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We deal with the distribution of N points placed consecutively around the circle by a fixed angle of α. From the proof of Tony van Ravenstein, we propose a detailed proof of the Steinhaus conjecture whose result is the following: the N points partition the circle into gaps of at most three different lengths.  We study the mathematical notions required for the proof of this theorem revealed during a formal proof carried out in Coq.

The Three Gap Theorem (Steinhaus Conjecture)