The Three Gap Theorem (Steinhauss Conjecture)
<|reference_start|>The Three Gap Theorem (Steinhauss Conjecture): 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.<|reference_end|>
@article{mayero2006the,
    title={The Three Gap Theorem (Steinhauss Conjecture)},
    author={Micaela Mayero (INRIA Futurs)},
    journal={Types for Proofs and Programs: International Workshop, TYPES'99,
  L\"{o}keberg, Sweden, June 1999. Selected Papers (2000) 162},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0609124},
    primaryClass={cs.LO}
}