@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:-M5Z96M15-F
  skos:prefLabel "nombre octogonal"@fr, "octagonal number"@en ;
  a skos:Concept ;
  skos:broader psr:-X7NSSF7W-1 .

psr:-X7NSSF7W-1
  skos:exactMatch <https://en.wikipedia.org/wiki/Polygonal_number>, <https://fr.wikipedia.org/wiki/Nombre_polygonal> ;
  skos:narrower psr:-DM50QH1X-J, psr:-M3N11P2M-V, psr:-LRPB5V08-Q, psr:-M5Z96M15-F, psr:-LRJ239K8-D, psr:-MVH6PC56-4, psr:-TTJRH5JV-B ;
  skos:definition """En mathématiques, un <b>nombre polygonal</b> est un nombre figuré qui peut être représenté par un polygone régulier. Les mathématiciens antiques ont découvert que des nombres pouvaient être représentés en disposant d'une certaine manière des cailloux ou des pois</span>. La formule générale pour le nombre <i>k</i>-gonal d'ordre <i>n</i> est <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_{k,n}={n~{\\ig (}(k-2)n-(k-4){\\ig )} \\\\over 2}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>P</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>k</mi>             <mo>,</mo>             <mi>n</mi>           </mrow>         </msub>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mi>n</mi>               <mtext> </mtext>               <mrow class="MJX-TeXAtom-ORD">                 <mrow class="MJX-TeXAtom-ORD">                   <mo maxsize="1.2em" minsize="1.2em">(</mo>                 </mrow>               </mrow>               <mo stretchy="false">(</mo>               <mi>k</mi>               <mo>−<!-- − --></mo>               <mn>2</mn>               <mo stretchy="false">)</mo>               <mi>n</mi>               <mo>−<!-- − --></mo>               <mo stretchy="false">(</mo>               <mi>k</mi>               <mo>−<!-- − --></mo>               <mn>4</mn>               <mo stretchy="false">)</mo>               <mrow class="MJX-TeXAtom-ORD">                 <mrow class="MJX-TeXAtom-ORD">                   <mo maxsize="1.2em" minsize="1.2em">)</mo>                 </mrow>               </mrow>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle P_{k,n}={n~{\\ig (}(k-2)n-(k-4){\\ig )} \\\\over 2}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/446ff12ecfce1940a26733c885783ff3c37ff5ac" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:30.346ex; height:6.009ex;" alt="{\\\\displaystyle P_{k,n}={n~{\\ig (}(k-2)n-(k-4){\\ig )} \\\\over 2}}"></span>. Avec inversion des lettres <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" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\\\\displaystyle n}"></span> 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 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/c3c9a2c7b599b37105512c5d570edc034056dd40" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\\\\displaystyle k}"></span>, la suite double <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_{n,k})_{n\\\\geqslant 1,k\\\\geqslant 2}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mo stretchy="false">(</mo>         <msub>           <mi>P</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>             <mo>,</mo>             <mi>k</mi>           </mrow>         </msub>         <msub>           <mo stretchy="false">)</mo>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>             <mo>⩾<!-- ⩾ --></mo>             <mn>1</mn>             <mo>,</mo>             <mi>k</mi>             <mo>⩾<!-- ⩾ --></mo>             <mn>2</mn>           </mrow>         </msub>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle (P_{n,k})_{n\\\\geqslant 1,k\\\\geqslant 2}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/946531919d30219b01c26862fdd28853e23c7314" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.567ex; height:3.009ex;" alt="{\\\\displaystyle (P_{n,k})_{n\\\\geqslant 1,k\\\\geqslant 2}}"></span> est répertoriée comme suite A057145 de l'OEIS.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_polygonal">https://fr.wikipedia.org/wiki/Nombre_polygonal</a>)"""@fr, """In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots are thought of as alphas (units). These are one type of 2-dimensional figurate numbers. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">https://en.wikipedia.org/wiki/Polygonal_number</a>)"""@en ;
  skos:related psr:-QPV3DS04-0 ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:prefLabel "polygonal number"@en, "nombre polygonal"@fr ;
  a skos:Concept ;
  skos:broader psr:-P3VL62TN-G ;
  skos:inScheme psr: .

psr:-M3N11P2M-V
  skos:prefLabel "nombre pentagonal"@fr, "pentagonal number"@en ;
  a skos:Concept ;
  skos:broader psr:-X7NSSF7W-1 .

psr:-TTJRH5JV-B
  skos:prefLabel "nombre triangulaire"@fr, "triangular number"@en ;
  a skos:Concept ;
  skos:broader psr:-X7NSSF7W-1 .

psr:-P3VL62TN-G
  skos:prefLabel "figurate number"@en, "nombre figuré"@fr ;
  a skos:Concept ;
  skos:narrower psr:-X7NSSF7W-1 .

psr:-DM50QH1X-J
  skos:prefLabel "hexagonal number"@en, "nombre hexagonal"@fr ;
  a skos:Concept ;
  skos:broader psr:-X7NSSF7W-1 .

psr: a skos:ConceptScheme .
psr:-LRJ239K8-D
  skos:prefLabel "decagonal number"@en, "nombre décagonal"@fr ;
  a skos:Concept ;
  skos:broader psr:-X7NSSF7W-1 .

psr:-LRPB5V08-Q
  skos:prefLabel "square number"@en, "nombre carré"@fr ;
  a skos:Concept ;
  skos:broader psr:-X7NSSF7W-1 .

psr:-QPV3DS04-0
  skos:prefLabel "polygone régulier"@fr, "regular polygon"@en ;
  a skos:Concept ;
  skos:related psr:-X7NSSF7W-1 .

psr:-MVH6PC56-4
  skos:prefLabel "heptagonal number"@en, "nombre heptagonal"@fr ;
  a skos:Concept ;
  skos:broader psr:-X7NSSF7W-1 .