Short, Ian and Walker, Mairi
(2014).
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Abstract
Singerman introduced to the theory of maps on surfaces an object that is a universal cover for any map. This object is a tessellation of the hyperbolic plane together with a certain subset of the ideal boundary. The 1-skeleton of this tessellation comprises the edges of an infinite tree whose vertices belong to the ideal boundary. Here we show how this tree can be used to give a beautiful geometric representation of even-integer continued fractions. We use this representation to prove some of the fundamental theorems on even-integer continued fractions that are already known, and we also prove some new theorems with this technique, which have familiar counterparts in the theory of regular continued fractions.
| Item Type: | Conference or Workshop Item | ||||||
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| Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) Faculty of Arts and Social Sciences (FASS) > Politics, Philosophy, Economics, Development, Geography Faculty of Arts and Social Sciences (FASS) |
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| Item ID: | 44446 | ||||||
| Depositing User: | Ian Short | ||||||
| Date Deposited: | 28 Sep 2015 09:28 | ||||||
| Last Modified: | 07 Dec 2018 18:06 | ||||||
| URI: | http://oro.open.ac.uk/id/eprint/44446 | ||||||
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