Small Convex Covers for Convex Unit Arcs
Wacharin Wichiramala* Author for corresponding; e-mail address: wacharin.w@chula.ac.th
Volume: Vol.37 No.2 (MAY 2010)
Research Article
DOI:
Received: 1 June 2009, Revised: -, Accepted: 8 March 2010, Published: -
Citation: Wichiramala W., Small Convex Covers for Convex Unit Arcs , Chiang Mai Journal of Science, 2010; 37(2): 185-194.
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.