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A Structural Approach to Understanding Nuclear and Sub-Nuclear Particles and the Electromagnetic Wave Spectrum ©WRHohenberger 1992-2014 By William R Hohenberger World Science Database February 22, 2014 Internet Video Presentation

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Table of Contents Part 1 – The Electromagnetic Wave Part 2 – The Octahedral Hexagonal Fractal Part 3 – Electron Cube Vs Octahedral Hexagonal Fractal Part 4 – Fractal Mass Scaling Ratios Part 5 – Charge Scaling Ratios Part 6 –Future Research ©WRHohenberger 1992-2014

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1.There is an aether that pervades all of the spaces within the universe including both the material and the nonmaterial worlds. Therefore, aether is a real substance!!! 2.Aether is a hyper-dynamic, non-homogeneous, elastic substance that contians a myriad of plethora's of various field structures, as holistic arrays of constantly changing motions and structures. I describe them as Field Vector Arrays. 3.Aether has a fine structure within which the smallest electromagnetic wave or highest frequency that can be manifested is directly related to or is a derivative of Planck's Length. I use the name ‘energy cell’ or ‘Aetheron’. 4.The electromagnetic wave is a rotating oscillating system within the aether with up to three generations of concentric waves. Of prime importance is the two generational dual concentric wave. 5.Assuming that aether is an elastic continuum, then whatever occurs in the inner (light) wave, the opposite must occur in the outer (dark) wave. This is a mechanical Universe. 6.Particles are fractal structures condensed from individual energy cells (aetherons) that are built from scalar multiples of the smallest electromagnetic wave at Planck's Frequency. Therefore, particles are condensed aether(ons). Some Basic Rules & Assumptions ©WRHohenberger 1992-2014

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Part 1 The Electromagnetic Wave ©WRHohenberger 1992-2014

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Static Energy (potential energy – zero velocity)Dynamic Energy (kinetic energy) PendulumLeft Side Height of PendulumForward Velocity – No Static Energy Right Side Height of PendulumReverse Velocity – No Static Energy Water WavePositive Height of water Forward Circular Motion of Water Negative Height of water Backwards Circular Motion of Water Clock Timing SpringTension of spring – No velocityForward Velocity of Rotational Mass (rotary oscillating system)Compression of spring – No velocityReverse Velocity of Rotational Mass (Electrostatic Energy – Charge)(Electromagnetic Energy - Motion) Electromagnetic WaveTension of Aether – No aethereal velocityForward Rotation of Aethereal Mass (rotary oscillating system) Compression of Aether – No aethereal velocityReverse Rotation of Aethereal Mass Various Oscillating Systems ©WRHohenberger 1992-2014

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1 st Generation EM Wave – (The Inner Light Wave) LIGHT WAVE ©WRHohenberger 1992-2014

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DARK WAVE 2 nd Generation EM Wave – (The Outer Dark Wave) ©WRHohenberger 1992-2014

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Combined Concentric Light & Dark 2 nd Generation EM Wave ©WRHohenberger 1992-2014

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360° Graph of an Electromagnetic Wave ©WRHohenberger 1992-2013 ©WRHohenberger 1992-2014

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360° Graph of an Electromagnetic Wave ©WRHohenberger 1992-2014

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Eq. 7.2 S = 0.5 (E x H) Eq. 7.3S = 0.5 ⋅ [(sinφ ⋅ E) ⋅ (sinφ ⋅ H) + (cosφ ⋅ H) ⋅ (cosφ ⋅ E)] Lockyer’s Summary A vector structure for the photon has been deduced that explains all of the questions raised by the paradox of electric E and magnetic H field strengths showing a paradoxical in- phase (sine/sine) that would not result in a lossless transport of the photon’s stored energy. The traveling wave of electromagnetic energy was shown to be the symbiosis of two conjugate resonances, and the paradoxes were explained logically by using a trigo- nometric identity (sin 2 φ + cos 2 φ =1). Chapter 7 - ENERGY (PHOTON) STRUCTURE Equation 7.2 gives the classic sinusoidal Poynting vector S effective power density value at a single peak value, but does not show the correct nature of the photon, over all cycle time. The correct sinusoidal mathematics that describes the above graphics is given in the trigonometric identity, Equation 7.3; Equation 7.3 gives the same effective value, as Equation 7.2, for the S Poynting vector, but uses the correct photon conjugate vector structure. From Tom Lockyer’s VPP, Pages 65 & 68

