An Improved Lower Bound for Moser's Worm Problem

Abstract

We show that any convex region which contains a unit segment, an equilateral triangle of sides 1/2, and a square of side 1/3 always has area at least 0.227498. Using grid-search algorithm, we attempt to find a configuration of these three objects with minimal convex hull area. Consequently, we improve a lower bound for Moser's worm problem from 0.2194 to 0.227498.

12 pages, 9 figures. v2: reorganized proof of the main theorem, added results and references