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Convex bodies with similar projections

Authors: R. J. Gardner and A. Volčič
Journal: Proc. Amer. Math. Soc. 121 (1994), 563-568
MSC: Primary 52A20
MathSciNet review: 1185262
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Abstract: By examining an example constructed by Petty and McKinney, we show that there are pairs of centered and coaxial bodies of revolution in $ {\mathbb{E}^d}, d \geq 3$, whose projections onto each two-dimensional subspace are similar, but which are not themselves even affinely equivalent.

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Keywords: Convex body, projection, section, direct homothety, similarity, affine equivalence
Article copyright: © Copyright 1994 American Mathematical Society