The Worm Problem of Leo Moser
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
One of Leo Moser's geometry problems is referred to as the Worm Problem : “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.
- A. S. Besicovitch. On arcs that cannot be covered by an open equilateral triangle of side 1.Math. Gaz. 49 (1965), 286–288.
- G. G. Chakerian and M. S. Klamkin. Minimal covers for closed curves.Math. Mag. 46 (1973), 55–61.
- J. Gerriets. An improved solution to Moser's Worm Problem. Unpublished. 1972.
- J. Gerriets and G. Poole. Convex regions which cover arcs of constant length.MAA Monthly 81 (1974), 36–41.
- R. K. Guy.Problems in the Geometry of Metric and Linear Spaces. Lecture Notes in Mathematics, Vol 490. Springer-Verlag, Berlin. 1975.
- R. H. Hudson and T. L. Markham. Alfred Brauer.Linear Algebra Appl. 59 (1974), 1–17.
- P. Jones and J. Schaer. The worm problem. Research Paper No. 100. University of Calgary. 1970.
- P. Kelly and M. Weiss.Geometry and Convexity. Wiley, New York, 1979.
- M. Laidacker and G. Poole. On the existence of minimal covers for families of closed bounded convex sets. Unpublished. 1986.
- L. Moser. Poorly formulated unsolved problems of combinatorial geometry. Mimeographed list. 1966.
- W. Moser and J. Pach. 100 Research problems in discrete geometry. Mimeographed. McGill University, Montreal. 1986.
- G. Poole and J. Gerriets. Minimum covers for arcs of constant length.Bull. Amer. Math. Soc. 79 (1973), 462–463.
- J. Schaer. The broadest curve of length 1. Research Paper No. 52. University of Calgary. 1968.
- J. Schaer and J. Wetzel. Boxes for curves of constant length.Israel J. Math. 12 (1972), 256–265.
- J. Wetzel. Triangular covers for closed curves of constant length.Elem. Math. 25 (1970), 78–81.
- J. Wetzel. On Moser's problem of accommodating closed curves in triangles.Elem. Math. 27 (1972), 35–36.
- J. Wetzel. Sectorial covers for curves of constant length.Canad. Math. Bull. 16 (1973), 367–376.
- The Worm Problem of Leo Moser
Discrete & Computational Geometry
Volume 7, Issue 1 , pp 153-162
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Industry Sectors