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class="mw-list-item"><a href="/wiki/Wikipedie:Pot%C5%99ebuji_pomoc" title="Pokud si nevíte rady, zeptejte se ostatních"><span>Potřebuji pomoc</span></a></li><li id="n-featuredcontent" class="mw-list-item"><a href="/wiki/Wikipedie:Nejlep%C5%A1%C3%AD_%C4%8Dl%C3%A1nky" title="Přehled článků, které jsou považovány za nejlepší na české Wikipedii"><span>Nejlepší články</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:N%C3%A1hodn%C3%A1_str%C3%A1nka" title="Přejít na náhodně vybranou stránku [x]" accesskey="x"><span>Náhodný článek</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Posledn%C3%AD_zm%C4%9Bny" title="Seznam posledních změn na této wiki [r]" accesskey="r"><span>Poslední změny</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedie:Port%C3%A1l_Wikipedie" title="O projektu, jak můžete pomoci, kde hledat"><span>Komunitní portál</span></a></li><li id="n-villagepump" class="mw-list-item"><a href="/wiki/Wikipedie:Pod_l%C3%ADpou" title="Hlavní diskusní fórum"><span>Pod lípou</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Speci%C3%A1ln%C3%AD_str%C3%A1nky"><span>Speciální stránky</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Hlavn%C3%AD_strana" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedie" src="/static/images/mobile/copyright/wikipedia-wordmark-cs.svg" style="width: 7.5em; height: 1.1875em;"> <img class="mw-logo-tagline" alt="Wikipedie: Otevřená encyklopedie" src="/static/images/mobile/copyright/wikipedia-tagline-cs.svg" width="118" height="13" style="width: 7.375em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Speci%C3%A1ln%C3%AD:Hled%C3%A1n%C3%AD" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Prohledat tuto wiki [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Hledání</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Hledat na 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přihlásit se, ovšem není to povinné. [o]" accesskey="o" class=""><span>Přihlášení</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Další možnosti" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Osobní nástroje" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Osobní nástroje</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Uživatelské menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=cs.wikipedia.org&uselang=cs"><span>Podpořte Wikipedii</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Vytvo%C5%99it_%C3%BA%C4%8Det&returnto=Bod" title="Doporučujeme vytvořit si účet a přihlásit se, ovšem není to povinné"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Vytvoření účtu</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:P%C5%99ihl%C3%A1sit&returnto=Bod" title="Doporučujeme vám přihlásit se, ovšem není to povinné. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Přihlášení</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Stránky pro odhlášené editory <a href="/wiki/N%C3%A1pov%C4%9Bda:%C3%9Avod" aria-label="Více informací o editování"><span>dozvědět se více</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Moje_p%C5%99%C3%ADsp%C4%9Bvky" title="Seznam editací provedených z této IP adresy [y]" accesskey="y"><span>Příspěvky</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Moje_diskuse" title="Diskuse o editacích provedených z této IP adresy [n]" accesskey="n"><span>Diskuse</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Projekt"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Obsah" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Obsah</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skrýt</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(úvod)</div> </a> </li> <li id="toc-Vlastnosti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vlastnosti"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Vlastnosti</span> </div> </a> <button aria-controls="toc-Vlastnosti-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Přepnout podsekci Vlastnosti</span> </button> <ul id="toc-Vlastnosti-sublist" class="vector-toc-list"> <li id="toc-Značení" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Značení"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Značení</span> </div> </a> <ul id="toc-Značení-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zápis_bodu" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zápis_bodu"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Zápis bodu</span> </div> </a> <ul id="toc-Zápis_bodu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vzdálenost" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vzdálenost"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Vzdálenost</span> </div> </a> <ul id="toc-Vzdálenost-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Typy_bodů" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Typy_bodů"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Typy bodů</span> </div> </a> <ul id="toc-Typy_bodů-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Odkazy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Odkazy</span> </div> </a> <button aria-controls="toc-Odkazy-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Přepnout podsekci Odkazy</span> </button> <ul id="toc-Odkazy-sublist" class="vector-toc-list"> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Související_články" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Související_články"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Související články</span> </div> </a> <ul id="toc-Související_články-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externí_odkazy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Externí_odkazy"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Externí odkazy</span> </div> </a> <ul id="toc-Externí_odkazy-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Obsah" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Obsah" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Přepnout obsah" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Přepnout obsah</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Bod</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 103 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-103" 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">103 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/Punt_(meetkunde)" title="Punt (meetkunde) – afrikánština" lang="af" hreflang="af" data-title="Punt (meetkunde)" data-language-autonym="Afrikaans" data-language-local-name="afrikánština" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Punkt_(Geometrie)" title="Punkt (Geometrie) – němčina (Švýcarsko)" lang="gsw" hreflang="gsw" data-title="Punkt (Geometrie)" data-language-autonym="Alemannisch" data-language-local-name="němčina (Švýcarsko)" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D9%82%D8%B7%D8%A9_(%D9%87%D9%86%D8%AF%D8%B3%D8%A9)" title="نقطة (هندسة) – arabština" lang="ar" hreflang="ar" data-title="نقطة (هندسة)" 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/%D9%86%D9%82%D8%B7%D8%A9_(%D9%84%D9%85%D8%A7%D8%B7)" title="نقطة (لماط) – arabština (marocká)" lang="ary" hreflang="ary" data-title="نقطة (لماط)" data-language-autonym="الدارجة" data-language-local-name="arabština (marocká)" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%A8%E0%A7%8D%E0%A6%A6%E0%A7%81" title="বিন্দু – ásámština" lang="as" hreflang="as" data-title="বিন্দু" data-language-autonym="অসমীয়া" data-language-local-name="ásámština" 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/Puntu_(xeometr%C3%ADa)" title="Puntu (xeometría) – asturština" lang="ast" hreflang="ast" data-title="Puntu (xeometría)" 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/N%C3%B6qt%C9%99_(h%C9%99nd%C9%99s%C9%99)" title="Nöqtə (həndəsə) – ázerbájdžánština" lang="az" hreflang="az" data-title="Nöqtə (həndəsə)" 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%86%D9%88%D9%82%D8%B7%D9%87_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA)" title="نوقطه (ریاضیات) – South Azerbaijani" lang="azb" hreflang="azb" data-title="نوقطه (ریاضیات)" 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%9D%D3%A9%D0%BA%D1%82%D3%99_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Нөктә (геометрия) – baškirština" lang="ba" hreflang="ba" data-title="Нөктә (геометрия)" 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/Punto" title="Punto – Central Bikol" lang="bcl" hreflang="bcl" data-title="Punto" 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%9F%D1%83%D0%BD%D0%BA%D1%82" title="Пункт – běloruština" lang="be" hreflang="be" data-title="Пункт" 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%9F%D1%83%D0%BD%D0%BA%D1%82_(%D0%B3%D0%B5%D0%B0%D0%BC%D1%8D%D1%82%D1%80%D1%8B%D1%8F)" title="Пункт (геамэтрыя) – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Пункт (геамэтрыя)" 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%A2%D0%BE%D1%87%D0%BA%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Точка (геометрия) – bulharština" lang="bg" hreflang="bg" data-title="Точка (геометрия)" data-language-autonym="Български" data-language-local-name="bulharština" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Poent_(geometriezh)" title="Poent (geometriezh) – bretonština" lang="br" hreflang="br" data-title="Poent (geometriezh)" data-language-autonym="Brezhoneg" data-language-local-name="bretonština" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Ta%C4%8Dka_(geometrija)" title="Tačka (geometrija) – bosenština" lang="bs" hreflang="bs" data-title="Tačka (geometrija)" data-language-autonym="Bosanski" data-language-local-name="bosenština" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Punt_(geometria)" title="Punt (geometria) – katalánština" lang="ca" hreflang="ca" data-title="Punt (geometria)" 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%AE%D8%A7%DA%B5_(%D8%A6%DB%95%D9%86%D8%AF%D8%A7%D8%B2%DB%95)" title="خاڵ (ئەندازە) – kurdština (sorání)" lang="ckb" hreflang="ckb" data-title="خاڵ (ئەندازە)" 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%9F%C4%83%D0%BD%D1%87%C4%83_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8)" title="Пăнчă (геометри) – čuvaština" lang="cv" hreflang="cv" data-title="Пăнчă (геометри)" data-language-autonym="Чӑвашла" data-language-local-name="čuvaština" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Pwynt_(geometreg)" title="Pwynt (geometreg) – velština" lang="cy" hreflang="cy" data-title="Pwynt (geometreg)" data-language-autonym="Cymraeg" data-language-local-name="velština" 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/Punkt" title="Punkt – dánština" lang="da" hreflang="da" data-title="Punkt" 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/Punkt_(Geometrie)" title="Punkt (Geometrie) – němčina" lang="de" hreflang="de" data-title="Punkt (Geometrie)" 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%A3%CE%B7%CE%BC%CE%B5%CE%AF%CE%BF" title="Σημείο – řečtina" lang="el" hreflang="el" data-title="Σημείο" 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/Point_(geometry)" title="Point (geometry) – angličtina" lang="en" hreflang="en" data-title="Point (geometry)" 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/Punkto_(matematiko)" title="Punkto (matematiko) – esperanto" lang="eo" hreflang="eo" data-title="Punkto (matematiko)" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Punto_(geometr%C3%ADa)" title="Punto (geometría) – španělština" lang="es" hreflang="es" data-title="Punto (geometría)" 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/Punkt_(matemaatika)" title="Punkt (matemaatika) – estonština" lang="et" hreflang="et" data-title="Punkt (matemaatika)" 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/Puntu_(geometria)" title="Puntu (geometria) – baskičtina" lang="eu" hreflang="eu" data-title="Puntu (geometria)" 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%86%D9%82%D8%B7%D9%87_(%D9%87%D9%86%D8%AF%D8%B3%D9%87)" title="نقطه (هندسه) – perština" lang="fa" hreflang="fa" data-title="نقطه (هندسه)" 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/Piste_(geometria)" title="Piste (geometria) – finština" lang="fi" hreflang="fi" data-title="Piste (geometria)" data-language-autonym="Suomi" data-language-local-name="finština" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Poidi_(jiometri)" title="Poidi (jiometri) – fidžijština" lang="fj" hreflang="fj" data-title="Poidi (jiometri)" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fidžijština" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Point_(g%C3%A9om%C3%A9trie)" title="Point (géométrie) – francouzština" lang="fr" hreflang="fr" data-title="Point (géométrie)" data-language-autonym="Français" data-language-local-name="francouzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Ponkt_(Geometrii)" title="Ponkt (Geometrii) – fríština (severní)" lang="frr" hreflang="frr" data-title="Ponkt (Geometrii)" data-language-autonym="Nordfriisk" data-language-local-name="fríština (severní)" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E9%BB%9E" title="點 – čínština (dialekty Gan)" lang="gan" hreflang="gan" data-title="點" data-language-autonym="贛語" data-language-local-name="čínština (dialekty Gan)" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Pwen_(j%C3%A9om%C3%A9tri)" title="Pwen (jéométri) – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Pwen (jéométri)" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Punto_(xeometr%C3%ADa)" title="Punto (xeometría) – galicijština" lang="gl" hreflang="gl" data-title="Punto (xeometría)" data-language-autonym="Galego" data-language-local-name="galicijština" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AC%E0%AA%BF%E0%AA%82%E0%AA%A6%E0%AB%81" title="બિંદુ – gudžarátština" lang="gu" hreflang="gu" data-title="બિંદુ" data-language-autonym="ગુજરાતી" data-language-local-name="gudžarátština" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A0%D7%A7%D7%95%D7%93%D7%94_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="נקודה (גאומטריה) – hebrejština" lang="he" hreflang="he" data-title="נקודה (גאומטריה)" 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%AC%E0%A4%BF%E0%A4%82%E0%A4%A6%E0%A5%81" title="बिंदु – hindština" lang="hi" hreflang="hi" data-title="बिंदु" 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/To%C4%8Dka_(geometrija)" title="Točka (geometrija) – chorvatština" lang="hr" hreflang="hr" data-title="Točka (geometrija)" data-language-autonym="Hrvatski" data-language-local-name="chorvatština" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Pont_(geometria)" title="Pont (geometria) – maďarština" lang="hu" hreflang="hu" data-title="Pont (geometria)" 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/%D4%BF%D5%A5%D5%BF" title="Կետ – arménština" lang="hy" hreflang="hy" data-title="Կետ" 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/Puncto_(geometria)" title="Puncto (geometria) – interlingua" lang="ia" hreflang="ia" data-title="Puncto (geometria)" data-language-autonym="Interlingua" data-language-local-name="interlingua" 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/Titik_(geometri)" title="Titik (geometri) – indonéština" lang="id" hreflang="id" data-title="Titik (geometri)" 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/Punto_(geometrio)" title="Punto (geometrio) – ido" lang="io" hreflang="io" data-title="Punto (geometrio)" 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/Punktur_(r%C3%BAmfr%C3%A6%C3%B0i)" title="Punktur (rúmfræði) – islandština" lang="is" hreflang="is" data-title="Punktur (rúmfræði)" 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/Punto_(geometria)" title="Punto (geometria) – italština" lang="it" hreflang="it" data-title="Punto (geometria)" 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/%E7%82%B9_(%E6%95%B0%E5%AD%A6)" title="点 (数学) – japonština" lang="ja" hreflang="ja" data-title="点 (数学)" 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-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Paint_(matimatix)" title="Paint (matimatix) – jamajská kreolština" lang="jam" hreflang="jam" data-title="Paint (matimatix)" data-language-autonym="Patois" data-language-local-name="jamajská kreolština" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Titik_(g%C3%A9om%C3%A8tri)" title="Titik (géomètri) – javánština" lang="jv" hreflang="jv" data-title="Titik (géomètri)" data-language-autonym="Jawa" data-language-local-name="javánština" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AC%E1%83%94%E1%83%A0%E1%83%A2%E1%83%98%E1%83%9A%E1%83%98_(%E1%83%92%E1%83%94%E1%83%9D%E1%83%9B%E1%83%94%E1%83%A2%E1%83%A0%E1%83%98%E1%83%90)" title="წერტილი (გეომეტრია) – gruzínština" lang="ka" hreflang="ka" data-title="წერტილი (გეომეტრია)" 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/Agaz_(tanzeggit)" title="Agaz (tanzeggit) – kabylština" lang="kab" hreflang="kab" data-title="Agaz (tanzeggit)" data-language-autonym="Taqbaylit" data-language-local-name="kabylština" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/Ica" title="Ica – kikujština" lang="ki" hreflang="ki" data-title="Ica" data-language-autonym="Gĩkũyũ" data-language-local-name="kikujština" class="interlanguage-link-target"><span>Gĩkũyũ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9D%D2%AF%D0%BA%D1%82%D0%B5_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Нүкте (геометрия) – kazaština" lang="kk" hreflang="kk" data-title="Нүкте (геометрия)" data-language-autonym="Қазақша" data-language-local-name="kazaština" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%90_(%EA%B8%B0%ED%95%98%ED%95%99)" title="점 (기하학) – korejština" lang="ko" hreflang="ko" data-title="점 (기하학)" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Xal" title="Xal – kurdština" lang="ku" hreflang="ku" data-title="Xal" data-language-autonym="Kurdî" data-language-local-name="kurdština" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Punctum_(mathematica)" title="Punctum (mathematica) – latina" lang="la" hreflang="la" data-title="Punctum (mathematica)" data-language-autonym="Latina" data-language-local-name="latina" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Ta%C5%A1kas_(geometrija)" title="Taškas (geometrija) – litevština" lang="lt" hreflang="lt" data-title="Taškas (geometrija)" 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/Punkts_(%C4%A3eometrija)" title="Punkts (ģeometrija) – lotyština" lang="lv" hreflang="lv" data-title="Punkts (ģeometrija)" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Teboka_(je%C3%B4metria)" title="Teboka (jeômetria) – malgaština" lang="mg" hreflang="mg" data-title="Teboka (jeômetria)" data-language-autonym="Malagasy" data-language-local-name="malgaština" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%A2%D0%BE%D1%87%D0%BA%D0%BE_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D0%B9)" title="Точко (геометрий) – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Точко (геометрий)" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%BE%D1%87%D0%BA%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Точка (геометрија) – makedonština" lang="mk" hreflang="mk" data-title="Точка (геометрија)" data-language-autonym="Македонски" data-language-local-name="makedonština" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Titik_(geometri)" title="Titik (geometri) – malajština" lang="ms" hreflang="ms" data-title="Titik (geometri)" 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%99%E1%80%BE%E1%80%90%E1%80%BA" title="အမှတ် – barmština" lang="my" hreflang="my" data-title="အမှတ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="barmština" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Punkt_(Geometrie)" title="Punkt (Geometrie) – dolnoněmčina" lang="nds" hreflang="nds" data-title="Punkt (Geometrie)" data-language-autonym="Plattdüütsch" data-language-local-name="dolnoněmčina" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AC%E0%A4%BF%E0%A4%A8%E0%A5%8D%E0%A4%A6%E0%A5%81" title="बिन्दु – nepálština" lang="ne" hreflang="ne" data-title="बिन्दु" data-language-autonym="नेपाली" data-language-local-name="nepálština" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%AB%E0%A5%81%E0%A4%A4%E0%A4%BF" title="फुति – névárština" lang="new" hreflang="new" data-title="फुति" data-language-autonym="नेपाल भाषा" data-language-local-name="névárština" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Punt_(wiskunde)" title="Punt (wiskunde) – nizozemština" lang="nl" hreflang="nl" data-title="Punt (wiskunde)" 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/Punkt_i_matematikk" title="Punkt i matematikk – norština (nynorsk)" lang="nn" hreflang="nn" data-title="Punkt i matematikk" 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/Punkt" title="Punkt – norština (bokmål)" lang="nb" hreflang="nb" data-title="Punkt" 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-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Punt_(geometria)" title="Punt (geometria) – okcitánština" lang="oc" hreflang="oc" data-title="Punt (geometria)" data-language-autonym="Occitan" data-language-local-name="okcitánština" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%AC%E0%AC%BF%E0%AC%A8%E0%AD%8D%E0%AC%A6%E0%AD%81" title="ବିନ୍ଦୁ – urijština" lang="or" hreflang="or" data-title="ବିନ୍ଦୁ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="urijština" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AC%E0%A8%BF%E0%A9%B0%E0%A8%A6%E0%A9%80_(%E0%A8%B0%E0%A9%87%E0%A8%96%E0%A8%BE%E0%A8%97%E0%A8%A3%E0%A8%BF%E0%A8%A4)" title="ਬਿੰਦੀ (ਰੇਖਾਗਣਿਤ) – paňdžábština" lang="pa" hreflang="pa" data-title="ਬਿੰਦੀ (ਰੇਖਾਗਣਿਤ)" 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/Punkt_(geometria)" title="Punkt (geometria) – polština" lang="pl" hreflang="pl" data-title="Punkt (geometria)" data-language-autonym="Polski" data-language-local-name="polština" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ponto_(matem%C3%A1tica)" title="Ponto (matemática) – portugalština" lang="pt" hreflang="pt" data-title="Ponto (matemática)" data-language-autonym="Português" data-language-local-name="portugalština" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Punct_(geometrie)" title="Punct (geometrie) – rumunština" lang="ro" hreflang="ro" data-title="Punct (geometrie)" data-language-autonym="Română" data-language-local-name="rumunština" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%BE%D1%87%D0%BA%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Точка (геометрия) – ruština" lang="ru" hreflang="ru" data-title="Точка (геометрия)" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A7%D0%BE%D0%BF" title="Чоп – jakutština" lang="sah" hreflang="sah" data-title="Чоп" data-language-autonym="Саха тыла" data-language-local-name="jakutština" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Puntu_(giomitr%C3%ACa)" title="Puntu (giomitrìa) – sicilština" lang="scn" hreflang="scn" data-title="Puntu (giomitrìa)" data-language-autonym="Sicilianu" data-language-local-name="sicilština" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Ta%C4%8Dka_(geometrija)" title="Tačka (geometrija) – srbochorvatština" lang="sh" hreflang="sh" data-title="Tačka (geometrija)" 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-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Tanqqi%E1%B8%8Dt_(as%C9%A3kl)" title="Tanqqiḍt (asɣkl) – tašelhit" lang="shi" hreflang="shi" data-title="Tanqqiḍt (asɣkl)" data-language-autonym="Taclḥit" data-language-local-name="tašelhit" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Point_(geometry)" title="Point (geometry) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Point (geometry)" 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/Bod_(geometria)" title="Bod (geometria) – slovenština" lang="sk" hreflang="sk" data-title="Bod (geometria)" 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/To%C4%8Dka_(geometrija)" title="Točka (geometrija) – slovinština" lang="sl" hreflang="sl" data-title="Točka (geometrija)" 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/Poyindi" title="Poyindi – šonština" lang="sn" hreflang="sn" data-title="Poyindi" data-language-autonym="ChiShona" data-language-local-name="šonština" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%B0%D1%87%D0%BA%D0%B0_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%98%D0%B0)" title="Тачка (геометрија) – srbština" lang="sr" hreflang="sr" data-title="Тачка (геометрија)" 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/Punkt_(geometri)" title="Punkt (geometri) – švédština" lang="sv" hreflang="sv" data-title="Punkt (geometri)" 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/Nukta" title="Nukta – svahilština" lang="sw" hreflang="sw" data-title="Nukta" 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%AA%E0%AF%81%E0%AE%B3%E0%AF%8D%E0%AE%B3%E0%AE%BF" title="புள்ளி – tamilština" lang="ta" hreflang="ta" data-title="புள்ளி" 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%AC%E0%B0%BF%E0%B0%82%E0%B0%A6%E0%B1%81%E0%B0%B5%E0%B1%81_(%E0%B0%9C%E0%B1%8D%E0%B0%AF%E0%B0%BE%E0%B0%AE%E0%B0%BF%E0%B0%A4%E0%B0%BF)" title="బిందువు (జ్యామితి) – telugština" lang="te" hreflang="te" data-title="బిందువు (జ్యామితి)" data-language-autonym="తెలుగు" data-language-local-name="telugština" 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%B8%88%E0%B8%B8%E0%B8%94_(%E0%B9%80%E0%B8%A3%E0%B8%82%E0%B8%B2%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95)" title="จุด (เรขาคณิต) – thajština" lang="th" hreflang="th" data-title="จุด (เรขาคณิต)" 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/Punto_(heometriya)" title="Punto (heometriya) – tagalog" lang="tl" hreflang="tl" data-title="Punto (heometriya)" 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/Nokta_(geometri)" title="Nokta (geometri) – turečtina" lang="tr" hreflang="tr" data-title="Nokta (geometri)" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%BE%D1%87%D0%BA%D0%B0" title="Точка – ukrajinština" lang="uk" hreflang="uk" data-title="Точка" 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%86%D9%82%D8%B7%DB%81_(%DB%81%D9%86%D8%AF%D8%B3%DB%81)" title="نقطہ (ہندسہ) – urdština" lang="ur" hreflang="ur" data-title="نقطہ (ہندسہ)" 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/Nuqta_(matematika)" title="Nuqta (matematika) – uzbečtina" lang="uz" hreflang="uz" data-title="Nuqta (matematika)" 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/Ponto" title="Ponto – benátština" lang="vec" hreflang="vec" data-title="Ponto" 