The Open UniversitySkip to content

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.

Full text available as:
PDF (Version of Record) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (351kB) | Preview
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


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)
Related URLs:
Item ID: 35905
Depositing User: Ian Short
Date Deposited: 13 Dec 2012 10:51
Last Modified: 17 Sep 2019 05:07
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU