arXiv subjects
Publications and source records attributed to Sergei Drozdov.
Given a Euclidean simplex of dimension $n\geqslant 2$ let its radii of inscribed and circumscribed spheres be $r$ and $R$, and the distance between the centers of the inscribed and circumscribed spheres be $d.$ Then, $(R-nr)(R+(n-2)r) \geqslant d^2.$
We study the iterations of the procedure of taking the contact simplex. We define the concept of the root of the simplex, which is a homothety image of contact simplex with a special coefficient greater than 1. The article shows that once we iterate the root of a given simplex, the circumcenter sequence of these simplices has two partial limits.