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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.

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URL: http://www.jstor.org/stable/10.4169/amer.math.mont...
DOI (Digital Object Identifier) Link: https://doi.org/10.4169/amer.math.monthly.121.05.391
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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.

Item Type: Journal Item
Copyright Holders: 2014 Mathematical Association of America
ISSN: 1930-0972
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
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Item ID: 35905
Depositing User: Ian Short
Date Deposited: 13 Dec 2012 10:51
Last Modified: 17 Jun 2019 17:58
URI: http://oro.open.ac.uk/id/eprint/35905
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