Journal of Combinatorics

Volume 2 (2011)

Number 3

Escape paths of Besicovitch triangles

Pages: 413 – 433

DOI: http://dx.doi.org/10.4310/JOC.2011.v2.n3.a4

Authors

Yevgenya Movshovich (Department of Mathematics and Computer Science, Eastern Illinois University, Charleston, Ill., U.S.A.)

John E. Wetzel (Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Ill., U.S.A.)

Abstract

The shortest arcs that do not fit in the interior of a compact, convexbody in the plane have been called its $escape paths$. We summarizesome basic general facts about such paths. Specializing to triangles,we study the escape paths of the so-called Besicovitch triangles,near-equilateral isosceles triangles recently shown by Coulton andMovshovich to be covers for the family of all arcs of unit length,and we show that each such triangle has exactly one escape path.

Keywords

worm problem, escape path, Besicovitch triangle

2010 Mathematics Subject Classification

Primary 52C15. Secondary 05Bxx.

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