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number > irrational number > golden ratio

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golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities ${\\displaystyle a}$ and ${\\displaystyle b}$ with ${\\displaystyle a>b>0}$ ,
${\\displaystyle {\ rac {a+b}{a}}={\ rac {a}{b}}=\\varphi }$
where the Greek letter phi ( ${\\displaystyle \\varphi }$ or ${\\displaystyle \\phi }$ ) denotes the golden ratio. The constant ${\\displaystyle \\varphi }$ satisfies the quadratic equation ${\\displaystyle \\varphi ^{2}=\\varphi +1}$ and is an irrational number with a value of
${\\displaystyle \\varphi ={\ rac {1+{\\sqrt {5}}}{2}}=}$ $1.618 033988749 ....$
The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Golden_ratio)

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RDF/XML TURTLE JSON-LD Date de création 25/07/2023, dernière modification le 18/10/2024