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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Simple continued fractions and special relativity


Author: Douglas Hensley
Journal: Proc. Amer. Math. Soc. 67 (1977), 219-220
MSC: Primary 10A30
DOI: https://doi.org/10.1090/S0002-9939-1977-0460229-0
MathSciNet review: 0460229
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Abstract: Let $ {E_0},{E_1}, \ldots ,{E_n}$ be inertial frames of reference in a one dimensional relativistic universe where the speed of light is $ c = \sqrt k $, k some natural number. For $ n \geqslant 1$ let $ {E_n}$ have velocity 1 with respect to $ {E_{n - 1}}$. Let $ {x_n}$ denote the velocity of $ {E_n}$ with respect to $ {E_0}$. Then only if $ k = 2,3$ or 5 will $ {x_n}$ be a simple continued fraction convergent of $ \sqrt k $ infinitely often.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0460229-0
Keywords: Special relativity, simple continued fraction, velocity addition laws
Article copyright: © Copyright 1977 American Mathematical Society