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A geometrical approach to measure irrationality

Research paper by Pedro Morales-Almazan

Indexed on: 02 Dec '15Published on: 02 Dec '15Published in: Mathematics - Number Theory



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.