955.51 At the heart of the vector equilibrium is the ball in the center of the rhombic dodecahedron. |
Fig. 955.52 |
955.52 Look at the picture which shows one-half of the rhombic dodecahedron. (See Illus. 955.52.) Of all the polyhedra, nothing falls so readily into a closest-packed group of its own kind as does the rhombic dodecahedron, the most common polyhedron found in nature. |
960.01 The Coordination of Number Powers and Geometrical Dimensions |
960.02 Powering means the multiplication of a number by itself. |
960.07 The time dimension is frequency. |
960.08 Any point can tune in any other point in Universe. All that is necessary is that they both employ the same frequency, the same resonance, the same system, center to center. |
960.11 Distance is time. Distance is only frequency-accountable. |
960.12 Newton's intermass attraction increases at the second power as the time- distance between is halved. Newton and Einstein deal only with mass and frequency to the second power. Their masses are relatively variable. In one, mass is acceleratingly expended; in the other, mass is acceleratingly collected. (See Sec. 1052.21.) |
961.00 Unitary Quantation of Tetrahedron |
961.01 The area of a triangle is arrived at by multiplying the length of the baseline by one-half of the triangle's apex altitude. |
961.02 The volume of a tetrahedron is the product of the area of the base and one- third of its altitude. |
961.03 A minimum garland of "granteds" combines only synergetically to disclose the following: |
961.10 Granted: A Slidable Model of Constant Volume: Granted any point A that is movable limitlessly anywhere within one of two planes parallel to one another at a given perpendicular distance X from one another, and, cogliding anywhere within the other parallel plane, two parallel lines lying at a given perpendicular distance Y from one another, and a point B that is slidable anywhere along one of the parallel lines, along the other line of which (two parallel lines) is a slidable pair of points, C and D, always slidable only at a constant and given distance Z from one another; it will be found that the vast variety of tetrahedra to be formed by interconnecting these four points (two independently variable and two only covariable) will always enclose the same volume. (See Sec. 923 and Illus. 923.10D.) |
961.41 Granted the volume of a tetrahedron is its base area times one-third of its altitude, we can now take the permitted, special condition discussed in Sec. 961.40 whereby C on line two is equidistant from both of line one's terminal-defining points A and B. We may next take a fourth point D, Lying in an infinitely extensible second plane which is parallel to the first infinitely extensible plane defined by points ABC. With D equidistant from A, B, and C, the volume of the regular tetrahedron ABCD will not be altered by letting D travel to any point in plane two while point C travels to any point on line two. Thus we learn that constant-volume tetrahedron ABCD might become so distended as to appear to be a line of no volume. Since there could be no volumeless line produced operationally, we may assume that all visible lines must be at minimum extended tetrahedra. |
961.42 These variabilities of the constant-volume tetrahedron and its constant-area faces will permit congruence of the four vertexes of the tetrahedron with any four points of Universe by simply taking the initial distance AB to suit the task. This unit linear adjustment is a familiar wavelength tuning function. Here we have the six cosmic degrees of freedom (see Sec. 537.10); whereby we are free to choose the length of only one line to be held constant, while allowing the other five edge-lines of the tetrahedron to take any size. We can connect any four points in Universe and produce a tetrahedron that is matchable with whole, unit, rational-number, volume increments of the A and B Quanta Modules. |
961.46 The A and B Quanta Modules become linear, as did the progression of concentric, common-base, uniform, linear, frequencied, electric-impulse conductors (see Sec. 923.21); and as also did the concentric, annually-frequencied, common-base-into- cone-rotated tetrahedra (see Sec. 541.30); the free energy put in at the base electronically, when you close the circuit at the beginning of the wire^{__}you get the same package out at the other end, the same quanta. The longer the wire gets^{__}or the tree grows^{__}as it approaches parallelism, the more the energy packages begin to precess and to branch out at right angles. |
962.00 Powering in the Synergetics Coordinate System |
962.02 In synergetics, powering means only the frequency modulation of the system; i.e., subdivision of the system. In synergetics, we have only two directions: radial and circumferential. |
962.03 In the XYZ system, three planes interact at 90 degrees (three dimensions). In synergetics, four planes interact at 60 degrees (four dimensions). |
962.05 Synergetic geometry discloses the rational fourth- and fifth-powering modelability of nature's coordinate transformings as referenced to the 60-degree equiangular isotropic-vector equilibrium. |
962.30 Calculation of Local Events: All local events of Universe may be calculatively anticipated in synergetics by inaugurating calculation with a local vector- equilibrium frame and identifying the disturbance initiating point, direction, and energy of relative asymmetric pulsing of the introduced resonance and intertransformative event. (Synergetics Corollary, see Sec. 240.39.) |
962.41 No time: No dimension. Time is dimension. |
Next Section: 963.00 |