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 larger 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.
Fibonacci's Muscle Man
Fibonacci’s Muscle Man uses the property of Fibonacci pentagons by placing consecutive figures together at the outer edges, thereby creating a pentagon rotated by 36º. In total there is a clockwise rotating spiral of pentagons. Thus, one full rotation requires 10 rotations. The neckline is reminiscent of a bodybuilder’s fist and muscles.
The spiral arrangement resulting from the construction produces several fascinating effects.
The image negative leaves an image of a sharp sawtooth blade on the inside. On the outside there is a gentler wave motion.
The pentagons seem to turn upside down with every rotation.
The harmonic growth of the pentagons can be felt in that the side of the larger pentagon is a diagonal of the next smaller pentagon.