Abstract
We combine geometric methods with a numerical box search algorithm to show that the minimal area of a convex set in the plane which can cover every closed plane curve of unit length is at least [Formula: see text]. This improves the best previous lower bound of [Formula: see text]. In fact, we show that the minimal area of the convex hull of circle, equilateral triangle, and rectangle of perimeter [Formula: see text] is between [Formula: see text] and [Formula: see text].
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