@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-RRKH1DMP-L
  skos:prefLabel "area of a triangle"@en, "aire d'un triangle"@fr ;
  a skos:Concept ;
  skos:narrower psr:-MCFGWNDL-M .

psr: a skos:ConceptScheme .
psr:-NQKFJ1Q2-3
  skos:prefLabel "triangle de Héron"@fr, "Heronian triangle"@en ;
  a skos:Concept ;
  skos:related psr:-MCFGWNDL-M .

psr:-MCFGWNDL-M
  skos:altLabel "Hero's formula"@en ;
  skos:prefLabel "formule de Héron"@fr, "Heron's formula"@en ;
  a skos:Concept ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Formule_de_H%C3%A9ron>, <https://en.wikipedia.org/wiki/Heron%27s_formula> ;
  skos:definition """En géométrie euclidienne, la <b>formule de Héron</b>, portant le nom de Héron d'Alexandrie, permet de calculer l'aire <span class="texhtml mvar" style="font-style:italic;">S</span> d'un triangle quelconque en ne connaissant que les longueurs <span class="texhtml mvar" style="font-style:italic;">a</span>, <span class="texhtml mvar" style="font-style:italic;">b</span> et <span class="texhtml mvar" style="font-style:italic;">c</span> de ses trois côtés&nbsp;:
<br/>
<br/><center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle S={\\\\sqrt {p(p-a)(p-b)(p-c)}}\\\\quad {\\	ext{avec}}\\\\quad p={\\rac {a+b+c}{2}}.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>S</mi>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <msqrt>
<br/>            <mi>p</mi>
<br/>            <mo stretchy="false">(</mo>
<br/>            <mi>p</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>a</mi>
<br/>            <mo stretchy="false">)</mo>
<br/>            <mo stretchy="false">(</mo>
<br/>            <mi>p</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>b</mi>
<br/>            <mo stretchy="false">)</mo>
<br/>            <mo stretchy="false">(</mo>
<br/>            <mi>p</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>c</mi>
<br/>            <mo stretchy="false">)</mo>
<br/>          </msqrt>
<br/>        </mrow>
<br/>        <mspace width="1em"></mspace>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mtext>avec</mtext>
<br/>        </mrow>
<br/>        <mspace width="1em"></mspace>
<br/>        <mi>p</mi>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi>a</mi>
<br/>              <mo>+</mo>
<br/>              <mi>b</mi>
<br/>              <mo>+</mo>
<br/>              <mi>c</mi>
<br/>            </mrow>
<br/>            <mn>2</mn>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle S={\\\\sqrt {p(p-a)(p-b)(p-c)}}\\\\quad {\\	ext{avec}}\\\\quad p={\\rac {a+b+c}{2}}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd4bbc2ce812dc7c17ff7ec8ba80ac4e05214c97" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:52.548ex; height:5.343ex;" alt="{\\\\displaystyle S={\\\\sqrt {p(p-a)(p-b)(p-c)}}\\\\quad {\\	ext{avec}}\\\\quad p={\\rac {a+b+c}{2}}.}"></span></center>La formule était déjà connue d'Archimède.
<br/> 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Formule_de_H%C3%A9ron">https://fr.wikipedia.org/wiki/Formule_de_H%C3%A9ron</a>)"""@fr, """In geometry, <b>Heron's formula</b> (or <b>Hero's formula</b>) gives the area of a triangle in terms of the three side lengths <span class="texhtml mvar" style="font-style:italic;">a</span>, <span class="texhtml mvar" style="font-style:italic;">b</span>, <span class="texhtml mvar" style="font-style:italic;">c</span>. If <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="{\\	extstyle s={\\	frac {1}{2}}(a+b+c)}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="false" scriptlevel="0">
<br/>        <mi>s</mi>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mstyle displaystyle="false" scriptlevel="0">
<br/>            <mfrac>
<br/>              <mn>1</mn>
<br/>              <mn>2</mn>
<br/>            </mfrac>
<br/>          </mstyle>
<br/>        </mrow>
<br/>        <mo stretchy="false">(</mo>
<br/>        <mi>a</mi>
<br/>        <mo>+</mo>
<br/>        <mi>b</mi>
<br/>        <mo>+</mo>
<br/>        <mi>c</mi>
<br/>        <mo stretchy="false">)</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\	extstyle s={\\	frac {1}{2}}(a+b+c)}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4145f3854d76a2e064aab41210bef32f0b8d0694" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.171ex; width:16.571ex; height:3.509ex;" alt="{\\	extstyle s={\\	frac {1}{2}}(a+b+c)}"></span> is the semiperimeter of the triangle, the area <span class="texhtml mvar" style="font-style:italic;">A</span> is,
<br/>
<br/><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={\\\\sqrt {s(s-a)(s-b)(s-c)}}.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>A</mi>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <msqrt>
<br/>            <mi>s</mi>
<br/>            <mo stretchy="false">(</mo>
<br/>            <mi>s</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>a</mi>
<br/>            <mo stretchy="false">)</mo>
<br/>            <mo stretchy="false">(</mo>
<br/>            <mi>s</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>b</mi>
<br/>            <mo stretchy="false">)</mo>
<br/>            <mo stretchy="false">(</mo>
<br/>            <mi>s</mi>
<br/>            <mo>−<!-- − --></mo>
<br/>            <mi>c</mi>
<br/>            <mo stretchy="false">)</mo>
<br/>          </msqrt>
<br/>        </mrow>
<br/>        <mo>.</mo>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle A={\\\\sqrt {s(s-a)(s-b)(s-c)}}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e8e1851a05e4cd4e764ec7dbe96c477989fcde3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:29.357ex; height:4.843ex;" alt="A={\\\\sqrt  {s(s-a)(s-b)(s-c)}}."> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Heron%27s_formula">https://en.wikipedia.org/wiki/Heron%27s_formula</a>)"""@en ;
  skos:inScheme psr: ;
  skos:broader psr:-RRKH1DMP-L ;
  dc:modified "2023-08-10"^^xsd:date ;
  skos:related psr:-RX61SX55-G, psr:-NQKFJ1Q2-3 ;
  dc:created "2023-08-09"^^xsd:date .

psr:-RX61SX55-G
  skos:prefLabel "triangle"@fr, "triangle"@en ;
  a skos:Concept ;
  skos:related psr:-MCFGWNDL-M .