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