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.
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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.