Premium
Newton's lemma XXVIII on integrable ovals in higher dimensions and reflection groups
Author(s) -
Vassiliev V. A.
Publication year - 2015
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdv002
Subject(s) - hyperplane , lemma (botany) , mathematics , bounded function , affine transformation , integrable system , regular polygon , euclidean geometry , reflection (computer programming) , pure mathematics , combinatorics , mathematical analysis , geometry , ecology , poaceae , computer science , biology , programming language
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 inR 2 , this is Lemma XXVIII from Newton's ‘Philosophiae naturalis principia mathematica’.