The Three Gap Theorem (Steinhauss Conjecture)

Details The Three Gap Theorem (Steinhauss Conjecture) The Three Gap Theorem (Steinhauss Conjecture)

2006-09-22

arxiv.org/abs/cs/0609124v1

Types for Proofs and Programs: International Workshop, TYPES'99, L\"{o}keberg, Sweden, June 1999. Selected Papers (2000) 162

Computer Science

Logic in Computer Science

Scientific paper

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.

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