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/%C4%90i%E1%BB%83m_(h%C3%ACnh_h%E1%BB%8Dc)" title="Điểm (hình học) – vietnamština" lang="vi" hreflang="vi" data-title="Điểm (hình học)" 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/Punto" title="Punto – warajština" lang="war" hreflang="war" data-title="Punto" 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/%E7%82%B9" title="点 – čínština (dialekty Wu)" lang="wuu" hreflang="wuu" data-title="点" 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-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%98_(%D7%92%D7%A2%D7%90%D7%9E%D7%A2%D7%98%D7%A8%D7%99%D7%A2)" title="פונקט (געאמעטריע) – jidiš" lang="yi" hreflang="yi" data-title="פונקט (געאמעטריע)" 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/%E7%82%B9" title="点 – čínština" lang="zh" hreflang="zh" data-title="点" 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/%E9%BB%9E" title="點 – čínština (klasická)" lang="lzh" hreflang="lzh" data-title="點" 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-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%BB%9E_(%E5%B9%BE%E4%BD%95)" title="點 (幾何) – kantonština" lang="yue" hreflang="yue" data-title="點 (幾何)" 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/Q44946#sitelinks-wikipedia" title="Editovat mezijazykové odkazy" class="wbc-editpage">Upravit odkazy</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Jmenné prostory"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Bod" title="Zobrazit obsahovou stránku [c]" accesskey="c"><span>Článek</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskuse:Bod" rel="discussion" title="Diskuse ke stránce [t]" accesskey="t"><span>Diskuse</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Změnit variantu jazyka" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">čeština</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Zobrazení"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Bod"><span>Číst</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Bod&veaction=edit" title="Editovat tuto stránku [v]" accesskey="v"><span>Editovat</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Bod&action=edit" title="Editovat zdrojový kód této stránky [e]" accesskey="e"><span>Editovat zdroj</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Bod&action=history" title="Starší verze této stránky. [h]" accesskey="h"><span>Zobrazit historii</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Nástroje ke stránce"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Nástroje" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Nástroje</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Nástroje</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skrýt</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Další možnosti" > <div class="vector-menu-heading"> Akce </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Bod"><span>Číst</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Bod&veaction=edit" title="Editovat tuto stránku [v]" accesskey="v"><span>Editovat</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Bod&action=edit" title="Editovat zdrojový kód této stránky [e]" accesskey="e"><span>Editovat zdroj</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Bod&action=history"><span>Zobrazit historii</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Obecné </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Co_odkazuje_na/Bod" title="Seznam všech wikistránek, které sem odkazují [j]" accesskey="j"><span>Odkazuje sem</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Souvisej%C3%ADc%C3%AD_zm%C4%9Bny/Bod" rel="nofollow" title="Nedávné změny stránek, na které je odkazováno [k]" accesskey="k"><span>Související změny</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=cs" title="Nahrát obrázky či jiná multimédia [u]" accesskey="u"><span>Načíst soubor</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Bod&oldid=24699925" title="Trvalý odkaz na současnou verzi této stránky"><span>Trvalý odkaz</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Bod&action=info" title="Více informací o této stránce"><span>Informace o stránce</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Citovat&page=Bod&id=24699925&wpFormIdentifier=titleform" title="Informace o tom, jak citovat tuto stránku"><span>Citovat stránku</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:UrlShortener&url=https%3A%2F%2Fcs.wikipedia.org%2Fwiki%2FBod"><span>Získat zkrácené URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:QrCode&url=https%3A%2F%2Fcs.wikipedia.org%2Fwiki%2FBod"><span>Stáhnout QR kód</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Tisk/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Kniha&bookcmd=book_creator&referer=Bod"><span>Vytvořit knihu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:DownloadAsPdf&page=Bod&action=show-download-screen"><span>Stáhnout jako PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Bod&printable=yes" title="Tato stránka v podobě vhodné k tisku [p]" accesskey="p"><span>Verze k tisku</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Na jiných projektech </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Points_(mathematics)" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiquote mw-list-item"><a href="https://cs.wikiquote.org/wiki/Bod" hreflang="cs"><span>Wikicitáty</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q44946" title="Odkaz na propojenou položku datového úložiště [g]" accesskey="g"><span>Položka Wikidat</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Nástroje ke stránce"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Vzhled"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Vzhled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skrýt</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Z Wikipedie, otevřené encyklopedie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="cs" dir="ltr"><div class="uvodni-upozorneni hatnote noprint">Tento článek je o <a href="/wiki/Geometrie" title="Geometrie">geometrickém</a> významu slova. Další významy jsou uvedeny na stránce <a href="/wiki/Bod_(rozcestn%C3%ADk)" class="mw-disambig" title="Bod (rozcestník)">Bod (rozcestník)</a>.