  Angular equivalence is introduced and shown to be an equivalence relation
among the norms on a fixed real vector space. It is a finer notion than the
usual (topological) notion of norm equivalence. Angularly equivalent norms
share certain geometric properties: A norm that is angularly equivalent to a
uniformly convex norm is itself uniformly convex. The same is true for strict
convexity. Extreme points of the unit balls of angularly equivalent norms occur
on the same rays, and if one unit ball is a polyhedron so is the other.
  Among norms arising from inner products, two norms are angularly equivalent
if and only if they are topological equivalent. But, unlike topological
equivalence, angular equivalence is able to distinguish between different norms
on a finite-dimensional space. In particular, no two $\ell^p$ norms on $\mathbb
R^n$ are angularly equivalent.
