Original Paper

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

, Volume 53, Issue 1, pp 97-103

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


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.


Convex body Folding Measure of axial symmetry Parallelogram

Mathematics Subject Classification (2000)

52A10 52A38