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Vzdálenost – Wikipedie

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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-Obecné_matematické_zavedení" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Obecné_matematické_zavedení"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Obecné matematické zavedení</span> </div> </a> <ul id="toc-Obecné_matematické_zavedení-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dráha" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dráha"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Dráha</span> </div> </a> <ul id="toc-Dráha-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externí_odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Obsah" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" 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">Vzdálenost</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 98 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-98" 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">98 jazyků</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Afstand" title="Afstand – afrikánština" lang="af" hreflang="af" data-title="Afstand" data-language-autonym="Afrikaans" data-language-local-name="afrikánština" 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%AD%E1%89%80%E1%89%B5" title="ርቀት – amharština" lang="am" hreflang="am" data-title="ርቀት" data-language-autonym="አማርኛ" data-language-local-name="amharština" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Distancia" title="Distancia – aragonština" lang="an" hreflang="an" data-title="Distancia" 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%85%D8%B3%D8%A7%D9%81%D8%A9" title="مسافة – arabština" lang="ar" hreflang="ar" data-title="مسافة" data-language-autonym="العربية" data-language-local-name="arabština" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%A8%D8%B9%D9%88%D8%AF%D9%8A%D8%A9" title="بعودية – arabština (marocká)" lang="ary" hreflang="ary" data-title="بعودية" data-language-autonym="الدارجة" data-language-local-name="arabština (marocká)" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Distancia" title="Distancia – asturština" lang="ast" hreflang="ast" data-title="Distancia" 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/M%C9%99saf%C9%99" title="Məsafə – ázerbájdžánština" lang="az" hreflang="az" data-title="Məsafə" 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/%D9%85%D8%B3%D8%A7%D9%81%D8%AA" title="مسافت – South Azerbaijani" lang="azb" hreflang="azb" data-title="مسافت" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D0%BB%D1%8B%D2%AB%D0%BB%D1%8B%D2%A1" title="Алыҫлыҡ – baškirština" lang="ba" hreflang="ba" data-title="Алыҫлыҡ" data-language-autonym="Башҡортса" data-language-local-name="baškirština" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Distansya" title="Distansya – Central Bikol" lang="bcl" hreflang="bcl" data-title="Distansya" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%B4%D0%BB%D0%B5%D0%B3%D0%BB%D0%B0%D1%81%D1%86%D1%8C" title="Адлегласць – běloruština" lang="be" hreflang="be" data-title="Адлегласць" 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%90%D0%B4%D0%BB%D0%B5%D0%B3%D0%BB%D0%B0%D1%81%D1%8C%D1%86%D1%8C" title="Адлегласьць – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Адлегласьць" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A0%D0%B0%D0%B7%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%B8%D0%B5" title="Разстояние – bulharština" lang="bg" hreflang="bg" data-title="Разстояние" data-language-autonym="Български" data-language-local-name="bulharština" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%A6%E0%A5%81%E0%A4%B0%E0%A4%A4%E0%A5%8D%E0%A4%B5" title="दुरत्व – Bhojpuri" lang="bh" hreflang="bh" data-title="दुरत्व" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A6%E0%A7%82%E0%A6%B0%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="দূরত্ব – bengálština" lang="bn" hreflang="bn" data-title="দূরত্ব" data-language-autonym="বাংলা" data-language-local-name="bengálština" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%97%D0%B0%D0%B9" title="Зай – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Зай" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Dist%C3%A0ncia" title="Distància – katalánština" lang="ca" hreflang="ca" data-title="Distància" data-language-autonym="Català" data-language-local-name="katalánština" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AF%D9%88%D9%88%D8%B1%DB%8C" title="دووری – kurdština (sorání)" lang="ckb" hreflang="ckb" data-title="دووری" data-language-autonym="کوردی" data-language-local-name="kurdština (sorání)" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%98%D0%BD%C3%A7%C4%95%D1%88" title="Инçĕш – čuvaština" lang="cv" hreflang="cv" data-title="Инçĕш" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Afstandsformlen" title="Afstandsformlen – dánština" lang="da" hreflang="da" data-title="Afstandsformlen" data-language-autonym="Dansk" data-language-local-name="dánština" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Abstand" title="Abstand – němčina" lang="de" hreflang="de" data-title="Abstand" 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%91%CF%80%CF%8C%CF%83%CF%84%CE%B1%CF%83%CE%B7_(%CE%B3%CE%B5%CF%89%CE%BC%CE%B5%CF%84%CF%81%CE%AF%CE%B1)" title="Απόσταση (γεωμετρία) – řečtina" lang="el" hreflang="el" data-title="Απόσταση (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/Distance" title="Distance – angličtina" lang="en" hreflang="en" data-title="Distance" 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/Distanco" title="Distanco – esperanto" lang="eo" hreflang="eo" data-title="Distanco" 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/Distancia" title="Distancia – španělština" lang="es" hreflang="es" data-title="Distancia" 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/Kaugus" title="Kaugus – estonština" lang="et" hreflang="et" data-title="Kaugus" data-language-autonym="Eesti" data-language-local-name="estonština" 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/Distantzia" title="Distantzia – baskičtina" lang="eu" hreflang="eu" data-title="Distantzia" data-language-autonym="Euskara" data-language-local-name="baskičtina" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%A7%D8%B5%D9%84%D9%87" title="فاصله – perština" lang="fa" hreflang="fa" data-title="فاصله" 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/V%C3%A4limatka" title="Välimatka – finština" lang="fi" hreflang="fi" data-title="Välimatka" data-language-autonym="Suomi" data-language-local-name="finština" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Distance_(math%C3%A9matiques)" title="Distance (mathématiques) – francouzština" lang="fr" hreflang="fr" data-title="Distance (mathématiques)" 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/Distancia" title="Distancia – galicijština" lang="gl" hreflang="gl" data-title="Distancia" data-language-autonym="Galego" data-language-local-name="galicijština" 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%9E%D7%A8%D7%97%D7%A7" title="מרחק – hebrejština" lang="he" hreflang="he" data-title="מרחק" data-language-autonym="עברית" data-language-local-name="hebrejština" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A6%E0%A5%82%E0%A4%B0%E0%A5%80" title="दूरी – hindština" lang="hi" hreflang="hi" data-title="दूरी" data-language-autonym="हिन्दी" data-language-local-name="hindština" 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/Daljina" title="Daljina – chorvatština" lang="hr" hreflang="hr" data-title="Daljina" 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/Distans" title="Distans – haitština" lang="ht" hreflang="ht" data-title="Distans" 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-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/T%C3%A1vols%C3%A1g" title="Távolság – maďarština" lang="hu" hreflang="hu" data-title="Távolság" data-language-autonym="Magyar" data-language-local-name="maďarština" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A5%D5%BC%D5%A1%D5%BE%D5%B8%D6%80%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%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="Հեռավորություն (երկրաչափություն) – arménština" lang="hy" hreflang="hy" data-title="Հեռավորություն (երկրաչափություն)" data-language-autonym="Հայերեն" data-language-local-name="arménština" 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/Distantia" title="Distantia – interlingua" lang="ia" hreflang="ia" data-title="Distantia" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Penyauh" title="Penyauh – ibanština" lang="iba" hreflang="iba" data-title="Penyauh" data-language-autonym="Jaku Iban" data-language-local-name="ibanština" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Jarak" title="Jarak – indonéština" lang="id" hreflang="id" data-title="Jarak" 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/Disto" title="Disto – ido" lang="io" hreflang="io" data-title="Disto" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Fjarl%C3%A6g%C3%B0" title="Fjarlægð – islandština" lang="is" hreflang="is" data-title="Fjarlægð" data-language-autonym="Íslenska" data-language-local-name="islandština" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Distanza_(matematica)" title="Distanza (matematica) – italština" lang="it" hreflang="it" data-title="Distanza (matematica)" 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/%E8%B7%9D%E9%9B%A2" title="距離 – japonština" lang="ja" hreflang="ja" data-title="距離" 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%9B%E1%83%90%E1%83%9C%E1%83%AB%E1%83%98%E1%83%9A%E1%83%98" title="მანძილი – gruzínština" lang="ka" hreflang="ka" data-title="მანძილი" data-language-autonym="ქართული" data-language-local-name="gruzínština" 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/Ameccaq" title="Ameccaq – kabylština" lang="kab" hreflang="kab" data-title="Ameccaq" data-language-autonym="Taqbaylit" data-language-local-name="kabylština" 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%90%D1%80%D0%B0%D2%9B%D0%B0%D1%88%D1%8B%D2%9B%D1%82%D1%8B%D2%9B" title="Арақашықтық – kazaština" lang="kk" hreflang="kk" data-title="Арақашықтық" data-language-autonym="Қазақша" data-language-local-name="kazaština" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%A6%E0%B3%82%E0%B2%B0" title="ದೂರ – kannadština" lang="kn" hreflang="kn" data-title="ದೂರ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannadština" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B1%B0%EB%A6%AC" title="거리 – korejština" lang="ko" hreflang="ko" data-title="거리" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-krc mw-list-item"><a href="https://krc.wikipedia.org/wiki/%D0%A3%D0%B7%D0%B0%D0%BA%D1%8A%D0%BB%D1%8B%D0%BA%D1%8A" title="Узакълыкъ – karačajevo-balkarština" lang="krc" hreflang="krc" data-title="Узакълыкъ" data-language-autonym="Къарачай-малкъар" data-language-local-name="karačajevo-balkarština" class="interlanguage-link-target"><span>Къарачай-малкъар</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/D%C3%BBrah%C3%AE" title="Dûrahî – kurdština" lang="ku" hreflang="ku" data-title="Dûrahî" data-language-autonym="Kurdî" data-language-local-name="kurdština" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D1%80%D0%B0%D0%BB%D1%8B%D0%BA" title="Аралык – kyrgyzština" lang="ky" hreflang="ky" data-title="Аралык" data-language-autonym="Кыргызча" data-language-local-name="kyrgyzština" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Ofstand" title="Ofstand – lucemburština" lang="lb" hreflang="lb" data-title="Ofstand" data-language-autonym="Lëtzebuergesch" data-language-local-name="lucemburština" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Aafstandj" title="Aafstandj – limburština" lang="li" hreflang="li" data-title="Aafstandj" data-language-autonym="Limburgs" data-language-local-name="limburština" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Atstumas" title="Atstumas – litevština" lang="lt" hreflang="lt" data-title="Atstumas" 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/Att%C4%81lums" title="Attālums – lotyština" lang="lv" hreflang="lv" data-title="Attālums" data-language-autonym="Latviešu" data-language-local-name="lotyština" 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%A0%D0%B0%D1%81%D1%82%D0%BE%D1%98%D0%B0%D0%BD%D0%B8%D0%B5" title="Растојание – makedonština" lang="mk" hreflang="mk" data-title="Растојание" data-language-autonym="Македонски" data-language-local-name="makedonština" 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%85%E0%A4%82%E0%A4%A4%E0%A4%B0" title="अंतर – maráthština" lang="mr" hreflang="mr" data-title="अंतर" data-language-autonym="मराठी" data-language-local-name="maráthština" 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/Jarak" title="Jarak – malajština" lang="ms" hreflang="ms" data-title="Jarak" data-language-autonym="Bahasa Melayu" data-language-local-name="malajština" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%80%E1%80%BD%E1%80%AC%E1%80%A1%E1%80%9D%E1%80%B1%E1%80%B8" title="အကွာအဝေး – barmština" lang="my" hreflang="my" data-title="အကွာအဝေး" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="barmština" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Afstand" title="Afstand – nizozemština" lang="nl" hreflang="nl" data-title="Afstand" data-language-autonym="Nederlands" data-language-local-name="nizozemština" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Avstand" title="Avstand – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Avstand" data-language-autonym="Norsk nynorsk" data-language-local-name="norština (nynorsk)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Avstand" title="Avstand – norština (bokmål)" lang="nb" hreflang="nb" data-title="Avstand" 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-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AA%E0%A9%88%E0%A8%82%E0%A8%A1%E0%A8%BE" title="ਪੈਂਡਾ – paňdžábština" lang="pa" hreflang="pa" data-title="ਪੈਂਡਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="paňdžábština" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Odleg%C5%82o%C5%9B%C4%87" title="Odległość – polština" lang="pl" hreflang="pl" data-title="Odległość" data-language-autonym="Polski" data-language-local-name="polština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D9%88%D8%A7%D9%BC%D9%86" title="واټن – paštština" lang="ps" hreflang="ps" data-title="واټن" data-language-autonym="پښتو" data-language-local-name="paštština" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Dist%C3%A2ncia" title="Distância – portugalština" lang="pt" hreflang="pt" data-title="Distância" data-language-autonym="Português" data-language-local-name="portugalština" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D1%81%D1%81%D1%82%D0%BE%D1%8F%D0%BD%D0%B8%D0%B5" title="Расстояние – ruština" lang="ru" hreflang="ru" data-title="Расстояние" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Distance" title="Distance – skotština" lang="sco" hreflang="sco" data-title="Distance" data-language-autonym="Scots" data-language-local-name="skotština" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Rastojanje" title="Rastojanje – srbochorvatština" lang="sh" hreflang="sh" data-title="Rastojanje" 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-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Distance" title="Distance – Simple English" lang="en-simple" hreflang="en-simple" data-title="Distance" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Vzdialenos%C5%A5" title="Vzdialenosť – slovenština" lang="sk" hreflang="sk" data-title="Vzdialenosť" 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/Razdalja" title="Razdalja – slovinština" lang="sl" hreflang="sl" data-title="Razdalja" data-language-autonym="Slovenščina" data-language-local-name="slovinština" 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/Nhambwe" title="Nhambwe – šonština" lang="sn" hreflang="sn" data-title="Nhambwe" data-language-autonym="ChiShona" data-language-local-name="šonština" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Distanca" title="Distanca – albánština" lang="sq" hreflang="sq" data-title="Distanca" 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%A0%D0%B0%D1%81%D1%82%D0%BE%D1%98%D0%B0%D1%9A%D0%B5" title="Растојање – srbština" lang="sr" hreflang="sr" data-title="Растојање" 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/Avst%C3%A5nd" title="Avstånd – švédština" lang="sv" hreflang="sv" data-title="Avstånd" data-language-autonym="Svenska" data-language-local-name="švédština" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Umbali" title="Umbali – svahilština" lang="sw" hreflang="sw" data-title="Umbali" data-language-autonym="Kiswahili" data-language-local-name="svahilština" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%82%E0%AE%B0%E0%AE%AE%E0%AF%8D" title="தூரம் – tamilština" lang="ta" hreflang="ta" data-title="தூரம்" data-language-autonym="தமிழ்" data-language-local-name="tamilština" 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%A6%E0%B1%82%E0%B0%B0%E0%B0%82" title="దూరం – telugština" lang="te" hreflang="te" data-title="దూరం" data-language-autonym="తెలుగు" data-language-local-name="telugština" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%81%D0%BE%D1%84%D0%B0" title="Масофа – tádžičtina" lang="tg" hreflang="tg" data-title="Масофа" data-language-autonym="Тоҷикӣ" data-language-local-name="tádžičtina" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%A3%E0%B8%B0%E0%B8%A2%E0%B8%B0%E0%B8%97%E0%B8%B2%E0%B8%87" title="ระยะทาง – thajština" lang="th" hreflang="th" data-title="ระยะทาง" data-language-autonym="ไทย" data-language-local-name="thajština" 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/Distansiya" title="Distansiya – tagalog" lang="tl" hreflang="tl" data-title="Distansiya" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Mesafe" title="Mesafe – turečtina" lang="tr" hreflang="tr" data-title="Mesafe" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Mpfhuka" title="Mpfhuka – tsonga" lang="ts" hreflang="ts" data-title="Mpfhuka" data-language-autonym="Xitsonga" data-language-local-name="tsonga" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D1%96%D0%B4%D1%81%D1%82%D0%B0%D0%BD%D1%8C" title="Відстань – ukrajinština" lang="uk" hreflang="uk" data-title="Відстань" data-language-autonym="Українська" data-language-local-name="ukrajinština" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%81%D8%A7%D8%B5%D9%84%DB%81" title="فاصلہ – urdština" lang="ur" hreflang="ur" data-title="فاصلہ" data-language-autonym="اردو" data-language-local-name="urdština" 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/Masofa" title="Masofa – uzbečtina" lang="uz" hreflang="uz" data-title="Masofa" 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-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Distansa" title="Distansa – benátština" lang="vec" hreflang="vec" data-title="Distansa" data-language-autonym="Vèneto" data-language-local-name="benátština" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Kho%E1%BA%A3ng_c%C3%A1ch" title="Khoảng cách – vietnamština" lang="vi" hreflang="vi" data-title="Khoảng cách" 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-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Distansiya" title="Distansiya – warajština" lang="war" hreflang="war" data-title="Distansiya" data-language-autonym="Winaray" data-language-local-name="warajština" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%B7%9D%E7%A6%BB" title="距离 – čínština (dialekty Wu)" lang="wuu" hreflang="wuu" data-title="距离" data-language-autonym="吴语" data-language-local-name="čínština (dialekty Wu)" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/Umgama" title="Umgama – xhoština" lang="xh" hreflang="xh" data-title="Umgama" data-language-autonym="IsiXhosa" data-language-local-name="xhoština" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%95%D7%95%D7%99%D7%99%D7%98%D7%A7%D7%99%D7%99%D7%98" title="ווייטקייט – jidiš" lang="yi" hreflang="yi" data-title="ווייטקייט" data-language-autonym="ייִדיש" data-language-local-name="jidiš" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%B7%9D%E7%A6%BB" title="距离 – čínština" lang="zh" hreflang="zh" data-title="距离" data-language-autonym="中文" data-language-local-name="čínština" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E8%B7%9D" title="距 – čínština (klasická)" lang="lzh" hreflang="lzh" data-title="距" data-language-autonym="文言" data-language-local-name="čínština (klasická)" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/K%C5%AB-l%C4%AB" title="Kū-lī – čínština (dialekty Minnan)" lang="nan" hreflang="nan" data-title="Kū-lī" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="čínština (dialekty Minnan)" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%B7%9D%E9%9B%A2" title="距離 – kantonština" lang="yue" hreflang="yue" data-title="距離" data-language-autonym="粵語" data-language-local-name="kantonština" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q126017#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" > 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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"><div class="noprint ambox labelced labelced-page labelced-page-type-content ambox-content plainlinks"> <div class="labelced_message"><div class="labelced_image ambox-image mbox-image"><span typeof="mw:File"><span><img alt="ikona" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Broom_icon.svg/48px-Broom_icon.svg.png" decoding="async" width="48" height="48" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Broom_icon.svg/72px-Broom_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Broom_icon.svg/96px-Broom_icon.svg.png 2x" data-file-width="400" data-file-height="400" /></span></span></div> <div class="labelced_message_inner"> <div class="labelced_message_headline ambox-text">Tento článek potřebuje úpravy.</div> <div class="labelced_message_text hide-when-compact ambox-text">Můžete Wikipedii pomoci tím, že ho <span class="editlink plainlinks" style=""><a class="external text" href="https://cs.wikipedia.org/w/index.php?title=Vzd%C3%A1lenost&amp;action=edit">vylepšíte</a></span>. Jak by měly články vypadat, popisují stránky <a href="/wiki/Wikipedie:Vzhled_a_styl" title="Wikipedie:Vzhled a styl">Vzhled a styl</a>, <a href="/wiki/Wikipedie:Encyklopedick%C3%BD_styl" title="Wikipedie:Encyklopedický styl">Encyklopedický styl</a> a <a href="/wiki/Wikipedie:Pr%C5%AFvodce_(odkazy)" title="Wikipedie:Průvodce (odkazy)">Odkazy</a>.