2022/04/06 by Robert J. Vanderbei, Vanderbei, Robert
Earth and Planetary Sciences · Social Sciences · Engineering · #Geophysics and Gravity Measurements #Historical Geography and Cartography #Inertial Sensor and Navigation
paper · pdf · doi:10.48550/arxiv.2204.02798
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.