An Improved Lower Bound for Moser's Worm Problem

Details An Improved Lower Bound for Moser's Worm Problem An Improved Lower Bound for Moser's Worm Problem

2007-01-14

arxiv.org/abs/math/0701391v2

Mathematics

Metric Geometry

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

Scientific paper

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.

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