Great Circles
The shortest distance between two points on a sphere follows a great circle — a circle whose plane passes through the sphere's center, dividing it into two equal hemispheres. Three-way triangulated intersections of great circles generate the grids that give geodesic structures their strength.
Fuller's Definition
Fuller defines a geodesic as "the most economical relationship between any two events" and identifies spherical great circles as geodesics (§702.01). Every great circle intercepts any other great circle twice, the interception points always 180-degree polar opposites (§703.13). A single great-circle band slides off a sphere; two can rotate to congruency and slip off together. Only with three noncommonly polarized great-circle bands do we get omnitriangulation that self-interstabilizes their spherical positioning (§706.20). The more minutely a sphere is subtriangulated by great circles, the greater the mutual-interpositioning integrity (§706.22).
Significance in Synergetics
Fuller calls the 25 great circles of the vector equilibrium the "only omni-intersystem-connecting 'railroad tracks' of energy in the Universe" — the Cosmic Railroad Tracks through which energy entities travel between closest-packed spheres (§1132.01, §1132.12). The 31 great circles of the icosahedron act as local-holding shunt patterns, while the VE great circles open switching to omniuniverse energy travel (§1132.02). Together, 25 + 31 great-circle sets (73 unique after subtracting 14 congruencies) generate all the fundamental geodesic grids. Three-way great-circle crossing produces the omnitriangulated compound curvature that gives the greatest strength with the least material (§706.10).
See Also
- Geodesic Structures — the built application of great-circle triangulation
- Vector Equilibrium — source of the 25 great circles of fundamental symmetry
- Isotropic Vector Matrix — the all-space array through which great-circle tracks run
- Jitterbug Transformation — the VE-icosa pumping that generates the composite great-circle sets
- Tensegrity — the structural principle great-circle grids embody
- Synergetics — Fuller's geometric system