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The Three Gap Theorem (Steinhaus Conjecture)

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Types for Proofs and Programs (TYPES 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1956))

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Abstract

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 [RAV88], 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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Author information

Authors and Affiliations

  1. Projet Coq, INRIA-Rocquencourt, INRIA-Rocquencourt, domaine de Voluceau, B.P. 105, 78153, Le Chesnay Cedex, France

    Micaela Mayero

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  1. Micaela Mayero
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Editor information

Editors and Affiliations

  1. Department of Computing Science, Chalmers University of Technology and University of Göteborg, 41296, Göteborg, Sweden

    Thierry Coquand , Peter Dybjer , Bengt Nordström  & Jan Smith , ,  & 

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Mayero, M. (2000). The Three Gap Theorem (Steinhaus Conjecture). In: Coquand, T., Dybjer, P., Nordström, B., Smith, J. (eds) Types for Proofs and Programs. TYPES 1999. Lecture Notes in Computer Science, vol 1956. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44557-9_10

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  • DOI: https://doi.org/10.1007/3-540-44557-9_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41517-6

  • Online ISBN: 978-3-540-44557-9

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