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.

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

• Funded Project Name	Project ID	Funding Body
  The Open University (OU)	Not Set	The Open University (OU)

• Academic Unit or 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)
• Related URLs
• • http://mcs.open.ac.uk/SIGMAP/(Other)
• Depositing User
• Ian Short