@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:-GR8X1BV4-T
  skos:inScheme psr: ;
  skos:related psr:-LXM4CK6S-X, psr:-WSC22G3S-3, psr:-CN7TH1V4-K, psr:-KHVRXGGV-W, psr:-BW19KG47-V, psr:-ZKM5SS8V-8, psr:-JLMR8X0R-R, psr:-NPQFSXL8-X, psr:-PDTQPM8R-7 ;
  skos:broader psr:-V3F2M3LL-D, psr:-RBFVN7DN-2, psr:-WX8H0134-J ;
  skos:prefLabel "golden ratio"@en, "nombre d'or"@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Nombre_d%27or>, <https://en.wikipedia.org/wiki/Golden_ratio> ;
  skos:definition """Le <b>nombre d'or</b> (ou <b>section dorée</b>, <b>proportion dorée</b>, ou encore <b>divine proportion</b>) est une proportion, définie initialement en géométrie comme l'unique rapport <span class="texhtml"><i>a</i>/<i>b</i></span> entre deux longueurs <span class="texhtml mvar" style="font-style:italic;">a</span> et <span class="texhtml mvar" style="font-style:italic;">b</span> telles que le rapport de la somme <span class="texhtml"><i>a</i> + <i>b</i></span> des deux longueurs sur la plus grande (<span class="texhtml mvar" style="font-style:italic;">a</span>) soit égal à celui de la plus grande (<span class="texhtml mvar" style="font-style:italic;">a</span>) sur la plus petite (<span class="texhtml mvar" style="font-style:italic;">b</span>), ce qui s'écrit :  <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 {\\rac {a+b}{a}}={\\rac {a}{b}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mi>a</mi>               <mo>+</mo>               <mi>b</mi>             </mrow>             <mi>a</mi>           </mfrac>         </mrow>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mi>a</mi>             <mi>b</mi>           </mfrac>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {a+b}{a}}={\\rac {a}{b}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7519151eb86b89c70404d135586c0ad1c480c93" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:11.068ex; height:5.509ex;" alt="{\\rac  {a+b}a}={\\rac  ab}"></span> avec <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 {\\rac {a}{b}}=\\\\varphi }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mi>a</mi>             <mi>b</mi>           </mfrac>         </mrow>         <mo>=</mo>         <mi>φ<!-- φ --></mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {a}{b}}=\\\\varphi }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbb3bbaa39f4f1ca7bb632c095370c8ed78e99a8" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:6.685ex; height:4.843ex;" alt="{\\\\displaystyle {\\rac {a}{b}}=\\\\varphi }"></span></center> Le découpage d'un segment en deux longueurs vérifiant cette propriété est appelé par Euclide découpage en « extrême et moyenne raison ». Le nombre d'or est maintenant souvent désigné par la lettre φ ou <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> (phi), et il est lié à l'angle d'or. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_d%27or">https://fr.wikipedia.org/wiki/Nombre_d%27or</a>)"""@fr, """In mathematics, two quantities are in the <b>golden ratio</b> if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities <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>       </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/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="a"></span> and <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}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>b</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle b}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="b"></span> with <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>b>0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>a</mi>         <mo>&gt;</mo>         <mi>b</mi>         <mo>&gt;</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a&gt;b&gt;0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dc57e5721ebc7b851b968ea2545913848bf7a01e" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.587ex; height:2.176ex;" alt="a > b > 0"></span>,  <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent" style="padding-left: 1.6em;"><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 {\\rac {a+b}{a}}={\\rac {a}{b}}=\\\\varphi }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mi>a</mi>               <mo>+</mo>               <mi>b</mi>             </mrow>             <mi>a</mi>           </mfrac>         </mrow>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mi>a</mi>             <mi>b</mi>           </mfrac>         </mrow>         <mo>=</mo>         <mi>φ<!-- φ --></mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {a+b}{a}}={\\rac {a}{b}}=\\\\varphi }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84314078c65d42092ea2b178a2017754ac4062ff" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.687ex; height:5.509ex;" alt="{\\\\displaystyle {\\rac {a+b}{a}}={\\rac {a}{b}}=\\\\varphi }"></span></div> where the Greek letter phi (<span class="nowrap"><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></span> or <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 \\\\phi }">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>ϕ<!-- ϕ --></mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\phi }</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="\\\\phi "></span>) denotes the golden ratio. The constant <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> satisfies the quadratic equation <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 ^{2}=\\\\varphi +1}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>φ<!-- φ --></mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>=</mo>         <mi>φ<!-- φ --></mi>         <mo>+</mo>         <mn>1</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\varphi ^{2}=\\\\varphi +1}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/642e4bbe73e89ff3b93588bf2dbbee3ad852d3eb" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.196ex; height:3.176ex;" alt="{\\\\displaystyle \\\\varphi ^{2}=\\\\varphi +1}"></span> and is an irrational number with a value of  <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent" style="padding-left: 1.6em;"><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 ={\\rac {1+{\\\\sqrt {5}}}{2}}=}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>φ<!-- φ --></mi>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mn>1</mn>               <mo>+</mo>               <mrow class="MJX-TeXAtom-ORD">                 <msqrt>                   <mn>5</mn>                 </msqrt>               </mrow>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>         <mo>=</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\varphi ={\\rac {1+{\\\\sqrt {5}}}{2}}=}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/994537567a6f46ee7357b0fb48005e212cf1bdd7" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:15.009ex; height:5.843ex;" alt="{\\\\displaystyle \\\\varphi ={\\rac {1+{\\\\sqrt {5}}}{2}}=}"></span><span class="texhtml"><span class="nowrap"><span data-sort-value="7000161803398874900♠"></span>1.618<span style="margin-left:.25em;">033</span><span style="margin-left:.25em;">988</span><span style="margin-left:.25em;">749</span></span>....</span></div> The golden ratio was called the <b>extreme and mean ratio</b> by Euclid, and the <b>divine proportion</b> by Luca Pacioli, and also goes by several other names.   
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio">https://en.wikipedia.org/wiki/Golden_ratio</a>)"""@en ;
  a skos:Concept ;
  dc:created "2023-07-25"^^xsd:date ;
  dc:modified "2024-10-18"^^xsd:date .

