Geodesic continued fractions

Beardon, A. F.; Hockman, M. and Short, I. (2012). Geodesic continued fractions. Michigan Mathematical Journal, 61(1) pp. 133–150.

DOI: https://doi.org/10.1307/mmj/1331222851

Abstract

There are infinitely many ways to express a rational number as a finite continued fraction with numerators 1 and integer denominators. We study the shortest continued fraction expansions for a given rational by interpreting these as geodesic paths in the Farey graph.

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