Discrete & Computational Geometry

, Volume 7, Issue 2, pp 153–162

The Worm Problem of Leo Moser

  • Rick Norwood
  • George Poole
  • Michael Laidacker
Article

DOI: 10.1007/BF02187832

Cite this article as:
Norwood, R., Poole, G. & Laidacker, M. Discrete Comput Geom (1992) 7: 153. doi:10.1007/BF02187832

Abstract

One of Leo Moser's geometry problems is referred to as the Worm Problem [10]: “What is the (convex) region of smallest area which will accommodate (or cover) every planar arc of length 1?” For example, it is easy to show that the circular disk with diameter 1 will cover every planar arc of length 1. The area of the disk is approximately 0.78539. Here we show that a solution to the Worm Problem of Moser is a region with area less than 0.27524.

Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • Rick Norwood
    • 1
  • George Poole
    • 1
  • Michael Laidacker
    • 2
  1. 1.East Tennessee State UniversityJohnson CityUSA
  2. 2.Lamar UniversityBeaumontUSA