986.240 The Sphere Experimentally Defined

986.241 The best physically demonstrable definition of the “spheric” experience is: an aggregate of energy events approximately equidistant, multidirectionally outwardly from approximately the same central event of an only approximately simultaneous set of external eventsthe more the quantity of external points measuringly identified and the more nearly simultaneous the radius-measuring events, the more satisfactorily “spherical.” With each of all the outward unit-radius events most economically and most fully triangularly interchorded with their most immediate neighborschords being shorter than their corresponding arcswe find that the “spheric” experience inherently describes only high-frequency, omnitriangularly faceted polyhedra. By geometrical definition these are geodesic structures whose volumes will always be something less than a theoretically perfect omni-arc-embraced sphere of the same radius as an omni-chord-embraced geodesic sphere’s uniformly radiused outer vertexes.

986.242 As is demonstrated in Sec. 224, the sum of the angles around all the vertexes of any system will always be 720 degrees less than the number of vertexes multiplied by 360 degrees. By the mathematicians’ definition a perfect arc-embraced sphere would have to have 360 degrees around every point on its surface, for the mathematicians assume that for an infinitesimal moment a sphere’s surface is congruent with the tangent plane. Trigonometry errs in that it assumes 360 degrees around every spherical surface point.