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Synergetics is Fuller's name for the geometry he advanced based on the patterns of energy that he saw in nature.

For him, geometry was a laboratory science with the touch and feel of physical models--not rules out of a textbook. He started with models of the closest packing of spheres. From that basic starting point he derived triangles as the most economical relationship between events.

He did not start with Euclid's lines in the sand or Descartes' cubes and square XYZ-coordinates. Fuller felt that the old classic approaches did not describe the way nature actually behaves. For instance, Euclid's lines were thought to go off to infinity. Fuller says lines are vectors of energy and he rejected the notion that anything physical could be extended indefinitely.

Descartes cubes are unstable forms. For Fuller, the world is built of stable, finite structures. His triangular coordination depends on tetrahedral models. (A tetrahedron is a pyramid with a triangular base.) Four spheres close pack into a stable tetrahedron: good. Eight spheres stack into an unstable cube: bad. His geometry hinges on the tetrahedron, the simplest structural system within insideness and outsideness: he advances it as the most economical way to measure space and to account all physical (and metaphysical!) experience.

This is what he calls synergetics: an empirical mathematical system in which
geometry and number mesh without fractions. It gains its validity not from
classic abstractions but from the results of individual physical experience.
His two-volume work "Synergetics" has the subtitle: Explorations in the Geometry
of Thinking.

E.J. Applewhite collaborated on the books Synergetics I and II with Buckminster Fuller. He recommends Kirby Urner's Synergetics on the Web for an excellent graphic introduction to Fuller's synergetic geometry, plus links to other sites describing synergetics--many with gorgeous color graphics.