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arXiv · 1511.09037

A geometrical approach to measure irrationality

Pedro Morales-Almazan
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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. 2015-12-02. A geometrical approach to measure irrationality. https://doi.org/10.7169/facm%2F1601

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