Solving some Moser's worm Problems Using Numerical Minimization

Abstract

One of the most difficult things to study Moser’s worm problem is how to prove whether or not the considered set is a cover. With the aid of numerical minimization, the lower bound of the un-coverable unit arc can be found. Clearly, if the lower bound is longer than 1 unit, then we have already proved that it’s a cover. In this research, an equilateral triangle, an isosceles right angled triangle, and a 30°- 60°- 90° triangle are tested. The method works quite better on covers with geometric symmetries.