</div> <p><b>Bod</b> je <i><a href="/wiki/Dimenze_vektorov%C3%A9ho_prostoru" title="Dimenze vektorového prostoru">bezrozměrný</a></i> <a href="/wiki/Z%C3%A1kladn%C3%AD_geometrick%C3%A9_%C3%BAtvary" class="mw-redirect" title="Základní geometrické útvary">základní geometrický útvar</a>. Jde tedy o abstraktní útvar bez velikosti, s konkrétní <a href="/wiki/Polohov%C3%BD_vektor" title="Polohový vektor">pozicí</a> v <a href="/wiki/Prostor_(fyzika)" title="Prostor (fyzika)">prostoru</a>. Pozice bodu je vztažena k <a href="/wiki/Soustava_sou%C5%99adnic" title="Soustava souřadnic">soustavě souřadnic</a>. Bezrozměrné body jsou využívány k definici <a href="/wiki/K%C5%99ivka" title="Křivka">křivky</a> v jednorozměrném prostoru, plochy v dvourozměrném prostoru a dalších objektů vyšších <a href="/wiki/Dimenze" title="Dimenze">dimenzí</a>. Bod může být určen jako průsečík dvou <a href="/wiki/K%C5%99ivka" title="Křivka">křivek</a> nebo tří <a href="/wiki/Rovina" title="Rovina">rovin</a>, tedy jako <a href="/wiki/Vrchol_(geometrie)" title="Vrchol (geometrie)">vrchol</a> <a href="/wiki/Geometrick%C3%BD_%C3%BAtvar" title="Geometrický útvar">geometrického útvaru</a>. V <a href="/wiki/Analytick%C3%A1_geometrie" title="Analytická geometrie">analytické geometrii</a> je bod definován souřadnicemi (<a href="/wiki/Uspo%C5%99%C3%A1dan%C3%A1_n-tice" title="Uspořádaná n-tice">uspořádanou n-ticí</a>) ve zvolené <a href="/wiki/Soustava_sou%C5%99adnic" title="Soustava souřadnic">soustavě souřadnic</a>. Body mohou tvořit <a href="/wiki/Mno%C5%BEina" title="Množina">množinu</a> bodů. <a href="/wiki/Izolovan%C3%BD_bod" title="Izolovaný bod">Izolovaný bod</a> je takový, který v jistém okolí nemá body ze stejné množiny bodů. </p><p><a href="/wiki/Eukleidovsk%C3%A1_geometrie" title="Eukleidovská geometrie">Eukleidovská geometrie</a> definuje bod jako primitivum, tedy „<i>něco, co nemá části</i>“ nelze to již dále dělit. Bod je v ní definován <a href="/wiki/Axiom" title="Axiom">axiomem</a>, který se nedokazuje a nepoužívá pro svou definici jiná primitiva. </p><p>Bod <a href="/wiki/%C4%8Casoprostor" title="Časoprostor">časoprostoru</a> se nazývá <a href="/wiki/Ud%C3%A1lost_(teorie_relativity)" title="Událost (teorie relativity)"><i>událost</i></a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Vlastnosti">Vlastnosti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bod&veaction=edit&section=1" title="Editace sekce: Vlastnosti" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bod&action=edit&section=1" title="Editovat zdrojový kód sekce Vlastnosti"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Všechny <a href="/wiki/Geometrick%C3%BD_%C3%BAtvar" title="Geometrický útvar">geometrické útvary</a> jsou definovány jako <a href="/wiki/Mno%C5%BEina" title="Množina">množina</a> bodů, zpravidla <a href="/wiki/Nekone%C4%8Dno" title="Nekonečno">nekonečně</a> velká (pouze samotný bod je <a href="/wiki/Jednoprvkov%C3%A1_mno%C5%BEina" title="Jednoprvková množina">jednoprvková množina</a>). Takovou definicí je např. „množina všech bodů v <a href="/wiki/Rovina" title="Rovina">rovině</a> <i>R</i> ležících ve vzdálenosti <i>r</i> od bodu <i>S</i>“ (definice <a href="/wiki/Kru%C5%BEnice" title="Kružnice">kružnice</a> o <a href="/wiki/Polom%C4%9Br" title="Poloměr">poloměru</a> <i>r</i> se středem <i>S</i>). </p><p>Dva body mohou být <a href="/wiki/Ekvivalence_(matematika)" title="Ekvivalence (matematika)">shodné</a> (tj. mají všechny souřadnice stejné), nebo <a href="/wiki/Nerovnost_(matematika)" title="Nerovnost (matematika)">rozdílné</a> (alespoň v jedné souřadnici se liší). Z rozdílu souřadnic dvou bodů vyplývá jejich <a href="/wiki/Vzd%C3%A1lenost" title="Vzdálenost">vzdálenost</a>. </p><p>Za bod lze také považovat <a href="/wiki/%C3%9Ase%C4%8Dka" title="Úsečka">úsečku</a> <a href="/wiki/Nula" title="Nula">nulové</a> <a href="/wiki/D%C3%A9lka" title="Délka">délky</a> (její krajní body jsou shodné). </p> <div class="mw-heading mw-heading3"><h3 id="Značení"><span id="Zna.C4.8Den.C3.AD"></span>Značení</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bod&veaction=edit&section=2" title="Editace sekce: Značení" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bod&action=edit&section=2" title="Editovat zdrojový kód sekce Značení"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Soubor:Zobrazeni_bod.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Zobrazeni_bod.svg/70px-Zobrazeni_bod.svg.png" decoding="async" width="70" height="99" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Zobrazeni_bod.svg/105px-Zobrazeni_bod.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Zobrazeni_bod.svg/140px-Zobrazeni_bod.svg.png 2x" data-file-width="744" data-file-height="1052" /></a><figcaption>Grafické znázornění bodu.</figcaption></figure> <p>Graficky se bod znázorňuje křížkem, malým kolečkem, kroužkem nebo čárkou (pokud leží na <a href="/wiki/%C3%9Ase%C4%8Dka" title="Úsečka">úsečce</a>, <a href="/wiki/P%C5%99%C3%ADmka" title="Přímka">přímce</a> či <a href="/wiki/K%C5%99ivka" title="Křivka">křivce</a>). Označuje se velkým tiskacím písmenem. </p> <div class="mw-heading mw-heading3"><h3 id="Zápis_bodu"><span id="Z.C3.A1pis_bodu"></span>Zápis bodu</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bod&veaction=edit&section=3" title="Editace sekce: Zápis bodu" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bod&action=edit&section=3" title="Editovat zdrojový kód sekce Zápis bodu"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Algebra" title="Algebra">Algebraicky</a> je každý bod pevně určen <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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}" /></span> <a href="/wiki/Soustava_sou%C5%99adnic" title="Soustava souřadnic">souřadnicemi</a>, kde <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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}" /></span> je <a href="/wiki/Dimenze_vektorov%C3%A9ho_prostoru" title="Dimenze vektorového prostoru">rozměr</a> <a href="/wiki/Prostor_(matematika)" title="Prostor (matematika)">prostoru</a>, ve kterém se nachází. Například v <a href="/wiki/2D" title="2D">dvojrozměrném</a> prostoru (tedy v <a href="/wiki/Plocha" title="Plocha">ploše</a>) je bod určen dvěma souřadnicemi, v <a href="/wiki/3D" title="3D">trojrozměrném</a> prostoru je bod pevně dán třemi souřadnicemi. Například v <a href="/wiki/Kart%C3%A9zsk%C3%A1_soustava_sou%C5%99adnic" title="Kartézská soustava souřadnic">kartézské soustavě souřadnic</a> je bod <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 A[2;3]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">[</mo> <mn>2</mn> <mo>;</mo> <mn>3</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A[2;3]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7005fcf212ceba0d8ca93fc7cf7d516737b8ba72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.396ex; height:2.843ex;" alt="{\displaystyle A[2;3]}" /></span> v rovině, bod <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X[3;-4;0]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo