A geometric representation of continued fractions

Beardon, Alan F. and Short, Ian (2014). A geometric representation of continued fractions. American Mathematical Monthly, 121(5) pp. 391–402.

DOI: https://doi.org/10.4169/amer.math.monthly.121.05.391

URL: http://www.jstor.org/stable/10.4169/amer.math.mont...

Abstract

Inspired by work of Ford, we describe a geometric representation of real and complex continued fractions by chains of horocycles and horospheres in hyperbolic space. We explore this representation using the isometric action of the group of Moebius transformations on hyperbolic space, and prove a classical theorem on continued fractions.

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