The Worm Problem of Leo Moser
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.
Norwood, Rick; Poole, George; and Laidacker, Michael. 1992. The Worm Problem of Leo Moser. Discrete andamp; Computational Geometry. Vol.7(1). 153-162. https://doi.org/10.1007/BF02187832 ISSN: 0179-5376