# Title: Optimal triangulation of polygons

## Speaker: Chris Bishop, Stony Brook University

## Date and time: 6pm (New York time), Tuesday, February 28, 2023

## Place: WWH1314 (room 1314 Warren Weaver Hall, 251 Mercer Street)

### ...and on Zoom, details on the seminar mailing list

It is a long-standing problem to triangulate a polygon using the best
possible shapes, e.g., to minimize the maximum angle used (MinMax), or
maximize the minimum angle (MaxMin). If we triangulate using only
diagonals of the polygon, then there are only finitely many possible
triangulations, and the Delaunay triangulation famously solves the
MaxMin problem. When extra vertices (Steiner points) are allowed, the
set of possible triangulations becomes infinite dimensional, but it
turns out that the optimal angle bounds for either the MinMax or
MaxMin problems in this case can be computed in linear time, and
that these bounds are (usually) attained by some finite triangulation
(which need not have a polynomial complexity bound). Several
surprising consequences follow from the proof, and many related
problems remain open.