Golden rectangle

In geometry, a golden rectangle is a rectangle with side lengths in aspect ratio⁠${\displaystyle \varphi :1}$⁠, the golden ratio, where ${\displaystyle \varphi ={\tfrac {1}{2}}{\bigl (}1+{\sqrt {5}}{\bigr )}\approx {}}$${\displaystyle 1.618}$. That is, one side of the rectangle is ⁠${\displaystyle \varphi }$⁠ times longer than another.

Golden rectangles exhibit a special form of self-similarity: if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.