251.01
The ability to identify all experience in terms of only angle and frequency.
251.02
The addition of angle and frequency to Euler’s inventory of crossings, areas, and lines as absolute characteristics of all pattern cognizance.
251.021
Synergetics adds four additional topological aspects to Euler’s three cosmically unique aspects of vertexes, faces, and edges. Synergetics adds (1) angles, (2) irrelevant untuned insideness and outsideness, (3) convexity and concavity, and (4) axis of spin, making a total of seven topological aspects (see Sec. 1044.00); synergetics has also recognized the addition of frequency as being always physically manifest in every special case.
251.03
The omnirational accommodation of both linear and angular acceleration in the same mathematical coordination system.
251.04
The discovery that the pattern of operative effectiveness of the gravitational constant will always be greater than that of the radiational constant — the excess effectiveness being exquisitely minute, but always operative, wherefore the disintegrative forces of Universe are effectively canceled out and embraced by the integrative forces.
251.05
The gravitational is comprehensively embracing and circumferentially contractive — ergo, advantaged over the centrally radiational by a 6:1 energy advantage; i.e., a circumference chord-to-radius vectorial advantage of contraction versus expansion, certified by the finite closure of the circumference, ergo, a cumulative series versus the independent, disassociating disintegration of the radii and their separating and dividing of energy effectiveness. (This is an inverse corollary of the age-old instinct to divide and conquer.) (See Secs. 529.03, 541.00 Radiation and Gravity and 1052.00.)
251.06
The gravitational-radiational constant 10F²+2.
251.07
The definition of gravity as a spherically circumferential force whose effectiveness has a constant advantage ratio of 12 to 1 over the radial inward mass- attraction.
251.10
The introduction of angular topology as the description of a structural system in terms of the sum of its surface angles.
251.11
The definition of structure as the pattern of self-stabilization of a complex of events with a minimum of six functions as three edges and three vertexes, speaking both vectorially and topologically.
251.12
The introduction of angular topology as comprised entirely of central-angle and surface-angle phenomena, with the surface angles accounting for concavity and convexity, and the thereby-derived maximum structural advantage of omni-self- triangulating systems.
251.13
As a result of the surface-angle concave-convex take-outs to provide self- closing finiteness of insideness and outsideness, central angles are generated, and they then function in respect to unique systems and differentiate between compoundings of systems.
251.14
One of the differences between atoms and chemical compounds is in the number of central-angle systems.
251.15
The tetrahedral trisecting of angles: the trisection of a 180-degree angle. (See Secs. 841.16 and 841.30.)
251.16
The rational volumetric quantation or constant proportionality of the octahedron, the cube, the rhombic triacontahedron, and the rhombic dodecahedron when referenced to the tetrahedron as volumetric unity. (See Sec. 1053.21.)
251.17
The rational and symmetric surface subdivision of the icosahedron, the octahedron, the cube, and the rhombic dodecahedron by the 48 spherical triangle tiles of the vector equilibrium’s 25-great-circle grid, rationally quantized in a reverse order of magnitude in whole, low-order, even numbers. (See Secs. 1053.20-21.)
251.18
The seven unique axes of great-circle spinnability that also describe the seven great circles foldable into bow ties. (See Sec. 1040.)
251.19
The definition of the omniequiangled and omnitriangulated tetrahedron, octahedron, and icosahedron, with respectively three, four, and five triangles around each of their vertexes, as altogether constituting the topological and finitely limited set of prime structural systems. (See Sec. 610.20.)
251.20
The discovery of the mathematically regular, three-way, greatcircle, spherical-coordinate cartographic grid of an infinite frequency series of progressive modular subdivisions, with the spherical radii that are perpendicular to the enclosing spherical field remaining vertical to the corresponding planar surface points of cartographic projection; and the commensurate identification of this same great-circle triangulation capability with the icosahedron and vector equilibrium, as well as with the octahedron and the tetrahedron. (See Secs. 527.24 and 1009.98.)
251.21
The development of the spherical triangular grid bases from the spherical tetrahedron, spherical cube, spherical octahedron, and the spherical vector equilibrium and its alternate, the icosahedron, and the discovery that there are no other prime spherical triangular grids. All other spherical grids are derivatives of these.
251.22
The spherical triangular grids are always identified uniquely only with the first four prime numbers 1, 2, 3 and 5: with the tetrahedron always identifying with the prime number l; the octahedron with 2, the face-triangulated cube with 3; and the vector equilibrium and icosahedron with the prime number 5; with the other Platonic, Archimedean, and other symmetrical polyhedra all being complex compoundings and developments of these first four prime numbers, with the numbers compounded disclosing the compounding of the original four base polyhedra.
