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2006 Obtuse Triangular Billiards I: Near the $(2,3,6)$ Triangle
Richard Evan Schwartz
Experiment. Math. 15(2): 161-182 (2006).

Abstract

Let $S_{\epsilon}$ denote the set of Euclidean triangles whose two small angles are within $\epsilon$ radians of $\frac{\pi}{6}$ and $\frac{\pi}{3}$ respectively. In this paper we prove two complementary theorems: (1) For any $\epsilon>0$ there exists a triangle in $S_{\epsilon}$ that has no periodic billiard path of combinatorial length less than $1/\epsilon$. (2) Every triangle in $S_{1/400}$ has a periodic billiard path.

Citation

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Richard Evan Schwartz. "Obtuse Triangular Billiards I: Near the $(2,3,6)$ Triangle." Experiment. Math. 15 (2) 161 - 182, 2006.

Information

Published: 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1112.37030
MathSciNet: MR2253003

Subjects:
Primary: 37E15

Keywords: Billiards , obtuse triangles , periodic trajectories

Rights: Copyright © 2006 A K Peters, Ltd.

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Vol.15 • No. 2 • 2006
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