The result, though not a true logarithmic spiral, closely approximates a golden spiral. The corners of these squares can be connected by quarter- circles. After continuing this process for an arbitrary number of steps, the result will be an almost complete partitioning of the rectangle into squares.

This rectangle can then be partitioned into a square and a similar rectangle and this rectangle can then be split in the same way. įor example, a golden spiral can be approximated by first starting with a rectangle for which the ratio between its length and width is the golden ratio. There are several comparable spirals that approximate, but do not exactly equal, a golden spiral. The next width is 1/φ², then 1/φ³, and so on. For a square with side length 1, the next smaller square is 1/φ wide. The length of the side of a larger square to the next smaller square is in the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.Īpproximations of the golden spiral Approximate and true golden spirals: the green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a golden spiral, a special type of logarithmic spiral. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio.

The shape is infinitely repeated when magnified. Self-similar curve related to golden ratio Golden spirals are self-similar.

Fibonacci golden spiral tattoo