A Smaller Cover of the Moser’s Worm Problem
Nattapol Ploymaklam and Wacharin Wichiramala* Author for corresponding; e-mail address: wacharin.w@chula.ac.th; nattapol.p@cmu.ac.th
Volume: Vol.45 No.6 (September 2018)
Research Article
DOI:
Received: 3 Febuary 2015, Revised: -, Accepted: 2 July 2018, Published: -
Citation: Ploymaklam N. and Wichiramala W., A Smaller Cover of the Moser’s Worm Problem, Chiang Mai Journal of Science, 2018; 45(6): 2528-2533.
Abstract
The Moser’s worm problem asks for a smallest set on the plane that contains a congruent copy of every unit arc. Such smallest covering set has not been found yet. The smallest known cover constructed by Norwood and Poole in 2003 [6] has area 0.260437. In this work, we adapt their idea to construct a smaller cover of area 0.26007. We also simplify the proof that the set constructed this way contains a congruent copy of every unit arc.