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.