A geometrical approach to measure irrationality

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.

References in corpus (1)

• Irrationality Measures, Irrationality Bases, and a Theorem of Jarnik