The Golden Ratio In Optics

Berton C. Willard

Like the irrational numbers Π and e, the golden ratio—itself an irrational number—keeps cropping up in the most diverse fields, from architecture to zoology. It was known in many forms, although not by the name golden ratio, to the mathematicians of the school of Pythagoras, the Greek philosopher (569-500 B.C.). Perhaps the simplest source is in finding the golden cut of a straight line. If a line is cut into two lengths, 1 and x, so that (1+x)/x = x/1, then the golden cut has been made and x is known as the golden ratio. This ratio has fascinated mathematicians and others ever since, but it was not until the early part of the 20th century that the Greek letter Φ was suggested as its designation.

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