986.520 Einstein's Equation |
986.523 In the Einstein equation the velocity^{__}lower-case c^{__}of all radiation taken to the second power is omnidirectional-ergo, its quasispheric surface-growth rate is at the second power of its radial-linear-arithmetic growth rate^{__}ergo, c^{2}. (Compare Secs. 1052.21 and 1052.30.) Thus Einstein's equation reads E = Mc^{2}, where E is the basic one quantum or one photon energy component of Universe. |
986.540 Volume-surface Ratios of E Quanta Module and Other Modules |
986.543 The 0.000517 radius difference between the 0.999483-radiused rhombic triacontahedron of exactly tetravolume 5 and its exquisitely minute greater radius-1.0000 (alpha) prime vector, is the exquisite difference between a local-in-Universe energy-containing module and that same energy being released to become energy radiant. Each of the 120 right-angle-cornered T Quanta Modules embraced by the tetravolume-5 rhombic triacontahedron is volumetrically identical to the A and B Quanta Modules, of which the A Modules hold their energy and the B Modules release their energy (Sec. 920). Each quanta module volume is 0.04166^{__}i.e., 1/24 of one regular primitive tetrahedron, the latter we recall being the minimum symmetric structural system of Universe. To avoid decimal fractions that are not conceptually simple, we multiply all the primitive hierarchy of symmetric, concentric, polyhedral volumes by 24^{__}after which we can discuss and consider energetic-synergetic geometry in always-whole-rational-integer terms. |
986.544 We have not forgotten that radius I is only half of the prime-unit vector of the isotropic vector matrix, which equals unity 2 (Sec. 986.160). Nor have we forgotten that every square is two triangles (Sec. 420.08); nor that the second-powering of integers is most economically readable as "triangling"; nor that nature always employs the most economical alternatives^{__}but we know that it is momentarily too distracting to bring in these adjustments of the Einstein formula at this point. |
986.550
Table: Relative Surface Areas Embracing the Hierarchy
of Energetic
Quanta Modules: Volumes are unit. All Module Volumes
are 1, except the radiant E
Module, whose Surface Area is experimentally evidenced
Unity:
ENERGY PACKAGE / SURFACE AREA
1 Unit vector of isotropic vector matrix
Mass = F = Relative frequency of primitive-system-subdivision energy-event occupation.
(Footnote 6: The VE surface displays the number of closest-packed spheres of the outer layer. That surface = f^{2}; ergo, the number of energy-package spheres in outer layer shell = surface, there being no continuum or solids.) |
986.560 Surprise Nestability of Minimod T into Maximod T |
Fig. 986.561 |
986.561 The 6 + 10 + 15 = 31 great circles of icosahedral symmetries (Fig. 901.03) produce the spherical-surface right triangle AC''B; CAB is subdivisible into four spherical right triangles CDA, CDE, DFE, and EFB. Since there are 120 CAB triangles, there are 480 subdivision-right-surface triangles. Among these subdivision-right triangles there are two back-to-back 90-degree surface angles at D^{__}CDA and CDE^{__}and two back-to-back degree surface angles at F^{__}CFE and EFB. The surface chord DE of the central angle DOE is identical in magnitude to the surface chord EB of the central angle EOB, both being 13.28 degrees of circular azimuth. Surface chord FB of central angle FOB and surface chord AD of central angle AOD are identical in magnitude, both being 10.8 degrees azimuth. In the same manner we find that surface chord EF of central angle EOF constitutes the mutual edge of the two surface right triangles CFE and BFE, the central- angle magnitude of EOF being 7.77 degrees azimuth. Likewise, the central angles COA and COF of the surface chords CA and CF are of the same magnitude, 20.9 degrees. All the above data suggest a surprising possibility: that the small corner triangle AC"B itself can be folded on its three internal chord lines CD, CE, and EF, while joining its two edges AC and CF, which are of equal magnitude, having central angles of 20.9 degrees. This folding and joining of F to A and of B to D cancels out the congruent-letter identities F and D to produce the tetrahedron ABEC. (See Fig. 986.561.) |
986.570 Range of Modular Orientations |
986.580 Consideration 15: Surface Constancy and Mass Discrepancy |
986.584 The volume of the T Quanta Module is identical with the volumes of the A and B Quanta Modules, which latter we have been able to identify with the quarks because of their clustering in the cosmically minimum, allspace-filling three-module Mites as A +, A -, and B, with both A's holding their energy charges and B discharging its energy in exact correspondence with the quark grouping and energy-holding-and-releasing properties, with the A Modules' energy-holding capabilities being based on their foldability from only one triangle, within which triangle the reflection patterning guarantees the energy conserving. (See Secs. 921 and 986.414) |
Next Section: 986.600 |