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class="vector-pinnable-header-label">Sisukord</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">vii külgpaanile</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">peida</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">Algus</div> </a> </li> <li id="toc-Antiikgeomeetria" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Antiikgeomeetria"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Antiikgeomeetria</span> </div> </a> <ul id="toc-Antiikgeomeetria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tänapäevane_sünteetiline_geomeetria" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tänapäevane_sünteetiline_geomeetria"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tänapäevane sünteetiline geomeetria</span> </div> </a> <ul id="toc-Tänapäevane_sünteetiline_geomeetria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Analüütiline_geomeetria" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Analüütiline_geomeetria"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Analüütiline geomeetria</span> </div> </a> <ul id="toc-Analüütiline_geomeetria-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ajalugu" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ajalugu"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Ajalugu</span> </div> </a> <ul id="toc-Ajalugu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vaata_ka" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vaata_ka"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Vaata ka</span> </div> </a> <ul id="toc-Vaata_ka-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Viited" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Viited"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Viited</span> </div> </a> <ul id="toc-Viited-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Välislingid" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Välislingid"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Välislingid</span> </div> </a> <ul id="toc-Välislingid-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sisukord" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Lülita sisukord ümber" > <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">Lülita sisukord ümber</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">Punkt (matemaatika)</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="Mine teises keeles artiklisse. Saadaval 102 keeles" > <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-102" 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">102 keelt</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) – afrikaani" lang="af" hreflang="af" data-title="Punt (meetkunde)" data-language-autonym="Afrikaans" data-language-local-name="afrikaani" 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) – šveitsisaksa" lang="gsw" hreflang="gsw" data-title="Punkt (Geometrie)" data-language-autonym="Alemannisch" data-language-local-name="šveitsisaksa" 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) – araabia" lang="ar" hreflang="ar" data-title="نقطة (هندسة)" data-language-autonym="العربية" data-language-local-name="araabia" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A6%BF%E0%A6%A8%E0%A7%8D%E0%A6%A6%E0%A7%81" title="বিন্দু – assami" lang="as" hreflang="as" data-title="বিন্দু" data-language-autonym="অসমীয়া" data-language-local-name="assami" 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) – astuuria" lang="ast" hreflang="ast" data-title="Puntu (xeometría)" data-language-autonym="Asturianu" data-language-local-name="astuuria" 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) – aserbaidžaani" lang="az" hreflang="az" data-title="Nöqtə (həndəsə)" data-language-autonym="Azərbaycanca" data-language-local-name="aserbaidžaani" 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) – lõunaaserbaidžaani" lang="azb" hreflang="azb" data-title="نوقطه (ریاضیات)" data-language-autonym="تۆرکجه" data-language-local-name="lõunaaserbaidžaani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Titik_(geometri)" title="Titik (geometri) – indoneesia" lang="id" hreflang="id" data-title="Titik (geometri)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneesia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Titik_(geometri)" title="Titik (geometri) – malai" lang="ms" hreflang="ms" data-title="Titik (geometri)" data-language-autonym="Bahasa