A lower bound on opaque sets

摘要

It is proved that the total length of any set of countably many rectifiable curves whose union meets all straight lines that intersect the unit square U is at least 2.00002. This is the first improvement on the lower bound of 2 known since 1964. A similar bound is proved for all convex sets U other than a triangle. (C) 2019 Published by Elsevier B.V.