Multiplication Only by Division: Three Ways of Progressive Halving from Primitive Unity or Tetrahedron
Buckminster Fuller (1895-1983) began experimenting with geodesics (defined as the arcs of great spheres) in the 1940s. This stimulated a shift in his interest towards the smooth and continuous tension of spherical surfaces as opposed to the rigid stress points created by right angles. Because they mirrored the form of the earth itself, spheres were a main component in Fuller’s argument that he was discovering the universal laws of nature occurring on “spaceship earth.” In analyzing spherical forms, Fuller extracted the tetrahedron — a pyramid with four sides — as the fundamental component from which one could abstract the structural behavior of all spheres. A series of regular and irregular tetrahedrons could be combined to constitute a near-spherical form, thereby distributing load through multiple points spaced throughout the structure. When he arrived at Black Mountain College in 1948, he collaborated with BMC sculpture student Kenneth Snelson in further developing what Fuller termed “tensegrity,” an engineering principle of discontinuous compression and continuous tension that extended his energetic geometry. Tensegrity was vital to Fuller’s later success in engineering geodesic domes.