The placement of points on a unit circle: the golden placement policy

Abstract

This article investigates patterns and properties among the points and the gaps that are formed when points are placed in a clockwise direction around a unit circle so that the distance between successive placements is the Golden Section (τ). It was shown that the use of τ corresponds to a policy of placing points in the oldest gap among all of the largest gaps.  The analyses examined the ordering of the points, i.e., their length, age, type, and the numbers of gap types formed. It demonstrated the importance of Fibonacci numbers in describing the patterns that emerge. The analyses provide insights into practical situations including the placement of transmitters and receivers as well as in phyllotaxis.