  If a smooth, closed, and embedded curve is deformed along its normal vector
field at a rate proportional to its curvature, it shrinks to a circular point.
This curve evolution is called Euclidean curve shortening and the result is
known as the Gage-Hamilton-Grayson Theorem. Motivated by the rendezvous problem
for mobile autonomous robots, we address the problem of creating a polygon
shortening flow. A linear scheme is proposed that exhibits several analogues to
Euclidean curve shortening: The polygon shrinks to an elliptical point, convex
polygons remain convex, and the perimeter of the polygon is monotonically
decreasing.
