Drawing a Triangle on the Thurston Model of Hyperbolic Space

Curtis D. Bennett; Blake Mellor; Patrick D. Shanahan

Drawing a Triangle on the Thurston Model of Hyperbolic Space

Curtis D. Bennett, Blake Mellor, Patrick D. Shanahan

Loyola Marymount University

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Pages (from-to)	83-99
Journal	Mathematics Magazine
Volume	83
Issue number	2
State	Published - Apr 2010

Keywords

Triangles
Vertices
Geometric angles
Mathematical theorems
Mathematical modeling
Geometric planes
Structural deflection
Line segments
Geometry

Disciplines

Algebraic Geometry

Cite this

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title = "Drawing a Triangle on the Thurston Model of Hyperbolic Space",

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{\textquoteright}s Theorem to differential geometry and the Gauss-Bonnet Theorem.",

keywords = "Triangles, Vertices, Geometric angles, Mathematical theorems, Mathematical modeling, Geometric planes, Structural deflection, Line segments, Geometry",

author = "Bennett, {Curtis D.} and Blake Mellor and Shanahan, {Patrick D.}",

note = "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.",

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AB - 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.

KW - Triangles

KW - Vertices

KW - Geometric angles

KW - Mathematical theorems

KW - Mathematical modeling

KW - Geometric planes

KW - Structural deflection

KW - Line segments

KW - Geometry

UR - https://digitalcommons.lmu.edu/math_fac/83

M3 - Article

SN - 1930-0980

VL - 83

SP - 83

EP - 99

JO - Mathematics Magazine

JF - Mathematics Magazine

IS - 2

ER -

Drawing a Triangle on the Thurston Model of Hyperbolic Space

Abstract

Keywords

Disciplines

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