On the measure of axial symmetry with respect to folding for parallelograms

Abstract

Let C m be a subset of a planar convex body C cut off by a straight line m, which remains in C after folding it along m. The maximum masf(C) of the ratio of the double area of C m to the area of C over all straight lines m is a measure of axial symmetry of C. We prove that \({{{\rm masf}}(P) > \frac{1}{2}}\) for every parallelogram P and that this inequality cannot be improved.