Rational Curvature of a Polytope - Algebraic Topology Lecture 15

Rational Curvature of a Polytope - Algebraic Topology Lecture 15

Explore a novel approach to defining the curvature of a polytope using rational numbers in this 50-minute lecture on Algebraic Topology. Learn about the concept of "turn-angle" or "tangle" and its application in calculating polygon curvature at vertices. Discover how this new definition relates to the Euler number and removes traditional pi-based formulas. Examine the importance of Harriot's theorem on spherical triangles and investigate opposite cones at vertices. Gain insights into this beginner-level course taught by Associate Professor N J Wildberger at UNSW, forming part of a comprehensive series on Algebraic Topology.