TITLE:
Hyperbolic Reflections Leading to the Digits of ln(2)
AUTHORS:
François Dubeau
KEYWORDS:
Dynamical System, Hyperbolic Setting, Reflection, Rotation, Digits, Logarithmic Constant
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.1,
January
19,
2022
ABSTRACT: We analyze a problem of interactions between elements of an ideal system which consists of two point masses and a wall in a hyperbolic setting. Thanks to a change of variables, the problem is reduced to a sequence of reflections on a hyperbola. For specific ratios of the two masses, the number of interactions is related to the first numerical digits of the logarithmic constant ln (2).