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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
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.

References [Enhancements On Off] (What's this?)

  • [1] I. Niven and H. S. Zuckerman, An introduction to the theory of numbers, 2nd ed., Wiley, New York, 1966, Theorems 7.19 and 7.22. MR 0195783 (33:3981)

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Keywords: Special relativity, simple continued fraction, velocity addition laws
Article copyright: © Copyright 1977 American Mathematical Society

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