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.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Nowicka, M. On the measure of axial symmetry with respect to folding for parallelograms. Beitr Algebra Geom 53, 97–103 (2012). https://doi.org/10.1007/s13366-011-0033-y
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DOI: https://doi.org/10.1007/s13366-011-0033-y