In geometry, a golden rectangle is a rectangle with side lengths in golden ratio 1 + 5 2 : 1 , {\displaystyle {\tfrac {1+{\sqrt {5}}}{2}}:1,} or φ : 1 , {\displaystyle \varphi :1,} with φ {\displaystyle \varphi } approximately equal to 1.618 or 89/55.
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.