https://rsk.wikipedia.org/wiki/%D0%9E%D0%B1%D1%81%D1%8F%D0%B3" title="Обсяг – Pannonian Rusyn" lang="rsk" hreflang="rsk" data-title="Обсяг" data-language-autonym="Руски" data-language-local-name="Pannonian Rusyn" class="interlanguage-link-target"><span>Руски</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B8%D0%BC%D0%B5%D1%82%D1%80" title="Периметр – orosz" lang="ru" hreflang="ru" data-title="Периметр" data-language-autonym="Русский" data-language-local-name="orosz" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Opseg" title="Opseg – szerbhorvát" lang="sh" hreflang="sh" data-title="Opseg" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="szerbhorvát" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Perimeter" title="Perimeter – Simple English" lang="en-simple" hreflang="en-simple" data-title="Perimeter" 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/Obseg" title="Obseg – szlovén" lang="sl" hreflang="sl" data-title="Obseg" data-language-autonym="Slovenščina" data-language-local-name="szlovén" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Pimamuganhu" title="Pimamuganhu – sona" lang="sn" hreflang="sn" data-title="Pimamuganhu" data-language-autonym="ChiShona" data-language-local-name="sona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Wareeg" title="Wareeg – szomáli" lang="so" hreflang="so" data-title="Wareeg" data-language-autonym="Soomaaliga" data-language-local-name="szomáli" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Perimetri" title="Perimetri – albán" lang="sq" hreflang="sq" data-title="Perimetri" data-language-autonym="Shqip" data-language-local-name="albán" 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%9E%D0%B1%D0%B8%D0%BC" title="Обим – szerb" lang="sr" hreflang="sr" data-title="Обим" data-language-autonym="Српски / srpski" data-language-local-name="szerb" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Sabudeureun" title="Sabudeureun – szundanéz" lang="su" hreflang="su" data-title="Sabudeureun" data-language-autonym="Sunda" data-language-local-name="szundanéz" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Omkrets" title="Omkrets – svéd" lang="sv" hreflang="sv" data-title="Omkrets" data-language-autonym="Svenska" data-language-local-name="svéd" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Uobw%C5%AFd" title="Uobwůd – sziléziai" lang="szl" hreflang="szl" data-title="Uobwůd" data-language-autonym="Ślůnski" data-language-local-name="sziléziai" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%81%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AE%B3%E0%AE%B5%E0%AF%81" title="சுற்றளவு – tamil" lang="ta" hreflang="ta" data-title="சுற்றளவு" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%9A%E0%B1%81%E0%B0%9F%E0%B1%8D%E0%B0%9F%E0%B1%81%E0%B0%95%E0%B1%8A%E0%B0%B2%E0%B0%A4" title="చుట్టుకొలత – telugu" lang="te" hreflang="te" data-title="చుట్టుకొలత" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%AA%E0%B9%89%E0%B8%99%E0%B8%A3%E0%B8%AD%E0%B8%9A%E0%B8%A3%E0%B8%B9%E0%B8%9B" title="เส้นรอบรูป – thai" lang="th" hreflang="th" data-title="เส้นรอบรูป" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Perimetro" title="Perimetro – tagalog" lang="tl" hreflang="tl" data-title="Perimetro" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B8%D0%BC%D0%B5%D1%82%D1%80" title="Периметр – ukrán" lang="uk" hreflang="uk" data-title="Периметр" data-language-autonym="Українська" data-language-local-name="ukrán" 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%85%D8%AD%DB%8C%D8%B7" title="محیط – urdu" lang="ur" hreflang="ur" data-title="محیط" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Perimetr" title="Perimetr – üzbég" lang="uz" hreflang="uz" data-title="Perimetr" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="üzbég" 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/Chu_vi" title="Chu vi – vietnámi" lang="vi" hreflang="vi" data-title="Chu vi" data-language-autonym="Tiếng Việt" data-language-local-name="vietnámi" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%91%A8%E9%95%BF" title="周长 – wu kínai" lang="wuu" hreflang="wuu" data-title="周长" data-language-autonym="吴语" data-language-local-name="wu kínai" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%9E%E1%83%94%E1%83%A0%E1%83%98%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98" title="პერიმეტრი – Mingrelian" lang="xmf" hreflang="xmf" data-title="პერიმეტრი" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%91%A8%E9%95%BF" title="周长 – kínai" lang="zh" hreflang="zh" data-title="周长" data-language-autonym="中文" data-language-local-name="kínai" 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/Q28474#sitelinks-wikipedia" title="Nyelvközi hivatkozások szerkesztése" class="wbc-editpage">Hivatkozások szerkesztése</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="Névterek"> <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/Ker%C3%BClet_(geometria)" title="A lap megtekintése [c]" accesskey="c"><span>Szócikk</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Vita:Ker%C3%BClet_(geometria)" rel="discussion" title="Az oldal tartalmának megvitatása [t]" accesskey="t"><span>Vitalap</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" 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<div id="mw-indicator-indicator-fr-review-status" class="mw-indicator"><indicator name="fr-review-status" class="mw-fr-review-status-indicator" id="mw-fr-revision-toggle"><span class="cdx-fr-css-icon-review--status--stable"></span><b>Ellenőrzött</b></indicator></div> </div> <div id="siteSub" class="noprint">A Wikipédiából, a szabad enciklopédiából</div> </div> <div id="contentSub"><div id="mw-content-subtitle"><div id="mw-fr-revision-messages"><div id="mw-fr-revision-details" class="mw-fr-revision-details-dialog" style="display:none;"><div tabindex="0"></div><div class="cdx-dialog cdx-dialog--horizontal-actions"><header class="cdx-dialog__header cdx-dialog__header--default"><div class="cdx-dialog__header__title-group"><h2 class="cdx-dialog__header__title">Változat állapota</h2><p class="cdx-dialog__header__subtitle">Ez a lap egy ellenőrzött változata</p></div><button class="cdx-button cdx-button--action-default cdx-button--weight-quiet
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							cdx-fr-css-icon--close"></span></button></header><div class="cdx-dialog__body">Ez a <a href="/wiki/Wikip%C3%A9dia:Jel%C3%B6lt_lapv%C3%A1ltozatok" title="Wikipédia:Jelölt lapváltozatok">közzétett változat</a>, <a class="external text" href="https://hu.wikipedia.org/w/index.php?title=Speci%C3%A1lis:Rendszernapl%C3%B3k&type=review&page=Speci%C3%A1lis:Badtitle/Message">ellenőrizve</a>: <i>2023. április 24.</i><p><table id="mw-fr-revisionratings-box" class="flaggedrevs-color-1" style="margin: auto;" cellpadding="0"><tr><td class="fr-text" style="vertical-align: middle;">Pontosság</td><td class="fr-value40" style="vertical-align: middle;">ellenőrzött</td></tr></table></p></div></div><div tabindex="0"></div></div></div></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="hu" dir="ltr"><p>A <a href="/wiki/Geometria" title="Geometria">geometriában</a> <b>kerület</b> alatt a <a href="/wiki/Dimenzi%C3%B3" title="Dimenzió">kétdimenziós</a> alakzatokat határoló <a href="/wiki/Vonal" title="Vonal">vonal</a> hosszát értjük. Jelentheti magát a határoló vonalat is, például a „kerület mentén” kifejezésben. </p><p>A kerületet magyarul <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 K}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.066ex; height:2.176ex;" alt="{\displaystyle K}"></span>-val rövidítjük. </p><p>Bizonyos képletekben (például a <a href="/wiki/H%C3%A9r%C3%B3n-k%C3%A9plet" title="Hérón-képlet">Hérón-képletben</a>) hasznosabb, ha a kerület felét, a <a href="/w/index.php?title=F%C3%A9lker%C3%BClet&action=edit&redlink=1" class="new" title="Félkerület (a lap nem létezik)">félkerületet</a> jelöljük betűvel. A félkerület jele a <a href="/wiki/Latin_nyelv" title="Latin nyelv">latin</a> <i>semi-</i> <i>(fél-)</i> előtag alapján az <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Gyakorlati_jelentősége"><span id="Gyakorlati_jelent.C5.91s.C3.A9ge"></span>Gyakorlati jelentősége</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ker%C3%BClet_(geometria)&action=edit&section=1" title="Szakasz szerkesztése: Gyakorlati jelentősége"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A kerület fogalma sokszor előkerül a hétköznapi életben is. Például egy telek körbekerítéséhez szükséges kerítés hosszát a telek kerülete adja meg. Egy gördülő kerék egyetlen fordulat alatt annyi utat tesz meg, mint amekkora a keresztmetszetének a kerülete. </p> <div class="mw-heading mw-heading2"><h2 id="Kiszámítása"><span id="Kisz.C3.A1m.C3.ADt.C3.A1sa"></span>Kiszámítása</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ker%C3%BClet_(geometria)&action=edit&section=2" title="Szakasz szerkesztése: Kiszámítása"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/F%C3%A1jl:Simple_polygon.