  We deal with the distribution of N points placed consecutively around the circle by a fixed angle of a. 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 (Steinhauss Conjecture)