Deduciendo el teorema de las tres brechas vía inducción Rauzy-Veech

• Weiss, Christian ^[1]
  1. [1] University of Applied Sciences
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 54, Nº. 1, 2020, págs. 31-37
• Idioma: español
• DOI: 10.15446/recolma.v54n1.89777
• Títulos paralelos:
  • Deducing Three Gap Theorem from Rauzy-Veech induction
• Enlaces
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• Resumen
  • español

    El teorema de las tres brechas indica que existen a lo sumo tres longitudes distintas de brechas si se sitúan n puntos en un círculo, en ángulos z, 2z, … nz a partir del punto inicial. El teorema se demostró primero en 1958 por Sós y muchas pruebas han sido encontradas desde entonces. En esta nota mostramos cómo el teorema de las tres brechas puede ser fácilmente deducido usando inducción de tipo Rauzy-Veech.

  • English

    The Three Gap Theorem states that there are at most three distinct lengths of gaps if one places n points on a circle, at angles of z, 2z, … nz from the starting point. The theorem was first proven in 1958 by Sós and many proofs have been found since then. In this note we show how the Three Gap Theorem can easily be deduced by using Rauzy-Veech induction.

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