Discrete & Computational Geometry

, Volume 29, Issue 3, pp 409–417

An Improved Upper Bound for Leo Moser's Worm Problem

  •  Norwood
  •  Poole

DOI: 10.1007/s00454-002-0774-3

Cite this article as:
Norwood & Poole Discrete Comput Geom (2003) 29: 409. doi:10.1007/s00454-002-0774-3

Abstract. A wormω is a continuous rectifiable arc of unit length in the Cartesian plane. Let W denote the class of all worms. A planar region C is called a cover for W if it contains a copy of every worm in W . That is, C will cover or contain any member ω of W after an appropriate translation and/ or rotation of ω is completed (no reflections). The open problem of determining a cover C of smallest area is attributed to Leo Moser [7], [8]. This paper reduces the smallest known upper bound for this area from 0.275237 [10] to 0.260437.

Copyright information

© 2003 Springer-Verlag New York Inc.

Authors and Affiliations

  •  Norwood
    • 1
  •  Poole
    • 1
  1. 1.Department of Mathematics, East Tennessee State University, Johnson City, TN 37614, USA norwoodr@etsu.edu,pooleg@etsu.eduUS