A Geometrical Proof of a Theorem of Hurwitz

Author:

Ford Lester R.

Abstract

In the study of rational approximations to irrational numbers the following problem presents itself: Let ω be a real irrational number, and let us consider the rational fractions satisfying the inequalityhow small can the positive quantity k be chosen with the certainty that there will always be an infinite number of fractions satisfying the inequality whatever the value (irrational) of ω?

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 16 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Singular matrices and geometry at infinity of products of symmetric spaces;Journal of the Mathematical Society of Japan;2023-04-21

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3. Continued Fractions and Congruence Subgroup Geodesics;Number Theory with an Emphasis on the Markoff Spectrum;2017-10-05

4. Second basic theorem of Hurwitz*;Lithuanian Mathematical Journal;2016-01

5. Even-Integer Continued Fractions and the Farey Tree;Symmetries in Graphs, Maps, and Polytopes;2016

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