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In Figure 7.1, the traveling wave appears, to our relativistic distorted view, to be in phase (100 percent power factor) on account of the time coincidence, between the E and H peak values. This (100 percent power factor) is not reality, because the vacuum is reactive, making the Poynting vectors E and H time coincidence inconsistent with the required (sine/cosine) reactive relationship. Also, in violation of nature, the energy seems to disappear, as E and H go to zero twice each cycle in the traveling wave. This energy disappearance is not natural, the photon energy is known to be continuous, not discontinuous as it appears, when viewed from our stationary frame of reference. Refer to Figure 7.1, the traveling wave paradox, of lost energy twice each cycle, as E and H identically pass through zero, is explained by using two conjugate resonances. The photon is a symbiosis of (two) E to H and H to E resonances combined into the axial (S) vector. This symbiosis not only gives the lateral (sine/sine) power factor but also gives the axial (cosine/cosine) loss-less resonances from each conjugate, separately, effectively storing the energy resonantly. Lateral events are not distorted by relativistic effects, so we do see the lateral E, H as they appear in both the stationary view and the relativistic view of the Poynting vector, as (sine/sine). The Lorentz-Fitzgerald contraction makes (S) appear to be zero briefly, from our stationary frame of view. Thus relativity modifies the classical equation for photon power density given in (Equation 7.2) into that shown in (Equation 7.3.) From Tom Lockyer’s VPP, Pages 65 & 66 Lockyer’s Explanation of Sine/Sine Paradox

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360° Graph of an Electromagnetic Wave ©WRHohenberger 1992-2014

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Quark Ball with a Baryon Octet Spin Vectors Method for Developing the DBQ Dodecahedron Quark Ball Dodecahedron Quark Ball Baryon Octet ©WRHohenberger 1992-2014

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Baryon Octet & Decuplet Families Meson Family Baryon Decuplet Baryon Octet DBQ Dodecahedron Quark Ball Particle Correlations ©WRHohenberger 1992-2014

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Poynting Vector Relationship to Dual Concentric Waves From Tom Lockyer’s VPP, Page 71

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From Tom Lockyer’s VPP, Page 70 Vector Development

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From Tom Lockyer’s VPP Vector Analysis ©WRHohenberger 1992-2014

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VPP Electron Cube Compared to DBQ Dodecahedron Quark Ball ©WRHohenberger 1992-2014

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Transposition Graphs ©WRHohenberger 1992-2014

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Transposition Graphs ©WRHohenberger 1992-2014

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Electromagnetic Photon Stores Energy Resonantly The photon resonant structure conserves and transports energy over vast distances, in the vacuum of space, with no apparent losses. (Rather than tired light, the red shift is thought to be a Doppler effect from an expanding universe.) The energy is alternately stored in the inductance (L = μ o λ ) and the capacitance is (C = ε o λ ) of the vacuum. For any frequency (f) the wavelength is (λ = c / f ) and the corresponding space inductance is (L = μ o λ ) and capacitance (C = ε o λ) and their combinations are analogous to the familiar (LC) electrical resonant circuit. From Tom Lockyer’s VPP, Page 67 Lockyer’s Explanation of Photon Resonant Light Energy

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Transposition Graphs ©WRHohenberger 1992-2014

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Neutrinos, Electrons, Positrons & Virtual Positrons Octahedron Contains an inner Octahedron Fractal at its center Electron/Neutrino Virtual Positron ©WRHohenberger 1992-2014

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Virtual Electron-Positron Lattice ©WRHohenberger 1992-2014

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Part 2 The Octahedral Hexagonal Fractal ©WRHohenberger 1992-2014

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N S = π / NS = sin π / N r 1 / r 2 r 1 / r r 2 / r 12.26179939.2588190451.86370331.349198186.650801814 11.28559933.2817325571.55946553.392239074.607760926 10.31415927.3090169941.23606799.447213595.552786405 9.34906585.342020143.923804400.519803365.480196635 8.39269908.382683432.613125930.619914404.380085596 7.44879895.433883739.304764871.766421615.233578385 6.52359878.500000000 0 1 0 Chart of Various Twist-Loop Fractals ©WRHohenberger 1992-2014

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o r2r1 r2r1 r R1R1 R2R2 R O 2r 2Θ R First, Second, & Third Generations of an 11 Twist-Loop Fractal ©WRHohenberger 1992-2014

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First & Second Generation 7 Twist-Loop Fractal ©WRHohenberger 1992-2014

