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Everything I Know, Section 8
gist
R. Buckminster Fuller starts geometry from Universe and the sphere, then rebuilds trigonometric functions from that whole instead of a Greek plane. Longhand decimal work spills only leftward and breaks the palindromic symmetry he can still feel. Tensegrity, catalyzed by Ken Snelson's tetrahedron, is Universe's own structural design: discontinuous compression islands held in continuous tension, which geodesic calculation then has to size with industrial accuracy.
ideas
- Geometry starts from the whole. Begin with Universe and a sphere, then subdivide. Plane geometry never quite proves the equilateral triangle.
- Trigonometry sizes chords, not arcs. Once radius is unity, sine, cosine, and chord factors tell you the length of every geodesic member.
- Decimal spill hides symmetry. Carrying only to the left breaks palindromes that whole-number longhand still lets you remember.
- Tensegrity is Universe's structure. Compression is islanded and discontinuous; tension is continuous. Snelson's tetrahedron opened the geometric connection.
quotes
“our geometry begins with a sphere, or at least with a system”
“there was a spilling only to the left”
“the Universe is actually designed with islanded compression”
“this is a tetrahedron made by Ken Snelson.”