stretchy="false">[</mo> <mn>3</mn> <mo>;</mo> <mo>−</mo> <mn>4</mn> <mo>;</mo> <mn>0</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X[3;-4;0]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dda48664b65da85f3db2045c3f0398c481b8a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.637ex; height:2.843ex;" alt="{\displaystyle X[3;-4;0]}" /></span> v prostoru. </p> <div class="mw-heading mw-heading3"><h3 id="Vzdálenost"><span id="Vzd.C3.A1lenost"></span>Vzdálenost</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bod&veaction=edit&section=4" title="Editace sekce: Vzdálenost" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bod&action=edit&section=4" title="Editovat zdrojový kód sekce Vzdálenost"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Vzd%C3%A1lenost" title="Vzdálenost">Vzdálenost</a> dvou bodů <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 A[x_{a};y_{a}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">[</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>;</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A[x_{a};y_{a}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ee63013d5f88c6d67275f9efe5348c8087bfe44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.743ex; height:2.843ex;" alt="{\displaystyle A[x_{a};y_{a}]}" /></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B[x_{b};y_{b}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo stretchy="false">[</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>;</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B[x_{b};y_{b}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/065bb74f59ff5de9cee444225efdb58f0dcefeb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.436ex; height:2.843ex;" alt="{\displaystyle B[x_{b};y_{b}]}" /></span> v <a href="/wiki/Rovina" title="Rovina">rovině</a> vypočteme:<sup id="cite_ref-vzdalenost_1-0" class="reference"><a href="#cite_note-vzdalenost-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </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 |AB|={\sqrt {(x_{b}-x_{a})^{2}+(y_{b}-y_{a})^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>A</mi> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |AB|={\sqrt {(x_{b}-x_{a})^{2}+(y_{b}-y_{a})^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d9460aaed4e88c12550edde7bdee0fc432b526f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:33.488ex; height:4.843ex;" alt="{\displaystyle |AB|={\sqrt {(x_{b}-x_{a})^{2}+(y_{b}-y_{a})^{2}}}}" /></span></dd></dl> <p>V <a href="/wiki/3D" title="3D">trojrozměrném</a> <a href="/wiki/Prostor_(matematika)" title="Prostor (matematika)">prostoru</a> vzdálenost bodů <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 A[x_{a};y_{a};z_{a}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo stretchy="false">[</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>;</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo>;</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A[x_{a};y_{a};z_{a}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be79ce51111b1333de3ffd3b5f612f21d3dcb9be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.96ex; height:2.843ex;" alt="{\displaystyle A[x_{a};y_{a};z_{a}]}" /></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle B[x_{b};y_{b};z_{b}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> <mo stretchy="false">[</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>;</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>;</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B[x_{b};y_{b};z_{b}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/361ed09719000431c57aaa9c3c13879e62de34cc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.489ex; height:2.843ex;" alt="{\displaystyle B[x_{b};y_{b};z_{b}]}" /></span> vypočteme:<sup id="cite_ref-vzdalenost_1-1" class="reference"><a href="#cite_note-vzdalenost-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </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 |AB|={\sqrt {(x_{b}-x_{a})^{2}+(y_{b}-y_{a})^{2}+(z_{b}-z_{a})^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>A</mi> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |AB|={\sqrt {(x_{b}-x_{a})^{2}+(y_{b}-y_{a})^{2}+(z_{b}-z_{a})^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aad9dc5eff2f68a25d010ab853ccec923cf8e537" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:46.234ex; height:4.843ex;" alt="{\displaystyle |AB|={\sqrt {(x_{b}-x_{a})^{2}+(y_{b}-y_{a})^{2}+(z_{b}-z_{a})^{2}}}}" /></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Typy_bodů"><span id="Typy_bod.C5.AF"></span>Typy bodů</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bod&veaction=edit&section=5" title="Editace sekce: Typy bodů" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bod&action=edit&section=5" title="Editovat zdrojový kód sekce Typy bodů"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Existují určité typy bodů, které mají svůj název a často také obvyklá písmena užívaná pro jejich označení (případně se k těmto písmenům přidávají číselné indexy nebo čárky). Mezi nejvýznamnější, nejčastěji užívané a s poměrně ustáleným značením patří: </p> <ul><li>krajní bod <a href="/wiki/%C3%9Ase%C4%8Dka" title="Úsečka">úsečky</a> nebo <a href="/wiki/Polop%C5%99%C3%ADmka" title="Polopřímka">polopřímky</a>, určující bod <a href="/wiki/P%C5%99%C3%ADmka" title="Přímka">přímky</a> nebo polopřímky (většina bodů má tento význam)</li> <li><a href="/wiki/Vrchol_(geometrie)" title="Vrchol (geometrie)">vrchol</a> (A, B, C…; K, L, M…) - viz zejména <a href="/wiki/Mnoho%C3%BAheln%C3%ADk" title="Mnohoúhelník">Mnohoúhelník</a></li> <li><a href="/wiki/Geometrick%C3%BD_st%C5%99ed" title="Geometrický střed">střed</a> (O, S)</li> <li><a href="/wiki/Pr%C5%AFse%C4%8D%C3%ADk" title="Průsečík">průsečík</a> (P)</li> <li><a href="/w/index.php?title=Bod_dotyku&action=edit&redlink=1" class="new" title="Bod dotyku (stránka neexistuje)">bod dotyku</a> (T)</li> <li><a href="/wiki/T%C4%9B%C5%BEi%C5%A1t%C4%9B" title="Těžiště">těžiště</a> (T)</li> <li><a href="/w/index.php?title=Pr%C5%AFse%C4%8D%C3%ADk_v%C3%BD%C5%A1ek&action=edit&redlink=1" class="new" title="Průsečík výšek (stránka neexistuje)">průsečík výšek</a> (V) - použitelné především u <a href="/wiki/Troj%C3%BAheln%C3%ADk" title="Trojúhelník">trojúhelníka</a></li> <li><a href="/w/index.php?title=Ohnisko_(geometrie)&action=edit&redlink=1" class="new" title="Ohnisko (geometrie) (stránka neexistuje)">ohnisko</a> (F, příp. také E u <a