Melayu" data-language-local-name="malai" class="interlanguage-link-target"><span>Bahasa Melayu</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) – baškiiri" lang="ba" hreflang="ba" data-title="Нөктә (геометрия)" data-language-autonym="Башҡортса" data-language-local-name="baškiiri" class="interlanguage-link-target"><span>Башҡортса</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 – valgevene" lang="be" hreflang="be" data-title="Пункт" data-language-autonym="Беларуская" data-language-local-name="valgevene" 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) – valgevene (taraškievitsa)" lang="be-tarask" hreflang="be-tarask" data-title="Пункт (геамэтрыя)" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="valgevene (taraškievitsa)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Punto" title="Punto – keskbikoli" lang="bcl" hreflang="bcl" data-title="Punto" data-language-autonym="Bikol Central" data-language-local-name="keskbikoli" class="interlanguage-link-target"><span>Bikol Central</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) – bosnia" lang="bs" hreflang="bs" data-title="Tačka (geometrija)" data-language-autonym="Bosanski" data-language-local-name="bosnia" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Poent_(geometriezh)" title="Poent (geometriezh) – bretooni" lang="br" hreflang="br" data-title="Poent (geometriezh)" data-language-autonym="Brezhoneg" data-language-local-name="bretooni" class="interlanguage-link-target"><span>Brezhoneg</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) – bulgaaria" lang="bg" hreflang="bg" data-title="Точка (геометрия)" data-language-autonym="Български" data-language-local-name="bulgaaria" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Punt_(geometria)" title="Punt (geometria) – katalaani" lang="ca" hreflang="ca" data-title="Punt (geometria)" data-language-autonym="Català" data-language-local-name="katalaani" class="interlanguage-link-target"><span>Català</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) – tšuvaši" lang="cv" hreflang="cv" data-title="Пăнчă (геометри)" data-language-autonym="Чӑвашла" data-language-local-name="tšuvaši" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Bod" title="Bod – tšehhi" lang="cs" hreflang="cs" data-title="Bod" data-language-autonym="Čeština" data-language-local-name="tšehhi" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Poyindi" title="Poyindi – šona" lang="sn" hreflang="sn" data-title="Poyindi" data-language-autonym="ChiShona" data-language-local-name="šona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Pwynt_(geometreg)" title="Pwynt (geometreg) – kõmri" lang="cy" hreflang="cy" data-title="Pwynt (geometreg)" data-language-autonym="Cymraeg" data-language-local-name="kõmri" 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 – taani" lang="da" hreflang="da" data-title="Punkt" data-language-autonym="Dansk" data-language-local-name="taani" class="interlanguage-link-target"><span>Dansk</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) – Maroko araabia" lang="ary" hreflang="ary" data-title="نقطة (لماط)" data-language-autonym="الدارجة" data-language-local-name="Maroko araabia" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Punkt_(Geometrie)" title="Punkt (Geometrie) – saksa" lang="de" hreflang="de" data-title="Punkt (Geometrie)" data-language-autonym="Deutsch" data-language-local-name="saksa" 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 – kreeka" lang="el" hreflang="el" data-title="Σημείο" data-language-autonym="Ελληνικά" data-language-local-name="kreeka" 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) – inglise" lang="en" hreflang="en" data-title="Point (geometry)" data-language-autonym="English" data-language-local-name="inglise" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Punto_(geometr%C3%ADa)" title="Punto (geometría) – hispaania" lang="es" hreflang="es" data-title="Punto (geometría)" data-language-autonym="Español" data-language-local-name="hispaania" class="interlanguage-link-target"><span>Español</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-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Puntu_(geometria)" title="Puntu (geometria) – baski" lang="eu" hreflang="eu" data-title="Puntu (geometria)" data-language-autonym="Euskara" data-language-local-name="baski" 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) – pärsia" lang="fa" hreflang="fa" data-title="نقطه (هندسه)" data-language-autonym="فارسی" data-language-local-name="pärsia" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Point_(g%C3%A9om%C3%A9trie)" title="Point (géométrie) – prantsuse" lang="fr" hreflang="fr" data-title="Point (géométrie)" data-language-autonym="Français" data-language-local-name="prantsuse" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Punto_(xeometr%C3%ADa)" title="Punto (xeometría) – galeegi" lang="gl" hreflang="gl" data-title="Punto (xeometría)" data-language-autonym="Galego" data-language-local-name="galeegi" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E9%BB%9E" title="點 – kani" lang="gan" hreflang="gan" data-title="點" data-language-autonym="贛語" data-language-local-name="kani" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/Ica" title="Ica – kikuju" lang="ki" hreflang="ki" data-title="Ica" data-language-autonym="Gĩkũyũ" data-language-local-name="kikuju" class="interlanguage-link-target"><span>Gĩkũyũ</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 – gudžarati" lang="gu" hreflang="gu" data-title="બિંદુ" data-language-autonym="ગુજરાતી" data-language-local-name="gudžarati" class="interlanguage-link-target"><span>ગુજરાતી</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) – korea" lang="ko" hreflang="ko" data-title="점 (기하학)" data-language-autonym="한국어" data-language-local-name="korea" class="interlanguage-link-target"><span>한국어</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 – armeenia" lang="hy" hreflang="hy" data-title="Կետ" data-language-autonym="Հայերեն" data-language-local-name="armeenia" class="interlanguage-link-target"><span>Հայերեն</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 – hindi" lang="hi" hreflang="hi" data-title="बिंदु" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/To%C4%8Dka_(geometrija)" title="Točka (geometrija) – horvaadi" lang="hr" hreflang="hr" data-title="Točka (geometrija)" data-language-autonym="Hrvatski" data-language-local-name="horvaadi" class="interlanguage-link-target"><span>Hrvatski</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-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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Punktur_(r%C3%BAmfr%C3%A6%C3%B0i)" title="Punktur (rúmfræði) – islandi" lang="is" hreflang="is" data-title="Punktur (rúmfræði)" data-language-autonym="Íslenska" data-language-local-name="islandi" 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) – itaalia" lang="it" hreflang="it" data-title="Punto (geometria)" data-language-autonym="Italiano" data-language-local-name="itaalia" class="interlanguage-link-target"><span>Italiano</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) – heebrea" lang="he" hreflang="he" data-title="נקודה (גאומטריה)" data-language-autonym="עברית" data-language-local-name="heebrea" class="interlanguage-link-target"><span>עברית</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) – jaava" lang="jv" hreflang="jv" data-title="Titik (géomètri)" data-language-autonym="Jawa" data-language-local-name="jaava" 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) – gruusia" lang="ka" hreflang="ka" data-title="წერტილი (გეომეტრია)" data-language-autonym="ქართული" data-language-local-name="gruusia" class="interlanguage-link-target"><span>ქართული</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) – kasahhi" lang="kk" hreflang="kk" data-title="Нүкте (геометрия)" data-language-autonym="Қазақша" data-language-local-name="kasahhi" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Nukta" title="Nukta – suahiili" lang="sw" hreflang="sw" data-title="Nukta" data-language-autonym="Kiswahili" data-language-local-name="suahiili" class="interlanguage-link-target"><span>Kiswahili</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) – Guajaana kreoolkeel" lang="gcr" hreflang="gcr" data-title="Pwen (jéométri)" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guajaana kreoolkeel" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Xal" title="Xal – kurdi" lang="ku" hreflang="ku" data-title="Xal" data-language-autonym="Kurdî" data-language-local-name="kurdi" 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) – ladina" lang="la" hreflang="la" data-title="Punctum (mathematica)" data-language-autonym="Latina" data-language-local-name="ladina" class="interlanguage-link-target"><span>Latina</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) – läti" lang="lv" hreflang="lv" data-title="Punkts (ģeometrija)" data-language-autonym="Latviešu" data-language-local-name="läti" class="interlanguage-link-target"><span>Latviešu</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) – leedu" lang="lt" hreflang="lt" data-title="Taškas (geometrija)" data-language-autonym="Lietuvių" data-language-local-name="leedu" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Pont_(geometria)" title="Pont (geometria) – ungari" lang="hu" hreflang="hu" data-title="Pont (geometria)" data-language-autonym="Magyar" data-language-local-name="ungari" class="interlanguage-link-target"><span>Magyar</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) – makedoonia" lang="mk" hreflang="mk" data-title="Точка (геометрија)" data-language-autonym="Македонски" data-language-local-name="makedoonia" class="interlanguage-link-target"><span>Македонски</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 – birma" lang="my" hreflang="my" data-title="အမှတ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birma" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Poidi_(geometry)" title="Poidi (geometry) – fidži" lang="fj" hreflang="fj" data-title="Poidi (geometry)" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fidži" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Punt_(wiskunde)" title="Punt (wiskunde) – hollandi" lang="nl" hreflang="nl" data-title="Punt (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="hollandi" class="interlanguage-link-target"><span>Nederlands</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 – nepali" lang="ne" hreflang="ne" data-title="बिन्दु" data-language-autonym="नेपाली" data-language-local-name="nepali" 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 – nevari" lang="new" hreflang="new" data-title="फुति" data-language-autonym="नेपाल भाषा" data-language-local-name="nevari" class="interlanguage-link-target"><span>नेपाल भाषा</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) – jaapani" lang="ja" hreflang="ja" data-title="点 (数学)" data-language-autonym="日本語" data-language-local-name="jaapani" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Ponkt_(Geometrii)" title="Ponkt (Geometrii) – põhjafriisi" lang="frr" hreflang="frr" data-title="Ponkt (Geometrii)" data-language-autonym="Nordfriisk" data-language-local-name="põhjafriisi" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Punkt" title="Punkt – norra bokmål" lang="nb" hreflang="nb" data-title="Punkt" data-language-autonym="Norsk bokmål" data-language-local-name="norra bokmål" class="interlanguage-link-target"><span>Norsk bokmål</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 – uusnorra" lang="nn" hreflang="nn" data-title="Punkt i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="uusnorra" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Punt_(geometria)" title="Punt (geometria) – oksitaani" lang="oc" hreflang="oc" data-title="Punt (geometria)" data-language-autonym="Occitan" data-language-local-name="oksitaani" class="interlanguage-link-target"><span>Occitan</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) – niidumari" lang="mhr" hreflang="mhr" data-title="Точко (геометрий)" data-language-autonym="Олык марий" data-language-local-name="niidumari" class="interlanguage-link-target"><span>Олык марий</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 – oria" lang="or" hreflang="or" data-title="ବିନ୍ଦୁ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="oria" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Nuqta_(matematika)" title="Nuqta (matematika) – usbeki" lang="uz" hreflang="uz" data-title="Nuqta (matematika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbeki" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</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) – pandžabi" lang="pa" hreflang="pa" data-title="ਬਿੰਦੀ (ਰੇਖਾਗਣਿਤ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="pandžabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Paint_(matimatix)" title="Paint (matimatix) – Jamaica kreoolkeel" lang="jam" hreflang="jam" data-title="Paint (matimatix)" data-language-autonym="Patois" data-language-local-name="Jamaica kreoolkeel" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Punkt_(Geometrie)" title="Punkt (Geometrie) – alamsaksa" lang="nds" hreflang="nds" data-title="Punkt (Geometrie)" data-language-autonym="Plattdüütsch" data-language-local-name="alamsaksa" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Punkt_(geometria)" title="Punkt (geometria) – poola" lang="pl" hreflang="pl" data-title="Punkt (geometria)" data-language-autonym="Polski" data-language-local-name="poola" 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) – portugali" lang="pt" hreflang="pt" data-title="Ponto (matemática)" data-language-autonym="Português" data-language-local-name="portugali" 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) – rumeenia" lang="ro" hreflang="ro" data-title="Punct (geometrie)" data-language-autonym="Română" data-language-local-name="rumeenia" 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) – vene" lang="ru" hreflang="ru" data-title="Точка (геометрия)" data-language-autonym="Русский" data-language-local-name="vene" 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 – jakuudi" lang="sah" hreflang="sah" data-title="Чоп" data-language-autonym="Саха тыла" data-language-local-name="jakuudi" 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) – sitsiilia" lang="scn" hreflang="scn" data-title="Puntu (giomitrìa)" data-language-autonym="Sicilianu" data-language-local-name="sitsiilia" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Point_(geometry)" title="Point (geometry) – lihtsustatud inglise" lang="en-simple" hreflang="en-simple" data-title="Point (geometry)" data-language-autonym="Simple English" data-language-local-name="lihtsustatud inglise" 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) – slovaki" lang="sk" hreflang="sk" data-title="Bod (geometria)" data-language-autonym="Slovenčina" data-language-local-name="slovaki" 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) – sloveeni" lang="sl" hreflang="sl" data-title="Točka (geometrija)" data-language-autonym="Slovenščina" data-language-local-name="sloveeni" class="interlanguage-link-target"><span>Slovenščina</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) – sorani" lang="ckb" hreflang="ckb" data-title="خاڵ (ئەندازە)" data-language-autonym="کوردی" data-language-local-name="sorani" class="interlanguage-link-target"><span>کوردی</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) – serbia" lang="sr" hreflang="sr" data-title="Тачка (геометрија)" data-language-autonym="Српски / srpski" data-language-local-name="serbia" class="interlanguage-link-target"><span>Српски / srpski</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) – serbia-horvaadi" lang="sh" hreflang="sh" data-title="Tačka (geometrija)" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbia-horvaadi" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Piste_(geometria)" title="Piste (geometria) – soome" lang="fi" hreflang="fi" data-title="Piste (geometria)" data-language-autonym="Suomi" data-language-local-name="soome" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Punkt_(geometri)" title="Punkt (geometri) – rootsi" lang="sv" hreflang="sv" data-title="Punkt (geometri)" data-language-autonym="Svenska" data-language-local-name="rootsi" class="interlanguage-link-target"><span>Svenska</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) – šilha" lang="shi" hreflang="shi" data-title="Tanqqiḍt (asɣkl)" data-language-autonym="Taclḥit" data-language-local-name="šilha" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Punto_(heometriya)" title="Punto (heometriya) – tagalogi" lang="tl" hreflang="tl" data-title="Punto (heometriya)" data-language-autonym="Tagalog" data-language-local-name="tagalogi" class="interlanguage-link-target"><span>Tagalog</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 – tamili" lang="ta" hreflang="ta" data-title="புள்ளி" data-language-autonym="தமிழ்" data-language-local-name="tamili" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Agaz_(tanzeggit)" title="Agaz (tanzeggit) – kabiili" lang="kab" hreflang="kab" data-title="Agaz (tanzeggit)" data-language-autonym="Taqbaylit" data-language-local-name="kabiili" class="interlanguage-link-target"><span>Taqbaylit</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) – telugu" lang="te" hreflang="te" data-title="బిందువు (జ్యామితి)" data-language-autonym="తెలుగు" data-language-local-name="telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%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) – tai" lang="th" hreflang="th" data-title="จุด (เรขาคณิต)" data-language-autonym="ไทย" data-language-local-name="tai" class="interlanguage-link-target"><span>ไทย</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) – vietnami" lang="vi" hreflang="vi" data-title="Điểm (hình học)" data-language-autonym="Tiếng Việt" data-language-local-name="vietnami" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Nokta_(geometri)" title="Nokta (geometri) – türgi" lang="tr" hreflang="tr" data-title="Nokta (geometri)" data-language-autonym="Türkçe" data-language-local-name="türgi" 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 – ukraina" lang="uk" hreflang="uk" data-title="Точка" data-language-autonym="Українська" data-language-local-name="ukraina" 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) – urdu" lang="ur" hreflang="ur" data-title="نقطہ (ہندسہ)" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Ponto" title="Ponto – veneti" lang="vec" hreflang="vec" data-title="Ponto" data-language-autonym="Vèneto" data-language-local-name="veneti" class="interlanguage-link-target"><span>Vèneto</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 – klassikaline hiina" lang="lzh" hreflang="lzh" data-title="點" data-language-autonym="文言" data-language-local-name="klassikaline hiina" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Punto" title="Punto – varai" lang="war" hreflang="war" data-title="Punto" data-language-autonym="Winaray" data-language-local-name="varai" 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 – uu" lang="wuu" hreflang="wuu" data-title="点" data-language-autonym="吴语" data-language-local-name="uu" 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) – jidiši" lang="yi" hreflang="yi" data-title="פונקט (געאמעטריע)" data-language-autonym="ייִדיש" data-language-local-name="jidiši" class="interlanguage-link-target"><span>ייִדיש</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) – kantoni" lang="yue" hreflang="yue" data-title="點 (幾何)" data-language-autonym="粵語" data-language-local-name="kantoni" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%82%B9" title="点 – hiina" lang="zh" hreflang="zh" data-title="点" data-language-autonym="中文" data-language-local-name="hiina" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q44946#sitelinks-wikipedia" title="Muuda keelelinke" class="wbc-editpage">Muuda linke</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="Nimeruumid"> <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/Punkt_(matemaatika)" title="Vaata sisulehekülge [c]" accesskey="c"><span>Artikkel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Arutelu:Punkt_(matemaatika)" rel="discussion" title="Arutelu selle lehekülje 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id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="et" dir="ltr"><p><b>Punkt</b> on <a href="/wiki/Elementaargeomeetria" title="Elementaargeomeetria">elementaargeomeetrias</a> <a href="/w/index.php?title=Objekt_(matemaatika)&action=edit&redlink=1" class="new" title="Objekt (matemaatika) (pole veel kirjutatud)">objekt</a>, mida näitlikustatakse mõõtmeteta ruumiosana. Geomeetria aksiomaatilises käsitluses on <b>punkt</b> üks <a href="/wiki/Algm%C3%B5iste" title="Algmõiste">algmõisteid</a>. </p><p>Mistahes <a href="/wiki/Meetriline_ruum" title="Meetriline ruum">meetrilise ruumi</a> või üldiselt <a href="/wiki/Topoloogiline_ruum" title="Topoloogiline ruum">topoloogilise ruumi</a> <a href="/wiki/Element_(matemaatika)" title="Element (matemaatika)">elemente</a> nimetatakse <b>punktideks</b>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Geomeetria" title="Geomeetria">Geomeetrias</a> nimetatakse <a href="/wiki/Hulk" title="Hulk">hulka</a>, mille elementideks on punktid, <a href="/wiki/Punktihulk" title="Punktihulk">punktihulgaks</a> või ka <a href="/wiki/Kujund" title="Kujund">kujundiks</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Antiikgeomeetria">Antiikgeomeetria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Punkt_(matemaatika)&veaction=edit&section=1" title="Muuda alaosa "Antiikgeomeetria"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Punkt_(matemaatika)&action=edit&section=1" title="Muuda alaosa "Antiikgeomeetria" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Punkti mõiste kujunes välja <a href="/wiki/Abstraktsioon" title="Abstraktsioon">abstraktsioonina</a> väikesest ruumiosast, sellele omistati <a href="/wiki/M%C3%B5%C3%B5tmed" title="Mõõtmed">mõõtmete</a> puudumine. <a href="/w/index.php?title=Proklos&action=edit&redlink=1" class="new" title="Proklos (pole veel kirjutatud)">Proklose</a> andmetel defineeris punkti esimesena <a href="/wiki/Pythagoras" title="Pythagoras">Pythagoras</a>, kelle järgi punkt on üks (<i>monas</i>), millel on asukoht. <a href="/wiki/Eukleides" title="Eukleides">Eukleidese</a> "<a href="/wiki/Elemendid_(Eukleides)" title="Elemendid (Eukleides)">Elementide</a>" (umbes 300 eKr) esimene definitsioon ütleb, et punkt (σημεῖον, <i><a href="/w/index.php?title=S%C4%93meion&action=edit&redlink=1" class="new" title="Sēmeion (pole veel kirjutatud)">sēmeion</a></i>, 'märk') on see, millel pole osi. Antiikfilosoofid, näiteks <a href="/wiki/Aristoteles" title="Aristoteles">Aristoteles</a> (<i><a href="/w/index.php?title=De_generatione_et_corruptione&action=edit&redlink=1" class="new" title="De generatione et corruptione (pole veel kirjutatud)">De generatione et corruptione</a></i>) arutasid raskusi seoses ulatuseta punktide ning nendest koosnevateks peetud ulatusega <a href="/wiki/Sirge" title="Sirge">sirgete</a> vahekorraga. </p> <div class="mw-heading mw-heading2"><h2 id="Tänapäevane_sünteetiline_geomeetria"><span id="T.C3.A4nap.C3.A4evane_s.C3.BCnteetiline_geomeetria"></span>Tänapäevane sünteetiline geomeetria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Punkt_(matemaatika)&veaction=edit&section=2" title="Muuda alaosa "Tänapäevane sünteetiline geomeetria"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Punkt_(matemaatika)&action=edit&section=2" title="Muuda alaosa "Tänapäevane sünteetiline geomeetria" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tänapäevases <a href="/w/index.php?title=S%C3%BCnteetiline_geomeetria&action=edit&redlink=1" class="new" title="Sünteetiline geomeetria (pole veel kirjutatud)">sünteetilises geomeetrias</a> ei ole punktide ja sirgete tõelise loomusel põhimõttelist tähtsust, loevad ainult geomeetriliste objektide omavahelised suhted, mille määrab <a href="/w/index.php?title=Aksiomaatika&action=edit&redlink=1" class="new" title="Aksiomaatika (pole veel kirjutatud)">aksiomaatika</a>. <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbertile</a> omistatakse ütlus, et "punktide, sirgete ja <a href="/wiki/Tasand" title="Tasand">tasandite</a>" asemel saab alati öelda "lauad, toolid ja õllekruusid", peaasi, et aksioomid on täidetud. Näiteks ütleb <a href="/w/index.php?title=Hilberti_aksiomaatika&action=edit&redlink=1" class="new" title="Hilberti aksiomaatika (pole veel kirjutatud)">Hilberti aksiomaatika</a> esimene <a href="/wiki/Aksioom" title="Aksioom">aksioom</a>: "Kaks eri punkti <i>P</i> ja <i>Q</i> määravad alati ühe sirge <i>g</i>." Punktimõiste tähendus tuleneb aksiomaatikast kui tervikust, punkti ei pea tingimata tõlgendama ulatuseta objektina. <a href="/w/index.php?title=Projektiivne_tasand&action=edit&redlink=1" class="new" title="Projektiivne tasand (pole veel kirjutatud)">Projektiivsel tasandil</a> on punkti ja sirge mõiste isegi täiesti vahetatavad. </p> <div class="mw-heading mw-heading2"><h2 id="Analüütiline_geomeetria"><span id="Anal.C3.BC.C3.BCtiline_geomeetria"></span>Analüütiline geomeetria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Punkt_(matemaatika)&veaction=edit&section=3" title="Muuda alaosa "Analüütiline geomeetria"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Punkt_(matemaatika)&action=edit&section=3" title="Muuda alaosa "Analüütiline geomeetria" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Tänapäeva <a href="/wiki/Anal%C3%BC%C3%BCtiline_geomeetria" title="Analüütiline geomeetria">analüütilises geomeetrias</a> kujutatakse geomeetrilist <a href="/wiki/Ruum_(matemaatika)" title="Ruum (matemaatika)">ruumi</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 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/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>-mõõtmelise <a href="/wiki/Vektorruum" title="Vektorruum">vektorruumina</a> üle <a href="/wiki/Korpus_(matemaatika)" title="Korpus (matemaatika)">korpuse</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 K}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.066ex; height:2.176ex;" alt="{\displaystyle K}"></span>. Selle vektorruumi <a href="/wiki/Element_(matemaatika)" title="Element (matemaatika)">elemente</a> nimetatakse punktideks. Selle vektorruumi <a href="/wiki/Baas_(matemaatika)" title="Baas (matemaatika)">baas</a> määrab <a href="/wiki/Koordinaadis%C3%BCsteem" title="Koordinaadisüsteem">koordinaadisüsteemi</a> ning <a href="/wiki/Vektor" title="Vektor">vektori</a> komponente selle baasi suhtes nimetatakse punkti <a href="/wiki/Koordinaadid" class="mw-redirect" title="Koordinaadid">koordinaatideks</a>. Punkti <a href="/wiki/M%C3%B5%C3%B5de" title="Mõõde">mõõde</a> on null. </p><p>Kõik teised geomeetrilised kujundid defineeritakse punktide <a href="/wiki/Hulk" title="Hulk">hulkadena</a> (<a href="/wiki/Punktihulk" title="Punktihulk">punktihulkadena</a>). Näiteks defineeritakse sirge ühemõõtmelise <a href="/w/index.php?title=Afiinne_alamruum&action=edit&redlink=1" class="new" title="Afiinne alamruum (pole veel kirjutatud)">afiinse alamruumina</a> ja tasand kahemõõtmelise afiinse alamruumina. <a href="/wiki/Kerapind" class="mw-redirect" title="Kerapind">Kerapind</a> defineeritakse teatud punktist teatud <a href="/wiki/Kaugus" title="Kaugus">kaugusel</a> asetsevate punktide hulgana. </p> <div class="mw-heading mw-heading2"><h2 id="Ajalugu">Ajalugu</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Punkt_(matemaatika)&veaction=edit&section=4" title="Muuda alaosa "Ajalugu"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Punkt_(matemaatika)&action=edit&section=4" title="Muuda alaosa "Ajalugu" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Punkti mõiste kujunes välja <a href="/wiki/Abstraktsioon" title="Abstraktsioon">abstraktsioonina</a> väikesest ruumiosast, sellele omistati <a href="/wiki/M%C3%B5%C3%B5tmed" title="Mõõtmed">mõõtmete</a> puudumine. <a href="/wiki/Eukleides" title="Eukleides">Eukleidese</a> "<a href="/wiki/Elemendid_(Eukleides)" title="Elemendid (Eukleides)">Elementides</a>" defineeritakse punkt kui "see, millel pole osi". </p><p><a href="/wiki/Anal%C3%BC%C3%BCtiline_geomeetria" title="Analüütiline geomeetria">Analüütilise geomeetria</a> loomine võimaldas punkte esitada <a href="/wiki/Koordinaadid" class="mw-redirect" title="Koordinaadid">koordinaatide</a> abil. </p><p><a href="/wiki/Hulgateooria" title="Hulgateooria">Hulgateooria</a> teke võimaldas käsitada <a href="/wiki/Ruum_(matemaatika)" title="Ruum (matemaatika)">ruumi</a> kui punktidest moodustatud <a href="/wiki/Hulk" title="Hulk">hulka</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Vaata_ka">Vaata ka</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Punkt_(matemaatika)&veaction=edit&section=5" title="Muuda alaosa "Vaata ka"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Punkt_(matemaatika)&action=edit&section=5" title="Muuda alaosa "Vaata ka" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Sirge" title="Sirge">Sirge</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Viited">Viited</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Punkt_(matemaatika)&veaction=edit&section=6" title="Muuda alaosa "Viited"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Punkt_(matemaatika)&action=edit&section=6" title="Muuda alaosa "Viited" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"> Ü. Kaasik, Matemaatikaleksikon (2002) </span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Välislingid"><span id="V.C3.A4lislingid"></span>Välislingid</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Punkt_(matemaatika)&veaction=edit&section=7" title="Muuda alaosa "Välislingid"" class="mw-editsection-visualeditor"><span>muuda</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Punkt_(matemaatika)&action=edit&section=7" title="Muuda alaosa "Välislingid" lähteteksti"><span>muuda lähteteksti</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.mathopenref.com/point.html">Point Definition</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Pärit leheküljelt "<a dir="ltr" href="https://et.wikipedia.org/w/index.php?title=Punkt_(matemaatika)&oldid=6128073">https://et.wikipedia.org/w/index.php?title=Punkt_(matemaatika)&oldid=6128073</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Eri:Kategooriad" title="Eri:Kategooriad">Kategooria</a>: <ul><li><a href="/wiki/Kategooria:Geomeetria" title="Kategooria:Geomeetria">Geomeetria</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"> Selle lehekülje viimane muutmine: 20:42, 24. juuni 2022.</li> <li id="footer-info-copyright">Tekst on kasutatav vastavalt Creative Commonsi litsentsile "<a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.et">Autorile viitamine + jagamine samadel tingimustel</a>"; sellele võivad lisanduda täiendavad tingimused. 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