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In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887. Other names frequently used for the golden ratio are the golden section (Latin: sectio aurea) and golden mean. Other terms encountered include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, golden number, and mean of Phidias. In this article the golden ratio is denoted by the Greek lowercase letter phi () , while its reciprocal, or , is denoted by the uppercase variant Phi ().
The figure on the right illustrates the geometric relationship that defines this constant. Expressed algebraically:
This equation has one positive solution in the set of algebraic irrational numbers: