The Fibonacci Pentagons collection shows arrangements of regular pentagons whose side lengths are Fibonacci numbers. A regular pentagon has five sides of equal length and five diagonals of equal length. The five interior angles are 108º, making a total of 540º.
Regular pentagons have the fascinating property that the ratio of their diagonals to the length of their sides is the golden ratio. For large Fibonacci numbers, the ratio of two consecutive Fibonacci numbers also approaches the golden ratio, so that the diagonal of a Fibonacci pentagon becomes the side length of the next largest Fibonacci pentagon.
Example: the Fibonacci pentagon with a side length of 55 cm has a diagonal length of 88,992 cm, which is very close to the side length of the next larger Fibonacci pentagon of 89 cm.
Cortex Vortex shows a sequence of superimposed, inscribed Fibonacci Pentagons. Two consecutive pentagons touch in one corner and along two sides. The smaller pentagon overlies the larger one. The touching corner moves counterclockwise by two corners at a time. The green hues of the pentagons get darker and darker towards the center until they end in red at the first Fibonacci pentagon with side length 1. The second Fibonacci Pentagon, which also has side length 1, is completely covered by the first.