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Vassiliev, V. A
The Bulletin of the London Mathematical Society, 04/2015, Letnik: 47, Številka: 2Journal Article
Abstract We prove that there are no bounded domains with smooth boundaries in even-dimensional Euclidean spaces, such that the volumes cut off from them by affine hyperplanes depend algebraically on these hyperplanes. For convex ovals in ${{{\mathbb R}}}^2$, this is Lemma XXVIII from Newton's 'Philosophiae naturalis principia mathematica'.
