# Optimal triangulation and related problems Long Chen, Penn State University

In this talk, we show the equivalence or duality of several problems in different fields, namely optimal piecewise linear approximation, optimal triangulation, optimal quantization, optimal polytope approximation to convex body, and sphere covering. In particular, we understand the Delaunay triangulation as the optimal piecewise linear interpolation to function $\|\mathbf x\|^2$ for a given points set. We also get some new results for the optimal polytope approximation problem and present a new approach to attack the sphere covering problem.

Anna L Mazzucato