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Short, Ian and Walker, Mairi
(2014).
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.
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- Item ORO ID
- 44446
- Item Type
- Conference or Workshop Item
- Project Funding Details
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Funded Project Name Project ID Funding Body The Open University (OU) Not Set The Open University (OU) - Academic Unit or School
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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) - Related URLs
- Depositing User
- Ian Short