Discrete & Computational Geometry

, Volume 37, Issue 2, pp 297–299

Covering n-Segment Unit Arcs Is Not Sufficient

Article

DOI: 10.1007/s00454-006-1258-7

Cite this article as:
Panraksa, C., Wetzel, J. & Wichiramala, W. Discrete Comput Geom (2007) 37: 297. doi:10.1007/s00454-006-1258-7

Abstract

In 1974 Gerriets and Poole conjectured for n = 3 that a convex set in the plane which contains a congruent copy of every n-segment polygonal arc of unit length must be a cover for the family of all unit arcs. We disprove this general conjecture by describing for each positive integer n a convex region Rn that contains a ongruent copy of every n-segment unit arc but not a congruent copy of every unit arc.

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Faculty of Science, Chulalongkorn UniversityBangkok 10330Thailand
  2. 2.Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green StreetUrbana, IL 61801USA
  3. 3.Department of Mathematics, Faculty of Science, Chulalongkorn UniversityBangkok 10330Thailand

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