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

Open AccessOriginal Paper

DOI: 10.1007/s13366-011-0033-y

Cite this article as:
Nowicka, M. Beitr Algebra Geom (2012) 53: 97. doi:10.1007/s13366-011-0033-y
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Abstract

Let Cm 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 Cm 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.

Keywords

Convex bodyFoldingMeasure of axial symmetryParallelogram

Mathematics Subject Classification (2000)

52A1052A38
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© The Author(s) 2011

Authors and Affiliations

  1. 1.University of TechnologyBydgoszczPoland