Golden rectangle

In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, ${\displaystyle 1:{\tfrac {1+{\sqrt {5}}}{2}}}$, which is ${\displaystyle 1:\varphi }$ (the Greek letter phi), where ${\displaystyle \varphi }$ 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.

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