psr:-WSC22G3S-3
  skos:prefLabel "almost integer"@en, "nombre presque entier"@fr ;
  a skos:Concept ;
  skos:related psr:-GR8X1BV4-T .

psr:-LXM4CK6S-X
  skos:prefLabel "angle d’or"@fr, "golden angle"@en ;
  a skos:Concept ;
  skos:related psr:-GR8X1BV4-T .

psr:-JLMR8X0R-R
  skos:prefLabel "Fibonacci sequence"@en, "suite de Fibonacci"@fr ;
  a skos:Concept ;
  skos:related psr:-GR8X1BV4-T .

psr:-RBFVN7DN-2
  skos:prefLabel "mathematical constant"@en, "constante mathématique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-GR8X1BV4-T .

psr:-V3F2M3LL-D
  skos:prefLabel "nombre algébrique"@fr, "algebraic number"@en ;
  a skos:Concept ;
  skos:narrower psr:-GR8X1BV4-T .

psr:-CN7TH1V4-K
  skos:prefLabel "Kepler triangle"@en, "triangle de Kepler"@fr ;
  a skos:Concept ;
  skos:related psr:-GR8X1BV4-T .

psr:-KHVRXGGV-W
  skos:prefLabel "pavage de Penrose"@fr, "Penrose tiling"@en ;
  a skos:Concept ;
  skos:related psr:-GR8X1BV4-T .

psr:-NPQFSXL8-X
  skos:prefLabel "Bilinski dodecahedron"@en, "dodécaèdre de Bilinski"@fr ;
  a skos:Concept ;
  skos:related psr:-GR8X1BV4-T .

psr: a skos:ConceptScheme .
psr:-BW19KG47-V
  skos:prefLabel "golden triangle"@en, "triangle d'or"@fr ;
  a skos:Concept ;
  skos:related psr:-GR8X1BV4-T .

psr:-WX8H0134-J
  skos:prefLabel "nombre irrationnel"@fr, "irrational number"@en ;
  a skos:Concept ;
  skos:narrower psr:-GR8X1BV4-T .

psr:-ZKM5SS8V-8
  skos:prefLabel "golden spiral"@en, "spirale d'or"@fr ;
  a skos:Concept ;
  skos:related psr:-GR8X1BV4-T .

psr:-PDTQPM8R-7
  skos:prefLabel "dodécaèdre régulier"@fr, "regular dodecahedron"@en ;
  a skos:Concept ;
  skos:related psr:-GR8X1BV4-T .