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Small Convex Covers for Convex Unit Arcs


Paper Type 
Contributed Paper
Title 
Small Convex Covers for Convex Unit Arcs
Author 
Wacharin Wichiramala
Email 
wacharin.w@chula.ac.th
Abstract:
More than 40 years ago, Leo Moser stated a geometry problem on the plane asking for the least-area set that contains a congruent copy of every unit arc. The smallest set known, by Norwood and Poole in 2004, has area 0.26043. One interesting related problem is to focus on a set that contains a congruent copy of every convex unit arc. Such a set is called a cover for convex unit arcs. The smallest cover known, by Wichiramala in 2005, has area 0.2464. In this work we establish a smaller cover for convex unit arcs of area less than 0.242.
Start & End Page 
185 - 194
Received Date 
2009-06-01
Revised Date 
Accepted Date 
2010-03-08
Full Text 
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Keyword 
covering by convex sets, convex unit arc, worm problem
Volume 
Vol.37 No.2 (MAY 2010)
DOI 
Citation 
Wichiramala W., Small Convex Covers for Convex Unit Arcs , Chiang Mai J. Sci., 2010; 37(2): 185-194.
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