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Simple_polygon.svg/150px-Simple_polygon.svg.png" decoding="async" width="150" height="133" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Simple_polygon.svg/225px-Simple_polygon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8f/Simple_polygon.svg/300px-Simple_polygon.svg.png 2x" data-file-width="588" data-file-height="521" /></a><figcaption>Hatszög</figcaption></figure> <p>A <a href="/wiki/Soksz%C3%B6g" title="Sokszög">sokszögek</a> kerülete egyenlő az oldalak hosszának <a href="/wiki/%C3%96sszegz%C3%A9s" title="Összegzés">összegével</a>. </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 K=a+b+c+\ldots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo>+</mo> <mo>…</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K=a+b+c+\ldots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fadbc5ac3ae2d3e7cc2c696b2e5d0204f6f13251" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:19.643ex; height:2.343ex;" alt="{\displaystyle K=a+b+c+\ldots }"></span></dd></dl> <p><a href="/wiki/Hat%C3%A1r%C3%A9rt%C3%A9k" title="Határérték">Határértékszámítás</a> segítségével a sokszögek kerületének definíciójából kiindulva görbe vonalakkal határolt alakzatoknak is meghatározhatjuk a kerületét. Ennek elméleti módszere a következő: </p><p>A határoló vonalat pontokkal részekre osztjuk, a pontokat megfelelő sorrendben összekötjük egy-egy <a href="/wiki/Szakasz_(geometria)" class="mw-redirect" title="Szakasz (geometria)">szakasszal</a>, majd kiszámítjuk a kapott sokszög kerületét. Ezután még több ponttal osztjuk fel a határoló vonalat, aztán még többel és még többel, közben ügyelve arra, hogy a segédsokszög leghosszabb oldalának hossza nullába <a href="/wiki/Hat%C3%A1r%C3%A9rt%C3%A9k" title="Határérték">tartson</a>. Ha a segédsokszögek kerületének sorozata <a href="/wiki/Konvergencia_(matematika)" title="Konvergencia (matematika)">konvergens</a>, akkor a kerületsorozat határértékét tekintjük az alakzatunk kerületének. </p> <div class="mw-heading mw-heading3"><h3 id="Kör"><span id="K.C3.B6r"></span>Kör</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ker%C3%BClet_(geometria)&action=edit&section=3" title="Szakasz szerkesztése: Kör"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="dablink noprint noviewer" style="padding-left: 2em; vertical-align: middle;" cellpadding="0" cellspacing="0"><tbody><tr><td style="padding-right:.25em;"><span typeof="mw:File"><a href="/wiki/F%C3%A1jl:Searchtool_right.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Searchtool_right.svg/14px-Searchtool_right.svg.png" decoding="async" width="14" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Searchtool_right.svg/21px-Searchtool_right.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Searchtool_right.svg/28px-Searchtool_right.svg.png 2x" data-file-width="60" data-file-height="60" /></a></span></td><td><i>Lásd még: <a href="/wiki/P%C3%AD_(sz%C3%A1m)" class="mw-redirect" title="Pí (szám)">Pí (szám)</a></i></td></tr></tbody></table> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/F%C3%A1jl:PiCamembert1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/PiCamembert1.svg/100px-PiCamembert1.svg.png" decoding="async" width="100" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c8/PiCamembert1.svg/150px-PiCamembert1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c8/PiCamembert1.svg/200px-PiCamembert1.svg.png 2x" data-file-width="265" data-file-height="256" /></a><figcaption>A kör közelítése sokszöggel.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/F%C3%A1jl:Pi-unrolled-720.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pi-unrolled-720.gif/300px-Pi-unrolled-720.gif" decoding="async" width="300" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pi-unrolled-720.gif/450px-Pi-unrolled-720.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2a/Pi-unrolled-720.gif/600px-Pi-unrolled-720.gif 2x" data-file-width="720" data-file-height="228" /></a><figcaption>Az egységnyi átmérőjű gördülő kör egy fordulat alatt a kerületével egyenlő, azaz <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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> egységnyi utat tesz meg.