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June 2017 A geometrical approach to measure irrationality
Pedro Morales-Almazan
Funct. Approx. Comment. Math. 56(2): 165-179 (June 2017). DOI: 10.7169/facm/1601

Abstract

We present a geometric way of describing the irrationality of a number using the area of a circular sector $A(r)$. We establish a connection between this and the continued fraction expansion of the number, and prove bounds for $A(r)$ as $r\to\infty$ by describing the asymptotic behavior of the ratios of the denominators of the convergents.

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Pedro Morales-Almazan. "A geometrical approach to measure irrationality." Funct. Approx. Comment. Math. 56 (2) 165 - 179, June 2017. https://doi.org/10.7169/facm/1601

Information

Published: June 2017
First available in Project Euclid: 27 January 2017

zbMATH: 06864152
MathSciNet: MR3660957
Digital Object Identifier: 10.7169/facm/1601

Subjects:
Primary: 11J82
Secondary: 11A55

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.56 • No. 2 • June 2017
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