2016/10/19 by Luis Montejano, Montejano, Luis, Javier Bracho +1
Mathematics · Computer Science · #Mathematics and Applications #Point processes and geometric inequalities #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1610.06232
A polytope P is circumscribed about a convex body Φ⊂ ℝn if Φ⊂ P and each facet of P is contained in a support hyperplane of Φ. We say that a convex body Φ⊂ ℝn is a rotor of a polytope P if for each rotation ρ of ℝn there exist a translation τ so that P is circumscribed about τρΦ. In this paper we shall prove that if P is a triangle, then there is a baricentric formula that describes the curvature of bdΦ at the contact points, \A1, A2,A3\. We prove also that if Φ⊂ ℝ3 is a convex body which is a rotor in a tetrahedron T and if Φ intersects the faces of T at the points \x1, …, x4\, then the normal lines of Φ at the contact points with T, \x1, …, x4\ generically belong to one ruling of a quadric surface.