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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Zaloguj się</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"> Strony dla anonimowych edytorów <a href="/wiki/Pomoc:Pierwsze_kroki" aria-label="Dowiedz się więcej na temat edytowania"><span>dowiedz się więcej</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/Specjalna:M%C3%B3j_wk%C5%82ad" title="Lista edycji wykonanych z tego adresu IP [y]" accesskey="y"><span>Edycje</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Specjalna:Moja_dyskusja" title="Dyskusja użytkownika dla tego adresu IP [n]" accesskey="n"><span>Dyskusja</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="Witryna"> <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="Spis treści" 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">Spis treści</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">przypnij</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ukryj</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">Początek</div> </a> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-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="Spis treści" 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="Przełącz stan spisu treści" > <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">Przełącz stan spisu treści</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">Współrzędne barycentryczne (matematyka)</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="Przejdź do artykułu w innym języku. Treść dostępna w 21 językach" > <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-21" 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">21 języków</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%A7%D9%85_%D8%A7%D9%84%D8%A5%D8%AD%D8%AF%D8%A7%D8%AB%D9%8A%D8%A7%D8%AA_%D8%A7%D9%84%D9%85%D8%B1%D8%AC%D8%AD%D9%8A%D8%A9" title="نظام الإحداثيات المرجحية – arabski" lang="ar" hreflang="ar" data-title="نظام الإحداثيات المرجحية" data-language-autonym="العربية" data-language-local-name="arabski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B0%D1%80%D0%B8%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%B8_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D0%B8" title="Барицентрични координати – bułgarski" lang="bg" hreflang="bg" data-title="Барицентрични координати" data-language-autonym="Български" data-language-local-name="bułgarski" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Baryzentrische_Koordinaten" title="Baryzentrische Koordinaten – niemiecki" lang="de" hreflang="de" data-title="Baryzentrische Koordinaten" data-language-autonym="Deutsch" data-language-local-name="niemiecki" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Barycentric_coordinate_system" title="Barycentric coordinate system – angielski" lang="en" hreflang="en" data-title="Barycentric coordinate system" data-language-autonym="English" data-language-local-name="angielski" 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/Coordenadas_baric%C3%A9ntricas_(n-simplex)" title="Coordenadas baricéntricas (n-simplex) – hiszpański" lang="es" hreflang="es" data-title="Coordenadas baricéntricas (n-simplex)" data-language-autonym="Español" data-language-local-name="hiszpański" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AF%D8%B3%D8%AA%DA%AF%D8%A7%D9%87_%D9%85%D8%AE%D8%AA%D8%B5%D8%A7%D8%AA_%DA%AF%D8%B1%D8%A7%D9%86%DB%8C%DA%AF%D8%A7%D9%87%DB%8C" title="دستگاه مختصات گرانیگاهی – perski" lang="fa" hreflang="fa" data-title="دستگاه مختصات گرانیگاهی" data-language-autonym="فارسی" data-language-local-name="perski" 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/Coordonn%C3%A9es_barycentriques" title="Coordonnées barycentriques – francuski" lang="fr" hreflang="fr" data-title="Coordonnées barycentriques" data-language-autonym="Français" data-language-local-name="francuski" 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/Coordenadas_baric%C3%A9ntricas" title="Coordenadas baricéntricas – galicyjski" lang="gl" hreflang="gl" data-title="Coordenadas baricéntricas" data-language-autonym="Galego" data-language-local-name="galicyjski" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Coordinate_baricentriche" title="Coordinate baricentriche – włoski" lang="it" hreflang="it" data-title="Coordinate baricentriche" data-language-autonym="Italiano" data-language-local-name="włoski" 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%A7%D7%95%D7%90%D7%95%D7%A8%D7%93%D7%99%D7%A0%D7%98%D7%95%D7%AA_%D7%91%D7%A8%D7%99%D7%A6%D7%A0%D7%98%D7%A8%D7%99%D7%95%D7%AA" title="קואורדינטות בריצנטריות – hebrajski" lang="he" hreflang="he" data-title="קואורדינטות בריצנטריות" data-language-autonym="עברית" data-language-local-name="hebrajski" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Barycentrische_co%C3%B6rdinaten" title="Barycentrische coördinaten – niderlandzki" lang="nl" hreflang="nl" data-title="Barycentrische coördinaten" data-language-autonym="Nederlands" data-language-local-name="niderlandzki" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Barysentriske_koordinater" title="Barysentriske