</figcaption></figure> <p>Mivel minden <a href="/wiki/K%C3%B6r_(geometria)" title="Kör (geometria)">kör</a> <a href="/w/index.php?title=Hasonl%C3%B3s%C3%A1g_(geometria)&action=edit&redlink=1" class="new" title="Hasonlóság (geometria) (a lap nem létezik)">hasonló</a>, a kerület <a href="/wiki/Egyenes_ar%C3%A1nyoss%C3%A1g" title="Egyenes arányosság">egyenesen arányos</a> a kör átmérőjével. Ezt a hasonlósági arányt <b><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 }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span></b>-nek nevezték el: </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 K=d\cdot \pi =2r\pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <mi>d</mi> <mo>⋅</mo> <mi>π</mi> <mo>=</mo> <mn>2</mn> <mi>r</mi> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K=d\cdot \pi =2r\pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/094680dcf1b36e91f47abe9229ad13019465a68c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:16.033ex; height:2.176ex;" alt="{\displaystyle K=d\cdot \pi =2r\pi }"></span></dd></dl> <p>ahol <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.216ex; height:2.176ex;" alt="{\displaystyle d}"></span> a kör átmérője, <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> pedig a <a href="/wiki/K%C3%B6r_(geometria)#sugár" title="Kör (geometria)">sugara</a>. </p><p>Ennek 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 \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> számnak a meghatározására használható a feljebb említett módszer, azaz a körvonal felosztása és a keletkező sokszög kerületének számítása, amit az egyszerűség kedvéért általában <a href="/wiki/Szab%C3%A1lyos_soksz%C3%B6g" title="Szabályos sokszög">szabályos sokszögekkel</a> végeznek. </p> <div class="mw-heading mw-heading3"><h3 id="Bonyolultabb_alakzatok">Bonyolultabb alakzatok</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ker%C3%BClet_(geometria)&action=edit&section=4" title="Szakasz szerkesztése: Bonyolultabb alakzatok"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="dablink noprint noviewer" style="padding-left: 2em; vertical-align: middle;" cellpadding="0" cellspacing="0"><tbody><tr><td style="padding-right:.25em;"><span typeof="mw:File"><a href="/wiki/F%C3%A1jl:Searchtool_right.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Searchtool_right.svg/14px-Searchtool_right.svg.png" decoding="async" width="14" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/Searchtool_right.svg/21px-Searchtool_right.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/Searchtool_right.svg/28px-Searchtool_right.svg.png 2x" data-file-width="60" data-file-height="60" /></a></span></td><td><i>Lásd még: <a href="/wiki/Riemann-integr%C3%A1l%C3%A1s#Ívhosszszámítás" title="Riemann-integrálás">Ívhosszszámítás</a></i></td></tr></tbody></table> <p>Bonyolultabb alakzatok kerületének kiszámítása <a href="/wiki/Integr%C3%A1l" title="Integrál">integrálással</a> végezhető, ami szintén a fent említett felosztásos módszeren alapszik. Olyan alakzatokat is lehet definiálni, amelyeknek a kerülete végtelen. Ilyen például a <a href="/wiki/Koch-g%C3%B6rbe" title="Koch-görbe">Koch-görbe</a>, egy <a href="/wiki/H%C3%B3pehely" title="Hópehely">hópehely</a> formájú <a href="/wiki/Frakt%C3%A1l" title="Fraktál">fraktál</a>. tehát a+b+c... vonal így kell kiszámítani </p> <div class="mw-heading mw-heading2"><h2 id="Kapcsolódó_szócikkek"><span id="Kapcsol.C3.B3d.C3.B3_sz.C3.B3cikkek"></span>Kapcsolódó szócikkek</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ker%C3%BClet_(geometria)&action=edit&section=5" title="Szakasz szerkesztése: Kapcsolódó szócikkek"><span>szerkesztés</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Ker%C3%BCleti_sz%C3%B6g" title="Kerületi szög">Kerületi szög</a></li> <li><a href="/wiki/Ter%C3%BClet_(matematika)" title="Terület (matematika)">Terület</a></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">A lap eredeti címe: „<a dir="ltr" href="https://hu.wikipedia.org/w/index.php?title=Kerület_(geometria)&oldid=26051956">https://hu.wikipedia.org/w/index.php?title=Kerület_(geometria)&oldid=26051956</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Wikip%C3%A9dia:Kateg%C3%B3ri%C3%A1k" title="Wikipédia:Kategóriák">Kategória</a>: <ul><li><a href="/wiki/Kateg%C3%B3ria:Abszol%C3%BAt_geometria" title="Kategória:Abszolút geometria">Abszolút geometria</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> A lap utolsó módosítása: 2023. április 24., 20:39</li> <li id="footer-info-copyright">A lap szövege <a rel="nofollow" class="external text" href="http://creativecommons.org/licenses/by-sa/4.0/deed.hu">Creative Commons Nevezd meg! – Így add tovább! 4.0</a> licenc alatt van; egyes esetekben más módon is felhasználható. 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