An Improved Lower Bound for Moser's Worm Problem
Metric Geometry
2009-06-05 v2
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.
Cite
@article{arxiv.math/0701391,
title = {An Improved Lower Bound for Moser's Worm Problem},
author = {Tirasan Khandhawit and Sira Sriswasdi},
journal= {arXiv preprint arXiv:math/0701391},
year = {2009}
}
Comments
12 pages, 9 figures. v2: reorganized proof of the main theorem, added results and references