251.23
The number of the external crossings of the three-way spherical grids always equals the prime number times the frequency of modular subdivision to the second power times two, plus the two extra crossings always assigned to the polar axis functioning to accommodate the independent spinnability of all systems.
251.24
The mathematical regularity identifies the second power of the linear dimensions of the system with the number of nonpolar crossings of the comprehensive three-way great circle gridding, in contradistinction to the previous mathematical identification of second powering exclusively with surface areas.
251.25
The synergetic discovery of the identification of the surface points of the system with second powering accommodates quantum mechanics’ discrete energy packaging of photons and elucidates Einstein’s equation, E =Mc², where the omnidirectional velocity of radiation to the second power — c² — identifies the rate of the rational order growth of the discrete energy quantation. This also explains synergetics’ discovery of the external point growth rate of systems. It also elucidates and identifies the second power factoring of Newton’s gravitational law. It also develops one-to-one congruence of all linear and angular accelerations, which are factorable rationally as the second power of wave frequency.
251.26
The definition of a system as the first subdivision of finite but nonunitary and nonsimultaneous conceptuality of the Universe into all the Universe outside the system, and all the Universe inside the system, with the remainder of the Universe constituting the system itself, which alone, for the conceptual moment, is conceptual.
251.27
The definition of Universe as a scenario of nonsimultaneous and only partially overlapping events, all the physical components of which are ever-transforming, and all the generalized metaphysical discoveries of which ever clarify more economically as eternally changeless.
251.28
The vector model for the magic numbers, which identifies the structural logic of the atomic isotopes in a symmetrical synergetic hierarchy.
251.29
The trigonometric identification of the great-circle trajectories of the seven axes of symmetry with the 120 basic disequilibrium LCD triangles of the spherical icosahedron. (See Sec. 1043.00.)
251.30
The rational identification of number with the hierarchy of all the geometries.
251.31
The A and B Quanta Modules.
251.32
The volumetric hierarchy of Platonic and other symmetrical geometricals based on the tetrahedron and the A and B Quanta Modules as unity of coordinate mensuration.
251.33
The identification of the nucleus with the vector equilibrium.
251.34
Omnirationality: the identification of triangling and tetrahedroning with second- and third-powering factors.
251.35
Omni-60-degree coordination versus 90-degree coordination.
251.36
The identification of waves with vectors as waviform vectors; the deliberately nonstraight line.
251.37
The comprehensive, closed-system foldability of the great circles and their identification with wave phenomena.
251.38
The accommodation of odd or even numbers in the shell-generating frequencies of the vector equilibrium.
251.39
The hierarchy of the symmetrically expanding and contracting pulsations of the interpolyhedral transformations, and their respective circumferentially and radially covarying states. (Also described as the symmetrical contraction, “jitterbugging,” and pumping models.)
251.40
The provision for the mathematical treatment of the domains of interferences as the domains of vertexes (crossings).
251.41
Mathematical proof of the four-color map theorem.
251.42
The introduction of the tensegrity structural system of discontinuous compression and continuous tension.
251.43
The identification of tensegrity with pneumatics and hydraulics.
251.44
The discovery of the number of primes factorial that form the positives and negatives of all the complex phenomena integratively generated by all possible permutations of all the 92 regenerative chemical elements.
251.45
The disclosure of he rational fourth-, fifth-, and sixth-powering modelability of nature’s coordinate transformings as referenced to the 60º equiangular, isotropic vector equilibrium.
251.46
The discovery that once a closed system is recognized as exclusively valid, the list of variables and the degrees of freedom are closed and limited to six positive and six negative alternatives of action for each local transformation event in Universe.
251.47
The discovery of the formula for the rational-whole-number expression of the tetrahedral volume of both the spherical and interstitial spaces of the first- and third- power concentric shell-growth rates of nuclear closest-packed vector equilibria.
251.48
The disclosure of a hierarchy of rational quantation and topological interrelationships of all physically experiential phenomena that are omnirationally accounted when we assume the volume of the tetrahedron and its six vectors to constitute both metaphysical and physical quantation unity. (See Secs. 221.01 and 620.12.)
251.50
The integration of geometry and philosophy in a single conceptual system providing a common language and accounting for both the physical and metaphysical.