Fuller made an original contribution to this field: the Dymaxion Map. This is part of his comprehensive consideration of Spaceship Earth.
Kline (1972, p.170) provides an introduction to projective geometry and to the standard gnomonic, stereographic, and perspective cylindrical projections. The latter method underlies Mercator's, Gall's and Peter's projections. Other projections include Mollweide's and the zenithal equidistant.
There are problems with projecting a spherical surface onto a plane. The zenithal projection preserves distances from the zenith at the expense of only being able to show half the world or less. Mercator's projection preserves shapes but distorts relative size. Peter's projection does the opposite. Gall's projection is a kind of compromise between the two. Hammer's projection preserves relative areas but the distortions at its edge are more extreme than with Gall's, and the latitude lines are not parallel.
There are also interrupted projections, like Mollweide's, which preserve parallel latitudes but forbid continuous planar depiction, as the term suggests. This means that sea and air routes cannot be clearly shown if land masses are left intact. The oblique Aitoff projection keeps areas equal and is uninterrupted, but land-masses at the map's edge seem unclear.
Fuller's projection is interrupted but provides for sectional rearrangement to emphasize differing geographical relationships. There is little distortion of shape or size, and it employs a geodesic grid reference. It also provides universal viewpoint: Earth's centre and the zenith are always perpendicularly below and above each point.
Fuller compares his map with traditional projections in Fluid Geography (pp.148-152).
See also Radio-Triangulation Mapping, Ecological Geometry, World Electric Power Grid, Geoscope, World Game, Mapping.
Association for Geographical Information
United States Geological Survey
THE FULLER MAP
© Paul Taylor 2001