"Generalized solid angle theory for real polytopes"

David DeSario
Georgetown College

Monday, March 24, 2008
4:00 pm, 112 Patterson Office Tower

Abstract:

The natural generalization of a two-dimensional angle to higher dimensions is called a solid angle. We extend many theorems from the theory of solid angles of polyhedra, which hold true for rational polytopes, to results for real polytopes that involve more general solid angles. A rational polytope is a polytope whose vertices all have rational coordinates, whereas a real polytope has vertices with arbitrary real coordinates.