You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:


Log in to your personal account or through your institution.

A Geometric Representation of Continued Fractions

Alan F. Beardon and Ian Short
The American Mathematical Monthly
Vol. 121, No. 5 (May 2014), pp. 391-402
DOI: 10.4169/amer.math.monthly.121.05.391
Stable URL:
Page Count: 12
Topics: Fractions, Integers
  • Download ($19.00)
  • Cite this Item
A Geometric Representation of Continued Fractions
Preview not available


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 Möbius transformations on hyperbolic space, and prove a classical theorem on continued fractions.

Page Thumbnails