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Even-integer continued fractions and the Farey tree

Short, Ian and Walker, Mairi (2014). Even-integer continued fractions and the Farey tree. In: SIGMAP 2014, 7 Jul 2014-11 July 2014, West Malvern, UK.

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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
Project Funding Details:
Funded Project NameProject IDFunding Body
The Open University (OU)Not SetThe Open University (OU)
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)
Related URLs:
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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