koordinater – norweski (bokmål)" lang="nb" hreflang="nb" data-title="Barysentriske koordinater" data-language-autonym="Norsk bokmål" data-language-local-name="norweski (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Coordenadas_baric%C3%AAntricas" title="Coordenadas baricêntricas – portugalski" lang="pt" hreflang="pt" data-title="Coordenadas baricêntricas" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%B0%D1%80%D0%B8%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B5_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D1%8B" title="Барицентрические координаты – rosyjski" lang="ru" hreflang="ru" data-title="Барицентрические координаты" data-language-autonym="Русский" data-language-local-name="rosyjski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Te%C5%BEi%C5%A1%C4%8Dni_koordinatni_sistem" title="Težiščni koordinatni sistem – słoweński" lang="sl" hreflang="sl" data-title="Težiščni koordinatni sistem" data-language-autonym="Slovenščina" data-language-local-name="słoweński" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Barysentrinen_koordinaatti_(geometria)" title="Barysentrinen koordinaatti (geometria) – fiński" lang="fi" hreflang="fi" data-title="Barysentrinen koordinaatti (geometria)" data-language-autonym="Suomi" data-language-local-name="fiński" 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/Barycentriska_koordinater" title="Barycentriska koordinater – szwedzki" lang="sv" hreflang="sv" data-title="Barycentriska koordinater" data-language-autonym="Svenska" data-language-local-name="szwedzki" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D0%B0%D1%80%D0%B8%D1%86%D0%B5%D0%BD%D1%82%D1%80%D0%B8%D1%87%D0%BD%D1%96_%D0%BA%D0%BE%D0%BE%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D1%82%D0%B8" title="Барицентричні координати – ukraiński" lang="uk" hreflang="uk" data-title="Барицентричні координати" data-language-autonym="Українська" data-language-local-name="ukraiński" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%E1%BB%8Da_%C4%91%E1%BB%99_t%E1%BB%89_c%E1%BB%B1" title="Tọa độ tỉ cự – wietnamski" lang="vi" hreflang="vi" data-title="Tọa độ tỉ cự" data-language-autonym="Tiếng Việt" data-language-local-name="wietnamski" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%87%8D%E5%BF%83%E5%BA%A7%E6%A8%99" title="重心座標 – kantoński" lang="yue" hreflang="yue" data-title="重心座標" data-language-autonym="粵語" data-language-local-name="kantoński" 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/%E9%87%8D%E5%BF%83%E5%9D%90%E6%A0%87" title="重心坐标 – chiński" lang="zh" hreflang="zh" data-title="重心坐标" data-language-autonym="中文" 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Poprawny opis w haśle <a href="/wiki/Sympleks_(matematyka)" title="Sympleks (matematyka)">sympleks (matematyka)</a>..</i><br /><span style="color: var(--color-subtle, #54595d); font-size:80%">Dokładniejsze informacje o tym, co należy poprawić, być może znajdują się w <a href="/wiki/Dyskusja:Wsp%C3%B3%C5%82rz%C4%99dne_barycentryczne_(matematyka)" title="Dyskusja:Współrzędne barycentryczne (matematyka)">dyskusji tego artykułu</a>.</span><br /><span style="color: var(--color-subtle, #54595d); font-size:80%"> Po wyeliminowaniu niedoskonałości należy usunąć szablon <a href="/wiki/Szablon:Dopracowa%C4%87" title="Szablon:Dopracować">{{Dopracować}}</a> z tego artykułu.</span></div></div> </div> <p><b>Współrzędne barycentryczne</b> – <a href="/wiki/Uk%C5%82ad_wsp%C3%B3%C5%82rz%C4%99dnych" title="Układ współrzędnych">układ współrzędnych</a> zdefiniowany przez wierzchołki <a href="/wiki/Sympleks_(matematyka)" title="Sympleks (matematyka)">sympleksu</a>. </p><p>Niech <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_{0},x_{1},\dots ,x_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{0},x_{1},\dots ,x_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b46fe2a80e1c83cd6301afcbb9464e6993f18b09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.528ex; height:2.009ex;" alt="{\displaystyle x_{0},x_{1},\dots ,x_{n}}"></span> będą wierzchołkami sympleksu w <i>n</i>-wymiarowej <a href="/wiki/Przestrze%C5%84_liniowa" title="Przestrzeń liniowa">przestrzeni liniowej</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 A.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a71bf21ad35b8fe05555041d54d1e17eeb0f490" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.39ex; height:2.176ex;" alt="{\displaystyle A.