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Aretxabaleta, X.M., Gonchenko, M., Harshman, N.L., Jackson, S.G., Olshanii, M. and Astrakharchik, G.E. (2020) The Dynamics of Digits: Calculating π with Galperin’s Billiards. Σ Mathematics, 8, 32 p.
https://doi.org/10.3390/math8040509

has been cited by the following article:

• TITLE: Collisions, or Reflections and Rotations, Leading to the Digits of π

  AUTHORS: François Dubeau

  KEYWORDS: Dynamical System, Elastic Collisions, Reflection, Rotation, Digits of π

  JOURNAL NAME: Applied Mathematics, Vol.13 No.9, September 2, 2022

  ABSTRACT: We analyze a problem of elastic collisions between elements of a system composed of two balls and a wall. Thanks to a change of variables, the problem is reduced to a sequence of reflections and rotations. Moreover, the total number of collisions is easily found. For specific ratios of ball weights, the number of collisions is related to the first successive digits of π.