Solution of the Knaster problem for polynomials of second degree on the two-dimensional sphere
The Knaster problem consists in the determination of configurations \(M\) of points on the sphere \(S^{n - 1} \subset \mathbb{R}^ n\), such that for any continuous function \(f\) on \(S^{n-1}\) there exists a rotation transforming \(M\) into a single level set of \(f\). In this short paper, a variant of the Knaster problem is discussed. It is shown that any four points on a circle \(S \subset S^ 2\) have the described property with respect to functions \(f\) which are polynomials of degree two.
scientific article; zbMATH DE number 567864
scientific article