href="/wiki/Elipsa" title="Elipsa">elipsy</a>)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Odkazy">Odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bod&veaction=edit&section=6" title="Editace sekce: Odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bod&action=edit&section=6" title="Editovat zdrojový kód sekce Odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Reference">Reference</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bod&veaction=edit&section=7" title="Editace sekce: Reference" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bod&action=edit&section=7" title="Editovat zdrojový kód sekce Reference"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-vzdalenost-1"><span class="mw-cite-backlink">↑ <a href="#cite_ref-vzdalenost_1-0"><sup style="font-style: italic; font-weight: bold; vertical-align: top">a</sup></a> <a href="#cite_ref-vzdalenost_1-1"><sup style="font-style: italic; font-weight: bold; vertical-align: top">b</sup></a></span> <span class="reference-text"><cite style="font-style:normal;"> Body – Umíme matiku. <i>umimematiku.cz</i> [online]. [cit. 2025-02-24]. <a rel="nofollow" class="external text" href="https://www.umimematiku.cz/book/cviceni-body-geometrie">Dostupné online</a>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/cs.wikipedia.org:templatecitaceelperiodika&rft.jtitle=umimematiku.cz&rft_id=https%3A%2F%2Fwww.umimematiku.cz%2Fbook%2Fcviceni-body-geometrie&rft.atitle=Body+%E2%80%93+Um%C3%ADme+matiku"><span style="display:none"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Související_články"><span id="Souvisej.C3.ADc.C3.AD_.C4.8Dl.C3.A1nky"></span>Související články</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bod&veaction=edit&section=8" 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=Bod&action=edit&section=8" 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/Geometrie" title="Geometrie">Geometrie</a></li> <li><a href="/wiki/Geometrick%C3%BD_%C3%BAtvar" title="Geometrický útvar">Geometrický útvar</a></li> <li><a href="/wiki/P%C5%99%C3%ADmka" title="Přímka">Přímka</a></li> <li><a href="/wiki/Rovina" title="Rovina">Rovina</a></li> <li><a href="/wiki/Prostor_(geometrie)" class="mw-redirect" title="Prostor (geometrie)">Prostor</a></li> <li><a href="/wiki/Ud%C3%A1lost_(teorie_relativity)" title="Událost (teorie relativity)">Událost</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bod&veaction=edit&section=9" 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=Bod&action=edit&section=9" 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:Points_(mathematics)" class="extiw" title="c:Category:Points (mathematics)">bod</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/Bod" class="extiw" title="q:Bod">Bod</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/bod" class="extiw" title="wikt:bod">bod</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" 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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 tr+tr>.navbox2-abovebelow,.mw-parser-output tr+tr>.navbox2-group,.mw-parser-output tr+tr>.navbox2-image,.mw-parser-output tr+tr>.navbox2-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox2 th,.mw-parser-output .navbox2-title{background-color:#e0e0e0}.mw-parser-output .navbox2-abovebelow,.mw-parser-output th.navbox2-group,.mw-parser-output .navbox2-subgroup .navbox2-title{background-color:#e7e7e7}.mw-parser-output .navbox2-subgroup .navbox2-title{font-size:88%}.mw-parser-output .navbox2-subgroup .navbox2-group,.mw-parser-output .navbox2-subgroup .navbox2-abovebelow{background-color:#f0f0f0}.mw-parser-output .navbox2-even{background-color:#f7f7f7}.mw-parser-output .navbox2-odd{background-color:transparent}.mw-parser-output .navbox2 .hlist td dl,.mw-parser-output .navbox2 .hlist td ol,.mw-parser-output .navbox2 .hlist td ul,.mw-parser-output .navbox2 td.hlist dl,.mw-parser-output .navbox2 td.hlist ol,.mw-parser-output .navbox2 td.hlist ul{padding:0.125em 0}</style><div role="navigation" class="navbox2" aria-labelledby="Autoritní_data_frameless_&#124;text-top_&#124;10px_&#124;alt=Editovat_na_Wikidatech_&#124;link=https&#58;//www.wikidata.org/wiki/Q44946#identifiers&#124;Editovat_na_Wikidatech" style="padding:2px"><table class="nowraplinks hlist navbox2-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Autoritní_data_frameless_&#124;text-top_&#124;10px_&#124;alt=Editovat_na_Wikidatech_&#124;link=https&#58;//www.wikidata.org/wiki/Q44946#identifiers&#124;Editovat_na_Wikidatech" scope="row" class="navbox2-group" style="width:1%"><a href="/wiki/Autoritn%C3%AD_kontrola" title="Autoritní kontrola">Autoritní data</a> <span class="mw-valign-text-top" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q44946#identifiers" title="Editovat na Wikidatech"><img alt="Editovat na Wikidatech" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox2-list navbox2-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/Gemeinsame_Normdatei" title="Gemeinsame Normdatei">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4298379-4">4298379-4</a></span></span></li></ul> </div></td></tr></tbody></table></div> <style data-mw-deduplicate="TemplateStyles:r16915398">.mw-parser-output div/**/#portallinks a{font-weight:bold}</style><div id="portallinks" class="catlinks"><a href="/wiki/Port%C3%A1l:Obsah" title="Portál:Obsah">Portály</a>: <a href="/wiki/Port%C3%A1l:Matematika" title="Portál:Matematika">Matematika</a> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Citováno z „<a dir="ltr" href="https://cs.wikipedia.org/w/index.php?title=Bod&oldid=24699925">https://cs.wikipedia.org/w/index.php?title=Bod&oldid=24699925</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/N%C3%A1pov%C4%9Bda:Kategorie" title="Nápověda:Kategorie">Kategorie</a>: <ul><li><a href="/wiki/Kategorie:Geometrie" title="Kategorie:Geometrie">Geometrie</a></li><li><a href="/wiki/Kategorie:Geometrick%C3%A9_%C3%BAtvary" title="Kategorie:Geometrické útvary">Geometrické útvary</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Skryté kategorie: <ul><li><a href="/wiki/Kategorie:Pah%C3%BDly" title="Kategorie:Pahýly">Pahýly</a></li><li><a href="/wiki/Kategorie:Monitoring:%C4%8Cl%C3%A1nky_s_identifik%C3%A1torem_GND" title="Kategorie:Monitoring:Články s identifikátorem GND">Monitoring:Články s identifikátorem GND</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Stránka byla naposledy editována 25. 2. 2025 v 08:33.</li> <li id="footer-info-copyright">Text je dostupný pod <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.cs">licencí Creative Commons Uveďte původ – Zachovejte licenci</a>, případně za dalších podmínek. 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