At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties.
The golden ratio is often denoted by the Greek letter ϕ (phi). The figure of a golden section illustrates the geometric relationship that defines this constant. Expressed algebraically:
This equation has as its unique positive solution the algebraic irrational number:
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