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Article
Drawing a Triangle on the Thurston Model of Hyperbolic Space
Mathematics Magazine
  • Curtis D. Bennett, Loyola Marymount University
  • Blake Mellor, Loyola Marymount University
  • Patrick D. Shanahan, Loyola Marymount University
Document Type
Article
Publication Date
4-1-2010
Disciplines
Abstract
In looking at a common physical model of the hyperbolic plane, the authors encountered surprising difficulties in drawing a large triangle. Understanding these difficulties leads to an intriguing exploration of the geometry of the Thurston model of the hyperbolic plane. In this exploration we encounter topics ranging from combinatorics and Pick’s Theorem to differential geometry and the Gauss-Bonnet Theorem.
Citation / Publisher Attribution

Permission has been granted by the Mathematical Association of America to supply this article for educational and research purposes. More info can be found about the Mathematics Magazine at http://www.maa.org/press/periodicals/mathematics-magazine.

Publisher Statement

© 2010 Mathematical Association of America. All Rights Reserved.

Citation Information
Curtis D. Bennett, Blake Mellor, and Patrick D. Shanahan. "Drawing a Triangle on the Thurston Model of Hyperbolic Space." Mathematics Magazine 83, no. 2 (2010): 83-99. doi:10.4169/002557010x482853.