¶ Three-Way Great Circling: Three-Way Grid
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Index Entry
While great circles are the shortest distances around spheres, a single great circle band around a sphere will readily slide off. Because there are an infinity of great circles through any two points on a sphere 180° apart, two great-circle bands-- automatically self-polarizing-- on a sphere can also rotate equatorially and approach congruency thereafter to act as one meridian and therefore slide off. Not until we have three-great circle bands as in a spherical octahedron providing omnitriangulation, do we have the great circles acting structurally to interstabilize their respective positions by closing finitely to provide triangularly fixed points less than 180° apart. Between the latter the single great circles-- or shortest distances between two points not 180° apart-- are thereafter spontaneously sought by the ‘spherical barrel’ bandings.