</div> </div> </div> </div> <p><b>Vzdálenost</b> je výraz pro odlehlost dvou bodů nebo útvarů (rovnocenných, bez vzájemného rozlišení, bez orientace směru) a pro vyjádření jejich vzájemné polohy. Ve <a href="/wiki/Fyzika" title="Fyzika">fyzice</a> zpravidla označuje prostorovou nebo časovou odlehlost věcí, v <a href="/wiki/Matematika" title="Matematika">matematice</a> však musí splňovat více kritérií. </p><p>Zvláštní případ vzdálenosti je <b>dálka</b>, kdy rozlišujeme výchozí, počáteční bod, místo pozorovatele, „odkud“ a vzdálený, koncový, cílový bod, „kam“. V běžném hovoru se zpravidla od pojmu "vzdálenost" neodlišuje. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Obecné_matematické_zavedení"><span id="Obecn.C3.A9_matematick.C3.A9_zaveden.C3.AD"></span>Obecné matematické zavedení</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vzd%C3%A1lenost&amp;veaction=edit&amp;section=1" title="Editace sekce: Obecné matematické zavedení" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vzd%C3%A1lenost&amp;action=edit&amp;section=1" title="Editovat zdrojový kód sekce Obecné matematické zavedení"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>V <a href="/wiki/Matematika" title="Matematika">matematice</a>, speciálně v <a href="/wiki/Geometrie" title="Geometrie">geometrii</a> je <b>vzdálenost</b> <a href="/wiki/Funkce_(matematika)" title="Funkce (matematika)">funkce</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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C1;<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>: M x M → R definovaná na dané <a href="/wiki/Mno%C5%BEina" title="Množina">množině</a> M splňující následující vlastnosti: </p> <ul><li>Každým dvěma bodům z množiny M je přiřazena vzdálenost.</li> <li>Je pozitivně definitní. <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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C1;<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>(<i>x</i>,<i>y</i>) ≥ 0, přičemž <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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C1;<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>(<i>x</i>,<i>y</i>) = 0 <a href="/wiki/Ekvivalence_(logika)" title="Ekvivalence (logika)">právě když</a> <i>x</i> = <i>y</i>. (Vzdálenost je vždy kladná jsou-li dané body různé, jsou-li stejné, je nulová).</li> <li>Je <a href="/wiki/Symetrie" title="Symetrie">symetrická</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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C1;<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>(<i>x</i>,<i>y</i>) = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C1;<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>(<i>y</i>,<i>x</i>). (Vzdálenost z <i>x</i> do <i>y</i> je stejná jako z <i>y</i> do <i>x</i>).</li> <li>Splňuje <a href="/wiki/Troj%C3%BAheln%C3%ADkov%C3%A1_nerovnost" title="Trojúhelníková nerovnost">trojúhelníkovou nerovnost</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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C1;<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>(<i>x</i>,<i>z</i>) ≤ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C1;<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>(<i>x</i>,<i>y</i>) + <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C1;<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>(<i>y</i>,<i>z</i>). (Vzdálenost dvou bodů není nikdy vyšší, než součet vzdáleností do třetího bodu od bodu prvního a od bodu druhého).</li></ul> <p>Takovouto <a href="/wiki/Funkce_(matematika)" title="Funkce (matematika)">funkci</a> nazýváme <a href="/wiki/Metrika" class="mw-disambig" title="Metrika">metrika</a>. Dvojice (M,<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 \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>&#x03C1;<!-- ρ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span>) se nazývá <a href="/wiki/Metrick%C3%BD_prostor" title="Metrický prostor">metrický prostor</a>. </p><p>Vzdálenost je definována i pro dva geometrické útvary (např. bod a přímka, přímka a rovina). Vzdálenost 2 útvarů se rovná nejmenší vzdálenosti 2 bodů, kde jeden bod patří jednomu útvaru a druhý bod druhému. Proto ji měříme na kolmici. </p> <div class="mw-heading mw-heading2"><h2 id="Dráha"><span id="Dr.C3.A1ha"></span>Dráha</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vzd%C3%A1lenost&amp;veaction=edit&amp;section=2" title="Editace sekce: Dráha" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vzd%C3%A1lenost&amp;action=edit&amp;section=2" title="Editovat zdrojový kód sekce Dráha"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="infobox" style="width:22em;width: 250px;"><tbody><tr><th colspan="2" style="text-align:center;font-size:125%;font-weight:bold">Dráha</th></tr><tr><th scope="row" style="text-align:left">Název <a href="/wiki/Fyzik%C3%A1ln%C3%AD_veli%C4%8Dina" title="Fyzikální veličina">veličiny</a><br />a její <a href="/wiki/Zna%C4%8Dka_fyzik%C3%A1ln%C3%AD_veli%C4%8Diny" class="mw-redirect" title="Značka fyzikální veličiny">značka</a></th><td>Dráha<br /><span class="texhtml"><var>s</var></span></td></tr><tr><th scope="row" style="text-align:left"><a href="/wiki/Hlavn%C3%AD_jednotka_SI" class="mw-redirect" title="Hlavní jednotka SI">Hlavní jednotka SI</a><br />a její značka</th><td><a href="/wiki/Metr" title="Metr">metr</a><br />m</td></tr><tr><th scope="row" style="text-align:left">Dle transformace složek</th><td><a href="/wiki/Skal%C3%A1r" title="Skalár">skalární</a></td></tr></tbody></table> <p>Ve <a href="/wiki/Fyzika" title="Fyzika">fyzice</a> označuje <b><a href="/wiki/Dr%C3%A1ha_(fyzika)" class="mw-redirect" title="Dráha (fyzika)">dráha</a></b> <a href="/wiki/D%C3%A9lka" title="Délka">délku</a> <a href="/wiki/Trajektorie" title="Trajektorie">trajektorie</a>, kterou <a href="/wiki/T%C4%9Bleso" title="Těleso">těleso</a> (<a href="/wiki/Hmotn%C3%BD_bod" title="Hmotný bod">hmotný bod</a>) urazí za určitou <a href="/wiki/%C4%8Cas" title="Čas">dobu</a>. Dráha je tedy vzdálenost, kterou těleso (hmotný bod) urazí mezi dvěma časovými okamžiky a měří se podél trajektorie. Dráha je charakteristikou <a href="/wiki/Mechanick%C3%BD_pohyb" title="Mechanický pohyb">mechanického pohybu</a>. </p><p>Uvažujeme-li těleso (hmotný bod) pohybující se po zvolené trajektorii, pak je dráha mezi dvěma <a href="/wiki/Bod" title="Bod">body</a> na této trajektorii vždy větší nebo rovna nejkratší vzdálenosti těchto bodů (dráha je rovna této vzdálenosti v případě <a href="/wiki/P%C5%99%C3%ADmo%C4%8Dar%C3%BD_pohyb" title="Přímočarý pohyb">přímočaré</a> trajektorie). </p><p>Dráhu obvykle značíme <b>s</b> a měříme v&#160;<a href="/wiki/Metr" title="Metr">metrech</a> a zkratku píšeme <b>m</b>. </p> <div class="mw-heading mw-heading2"><h2 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vzd%C3%A1lenost&amp;veaction=edit&amp;section=3" title="Editace sekce: Související články" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vzd%C3%A1lenost&amp;action=edit&amp;section=3" title="Editovat zdrojový kód sekce Související články"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/D%C3%A9lka" title="Délka">Délka</a></li> <li><a href="/wiki/%C4%8Casoprostor#Vzdálenost_v_časoprostoru" title="Časoprostor">Vzdálenost v časoprostoru</a></li> <li><a href="/wiki/Hammingova_vzd%C3%A1lenost" title="Hammingova vzdálenost">Hammingova vzdálenost</a></li> <li><a href="/wiki/Eukleidovsk%C3%A1_metrika" title="Eukleidovská metrika">Eukleidovská metrika</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Vzd%C3%A1lenost&amp;veaction=edit&amp;section=4" title="Editace sekce: Externí odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Vzd%C3%A1lenost&amp;action=edit&amp;section=4" title="Editovat zdrojový kód sekce Externí odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="wd"><span class="sisterproject sisterproject-commons"><span class="sisterproject_image"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></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:Distance" class="extiw" title="c:Category:Distance">vzdálenost</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/Vzd%C3%A1lenost" class="extiw" title="q:Vzdálenost">Vzdálenost</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/vzd%C3%A1lenost" class="extiw" title="wikt:vzdálenost">vzdálenost</a></span><span class="sisterproject_text_suffix"> ve Wikislovníku</span></span></span></li></ul> <table class="plainlinks metadata noprint pahyl" cellpadding="2" style="background: transparent;"> <tbody><tr> <td><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/Soubor:Wiki_letter_w.svg" class="mw-file-description" title="Pahýl"><img alt="Pahýl" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a><figcaption>Pahýl</figcaption></figure> </td> <td><i>Tento článek je příliš stručný nebo <a href="/wiki/Wikipedie:Pah%C3%BDl" title="Wikipedie:Pahýl">postrádá důležité informace</a>.<br />Pomozte Wikipedii tím, že jej vhodně <a class="external text" href="https://cs.wikipedia.org/w/index.php?title=Vzd%C3%A1lenost&amp;action=edit">rozšíříte</a>. Nevkládejte však <a href="/wiki/Wikipedie:Autorsk%C3%A9_pr%C3%A1vo#Publikování_cizích_autorských_děl" title="Wikipedie:Autorské právo">bez oprávnění</a> cizí texty.</i> </td></tr></tbody></table> <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 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