The paper deals with a problem of finding natural geometry problem, that is, not specifically built up for the only purpose of having some concrete property, where the hypothesis is not described by a radical ideal. This problem was posed by Chou long ago. Regular polygons in the Euclidean space E~d and their existence in spaces of various dimensions are studied by the technique of Groebner bases. When proving that regular pentagons and heptagons span spaces of even dimension one encounters the case that the ideal describing the hypotheses is not radical. Thus, in order to prove that H → T one needs to show that T belongs to the radical of the ideal describing H.
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