Simple continued fractions and special relativity
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- by Douglas Hensley PDF
- Proc. Amer. Math. Soc. 67 (1977), 219-220 Request permission
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
- Ivan Niven and Herbert S. Zuckerman, An introduction to the theory of numbers, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0195783
Additional Information
- © Copyright 1977 American Mathematical Society
- 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