}"></span> </p><p>Jeśli dla pewnego punktu <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 p\in A{:}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>∈</mo> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>:</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p\in A{:}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b3e40bb2f0f43b34034e7bf963d62218d499e6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:6.489ex; height:2.509ex;" alt="{\displaystyle p\in A{:}}"></span> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (a_{0}+\ldots +a_{n})p=a_{0}x_{0}+\ldots +a_{n}x_{n},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mo>…</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>p</mi> <mo>=</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mo>…</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a_{0}+\ldots +a_{n})p=a_{0}x_{0}+\ldots +a_{n}x_{n},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6699bce1b2a862b20ca20c36bb75b90dc8dfdf5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.929ex; height:2.843ex;" alt="{\displaystyle (a_{0}+\ldots +a_{n})p=a_{0}x_{0}+\ldots +a_{n}x_{n},}"></span></dd></dl> <p>to <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_{0},\dots ,a_{n})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a_{0},\dots ,a_{n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10af1a71845fb2562c8b6b5c67e9def323aac046" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.72ex; height:2.843ex;" alt="{\displaystyle (a_{0},\dots ,a_{n})}"></span> są współrzędnymi barycentrycznymi punktu <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 p.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88532f4eab1d4cef71ef96c0f8c98cac36fd9257" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.906ex; height:2.009ex;" alt="{\displaystyle p.}"></span> </p><p>Punkt </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 b={\frac {a_{0}+\ldots +a_{n}}{n+1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mo>…</mo> <mo>+</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b={\frac {a_{0}+\ldots +a_{n}}{n+1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/273ec024954ab0d7df3aa97de2d6f72a85a54413" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.069ex; height:5.176ex;" alt="{\displaystyle b={\frac {a_{0}+\ldots +a_{n}}{n+1}}}"></span></dd></dl> <p>jest barycentrum (<a href="/wiki/%C5%9Arodek_masy" title="Środek masy">środkiem masy</a>) sympleksu, stąd nazwa tego układu. </p> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wsp%C3%B3%C5%82rz%C4%99dne_barycentryczne_(matematyka)&veaction=edit&section=1" title="Edytuj sekcję: Bibliografia" class="mw-editsection-visualeditor"><span>edytuj</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wsp%C3%B3%C5%82rz%C4%99dne_barycentryczne_(matematyka)&action=edit&section=1" title="Edytuj kod źródłowy sekcji: Bibliografia"><span>edytuj kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation journal"><a href="/wiki/Jerzy_Mioduszewski" title="Jerzy Mioduszewski">Jerzy Mioduszewski</a>. <em>Wykłady z topologii. Topologia przestrzeni euklidesowych</em>. „Skrypty Uniwersytetu Śla̜skiego”, 1994. Katowice: <a href="/wiki/Wydawnictwo_Uniwersytetu_%C5%9Al%C4%85skiego" title="Wydawnictwo Uniwersytetu Śląskiego">Wydawnictwo Uniwersytetu Śląskiego</a>. <span class="issn"><a href="/wiki/International_Standard_Serial_Number" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/0239-6432">0239-6432</a></span>.</cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Wyk%C5%82ady+z+topologii.+Topologia+przestrzeni+euklidesowych&rft.jtitle=Skrypty+Uniwersytetu+%C5%9Ala%CC%9Cskiego&rft.date=1994&rft.aulast=Mioduszewski&rft.aufirst=Jerzy&rft.issn=0239-6432"><span style="display: none;"> </span></span><span class="problemy" aria-hidden="true" data-nosnippet="">brak numeru strony</span></li></ul></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Źródło: „<a dir="ltr" href="https://pl.wikipedia.org/w/index.php?title=Współrzędne_barycentryczne_(matematyka)&oldid=70675212">https://pl.wikipedia.org/w/index.php?title=Współrzędne_barycentryczne_(matematyka)&oldid=70675212</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Specjalna:Kategorie" title="Specjalna:Kategorie">Kategorie</a>: <ul><li><a href="/wiki/Kategoria:Uk%C5%82ady_wsp%C3%B3%C5%82rz%C4%99dnych" title="Kategoria:Układy współrzędnych">Układy współrzędnych</a></li><li><a href="/wiki/Kategoria:Zbiory_wypuk%C5%82e" title="Kategoria:Zbiory wypukłe">Zbiory wypukłe</a></li><li><a href="/wiki/Kategoria:Geometria_afiniczna" title="Kategoria:Geometria afiniczna">Geometria afiniczna</a></li><li><a href="/wiki/Kategoria:Tr%C3%B3jk%C4%85ty" title="Kategoria:Trójkąty">Trójkąty</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Ukryte kategorie: <ul><li><a href="/wiki/Kategoria:Artyku%C5%82y_wymagaj%C4%85ce_dopracowania" title="Kategoria:Artykuły wymagające dopracowania">Artykuły wymagające dopracowania</a></li><li><a href="/wiki/Kategoria:Szablon_cytowania_czasopisma_%E2%80%93_brak_numeru_strony" title="Kategoria:Szablon cytowania czasopisma – brak numeru strony">Szablon cytowania czasopisma – brak numeru strony</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"> Tę stronę ostatnio edytowano 18 cze 2023, 13:12.</li> <li id="footer-info-copyright">Tekst udostępniany na licencji <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.pl">Creative Commons: uznanie autorstwa, na tych samych warunkach</a>, z możliwością obowiązywania dodatkowych ograniczeń. 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