Covering n-Segment Unit Arcs Is Not Sufficient
- Cite this article as:
- Panraksa, C., Wetzel, J. & Wichiramala, W. Discrete Comput Geom (2007) 37: 297. doi:10.1007/s00454-006-1258-7
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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.