@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: a skos:ConceptScheme .
psr:-RMGFLLZT-6
  dc:created "2023-08-01"^^xsd:date ;
  skos:broader psr:-M8072G8C-1 ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Cl%C3%A9lie>, <https://fr.wikipedia.org/wiki/Cl%C3%A9lie_(math%C3%A9matiques)> ;
  dc:modified "2023-08-01"^^xsd:date ;
  skos:definition """En mathématiques, une <b>clélie</b> est une courbe sphérique paramétrée de formule&nbsp;:
<br/><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 {\\egin{cases}x=a\\\\sin({m\\	heta })\\\\cos({\\	heta })\\\\\\\\y=a\\\\sin({m\\	heta })\\\\sin({\\	heta })\\\\\\\\z=a\\\\cos({m\\	heta })\\\\end{cases}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mrow>
<br/>            <mo>{</mo>
<br/>            <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false">
<br/>              <mtr>
<br/>                <mtd>
<br/>                  <mi>x</mi>
<br/>                  <mo>=</mo>
<br/>                  <mi>a</mi>
<br/>                  <mi>sin</mi>
<br/>                  <mo>⁡<!-- ⁡ --></mo>
<br/>                  <mo stretchy="false">(</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>m</mi>
<br/>                    <mi>θ<!-- θ --></mi>
<br/>                  </mrow>
<br/>                  <mo stretchy="false">)</mo>
<br/>                  <mi>cos</mi>
<br/>                  <mo>⁡<!-- ⁡ --></mo>
<br/>                  <mo stretchy="false">(</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>θ<!-- θ --></mi>
<br/>                  </mrow>
<br/>                  <mo stretchy="false">)</mo>
<br/>                </mtd>
<br/>              </mtr>
<br/>              <mtr>
<br/>                <mtd>
<br/>                  <mi>y</mi>
<br/>                  <mo>=</mo>
<br/>                  <mi>a</mi>
<br/>                  <mi>sin</mi>
<br/>                  <mo>⁡<!-- ⁡ --></mo>
<br/>                  <mo stretchy="false">(</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>m</mi>
<br/>                    <mi>θ<!-- θ --></mi>
<br/>                  </mrow>
<br/>                  <mo stretchy="false">)</mo>
<br/>                  <mi>sin</mi>
<br/>                  <mo>⁡<!-- ⁡ --></mo>
<br/>                  <mo stretchy="false">(</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>θ<!-- θ --></mi>
<br/>                  </mrow>
<br/>                  <mo stretchy="false">)</mo>
<br/>                </mtd>
<br/>              </mtr>
<br/>              <mtr>
<br/>                <mtd>
<br/>                  <mi>z</mi>
<br/>                  <mo>=</mo>
<br/>                  <mi>a</mi>
<br/>                  <mi>cos</mi>
<br/>                  <mo>⁡<!-- ⁡ --></mo>
<br/>                  <mo stretchy="false">(</mo>
<br/>                  <mrow class="MJX-TeXAtom-ORD">
<br/>                    <mi>m</mi>
<br/>                    <mi>θ<!-- θ --></mi>
<br/>                  </mrow>
<br/>                  <mo stretchy="false">)</mo>
<br/>                </mtd>
<br/>              </mtr>
<br/>            </mtable>
<br/>            <mo fence="true" stretchy="true" symmetric="true"></mo>
<br/>          </mrow>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\egin{cases}x=a\\\\sin({m\\	heta })\\\\cos({\\	heta })\\\\\\\\y=a\\\\sin({m\\	heta })\\\\sin({\\	heta })\\\\\\\\z=a\\\\cos({m\\	heta })\\\\end{cases}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c0f89c59946ddb7f9a2ebaeea0dfae419e15027" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.838ex; width:23.056ex; height:8.843ex;" alt="{\\\\displaystyle {\\egin{cases}x=a\\\\sin({m\\	heta })\\\\cos({\\	heta })\\\\\\\\y=a\\\\sin({m\\	heta })\\\\sin({\\	heta })\\\\\\\\z=a\\\\cos({m\\	heta })\\\\end{cases}}}"></span> 
<br/>où <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}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>a</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle a}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="a"></span> est le rayon de la sphère et <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 m\\\\in \\\\mathbb {R} }">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mi>m</mi>
<br/>        <mo>∈<!-- ∈ --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mi mathvariant="double-struck">R</mi>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle m\\\\in \\\\mathbb {R} }</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b9aa033deb5e523e2d98098c1b1418f97b33e5b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:6.559ex; height:2.176ex;" alt="{\\\\displaystyle m\\\\in \\\\mathbb {R} }"></span>. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Cl%C3%A9lie_(math%C3%A9matiques)">https://fr.wikipedia.org/wiki/Cl%C3%A9lie_(math%C3%A9matiques)</a>)"""@fr, """In mathematics, a <b>Clélie</b> or <b>Clelia curve</b> is a curve on a sphere with the property:
         
         <ul><li>If the surface of a sphere is described as usual by the longitude (angle <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 \\\\varphi }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>φ<!-- φ --></mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\varphi }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="\\\\varphi "></span>) and the colatitude (angle <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 \\	heta }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>θ<!-- θ --></mi>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\	heta }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="\\	heta "></span>) then</li></ul>
         <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 \\\\varphi =c\\\\;\\	heta ,\\\\quad c>0}">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mi>φ<!-- φ --></mi>
         <mo>=</mo>
         <mi>c</mi>
         <mspace width="thickmathspace"></mspace>
         <mi>θ<!-- θ --></mi>
         <mo>,</mo>
         <mspace width="1em"></mspace>
         <mi>c</mi>
         <mo>></mo>
         <mn>0</mn>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\varphi =c\\\\;\\	heta ,\\\\quad c>0}</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de2234630beaa722f2a2e70a3cf6cfa33a7ea116" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.985ex; height:2.676ex;" alt="{\\\\displaystyle \\\\varphi =c\\\\;\\	heta ,\\\\quad c>0}"></span>.</dd></dl>
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Cl%C3%A9lie">https://en.wikipedia.org/wiki/Cl%C3%A9lie</a>)"""@en ;
  skos:prefLabel "Clélie"@en, "Clélie"@fr ;
  skos:altLabel "Clelia curve"@en ;
  skos:inScheme psr: ;
  a skos:Concept .

psr:-M8072G8C-1
  skos:prefLabel "spherical geometry"@en, "géométrie sphérique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-RMGFLLZT-6 .