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In geometry, a **golden rectangle** is a rectangle whose side lengths are in the golden ratio, , which is (the Greek letter phi), where is approximately 1.618.

A golden rectangle can be constructed with only straightedge and compass by four simple steps:

A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle; that is, with the same aspect ratio as the first. Square removal can be repeated infinitely, in which case corresponding corners of the squares form an infinite sequence of points on the golden spiral, the unique logarithmic spiral with this property.

An alternative construction of the golden rectangle uses three polygons circumscribed by congruent circles: a regular decagon, hexagon, and pentagon. The respective lengths *a*, *b*, and *c* of the sides of these three polygons satisfy the equation *a*^{2} + *b*^{2} = *c*^{2}, so line segments with these lengths form a right triangle (by the converse of the Pythagorean theorem). The ratio of the side length of the hexagon to the decagon is the golden ratio, so this triangle forms half of a golden rectangle.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Golden_rectangle

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