Abstract
It is proved that every convex body in the plane has a point such that the union of the body and its image under reflection in the point is convex. If the body is not centrally symmetric, then it has, in fact, three affinely independent points with this property.
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Reference
R. Schneider, Convex bodies: the Brunn-Minkowski Theory, in Encyclopedia of Mathematics and Its Applications, vol. 151, 2nd edn. (Cambridge University Press, Cambridge, 2014)
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© 2016 Springer International Publishing Switzerland
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Schneider, R. (2016). Reflections of Planar Convex Bodies. In: Adiprasito, K., Bárány, I., Vilcu, C. (eds) Convexity and Discrete Geometry Including Graph Theory. Springer Proceedings in Mathematics & Statistics, vol 148. Springer, Cham. https://doi.org/10.1007/978-3-319-28186-5_6
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DOI: https://doi.org/10.1007/978-3-319-28186-5_6
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