  In this paper we describe a mathematically interesting but relatively minor
improvement to the Gott-Goldberg-Vanderbei (GGV) map projection. This new
projection can be described as what one would get by making a spherical rubber
ball representation of the Earth and then stretching the ball circularly around
the equator until the Northern and Southern hemispheres flatten to a disk. It
is interesting that this new projection is very similar to but not exactly the
same as the GGV projection. And, the mathematics required to solve this
flattening problem is a very nice example of using the calculus of variations
to solve an infinite dimensional optimization problem.