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First and Second Generation 9.5 Twist-Loop Fractal ©WRHohenberger 1992-2014

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First, Second, & Third Generation Hexagonal Fractal ©WRHohenberger 1992-2014

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The Hexagonal Fractal ©WRHohenberger 1992-2014

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The Octahedral Hexagonal Fractal and the Dodecahedron Quark Ball ©WRHohenberger 1992-2014

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Sierpinksi’s Pyramid & The Octahedral Hexagonal Fractal ©WRHohenberger 1992-2014

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Constructing an Octahedron ©WRHohenberger 1992-2014

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Part 3 (VPP) Electron Cube Vs (OHF) Octagonal Hexagonal Fractal ©WRHohenberger 1992-2014

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R.707R = R c.5R = R m Volume Cube = R 3 Volume Cylinder (Rotating Cube) = (.707R) 2 x R = R 3 /2 = ( /2) R 3 Cube Vs Octahedron ©WRHohenberger 1992-2014

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Lockyer’s Calculated Results for Electron Charge From Tom Lockyer’s VPP, Pages 72 & 76

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Vol. (Rotating Octahedron) = ( /2) R 3 /6 1/6 #.166 1/# 6.0 √1/# 2.4449 SA (Rotating Octahedron) (√2/2)R 2 #.7071 Vol. (Rotating Octahedron) = (√2/3)( /2) R 3 √2/3.4714 2.1213 1.4565 SA (Rotating Octahedron) = √2 R 2 1.4142 Vol. (Rotating Octahedron) = (4/3)( /2) R 3 4/3 1.3333.7500.8660 SA (Rotating Octahedron). = 2√2 R 2 2.8284 Comparing Octahedrons Surface Area = 6R 2 Volume Cube = R 3 Surface Area 2 Ends Rotating Cube = R 2 Volume Rotating Cube = ( /2) R 3 Surface Area Sides Rotating Cube = 2√2 R 2 ©WRHohenberger 1992-2014

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Vol. (Rotating Octahedron) = (1/6)(/2)R 3 #.1666.0061728395062 1/# 6.0000162 √1/# 2.449412.72792206135 Surface Area (Rotating Octahedron) = (√2/2)R 2 #.7071.0758674201318 Deriving the Octahedron Correction Scaling Factor 1/√[1/(1/6)R v 3 ] = (√2/2)R v 2 1/√[6/R v 3 ] = (√2/2) R v 2 1 = √[6/R v 3 ] (√2/2) R v 2 1 = [6/R v 3 ] (1/2) R v 4 1 = (6/2) R v R v = 1/3 R v =.33333333333333R Volume Cube = R 3 Volume Rotating Cube = (/2) R 3 Surface Area = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sides Rotating Cube = 2√2 R 2 ©WRHohenberger 1992-2014

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Calculating Octahedron Electron Charge Js = 5.97441869080294 x 10 -16 Vol 2 = [. 006172839506173 ]Vol. Vol 2 =.055834706642392 x 10 -38 Pe = 641.5671442167432 x 10 -30 E = 49.16276958706 x 10 16 D = 43.529639552774 x 10 5 SA = L2 [. 0785674201318 ] SA =.368065646670 x 10 -25 e = 1.60217648697431 x 10 -19 ©WRHohenberger 1992-2014

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Volume Sphere = 4/3 ( Radius) 3 = (4/3)(R/2) 3 = (4/3)(1/8)R 3 = (1/3)(/2)R 3 # 0.3333.0123456790123 1/# 3.000081 √1/# 1.73219 Surface Area Sphere = 4 ( Radius) 2 = 4(R/2) 2 = R 2 # 1.0000.11111111111111 Deriving the Sphere Correction Scaling Factor 1/√[1/(1/3) R v 3 ] = R v 2 1/√[3/R v 3 ] = R v 2 1 = √[3/R v 3 ] R v 2 1 = [3/R v 3 ] R v 4 1 = 3R v R = 1/3 R v = 0.33333333333R Volume Cube = R 3 Volume Rotating Cube = (/2) R 3 Surface Area = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sides Rotating Cube = 2√2 R 2 ©WRHohenberger 1992-2014.5R R c =.707R R R m =.5R

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Volume Rotating VPP Cube (Cylinder) [( √2/2)R] 2 R = ( /2) R 3 # 1.00001.00000000 1/# 1.00001.00000000 √1/# 1.00001.00000000 Surface Area 2 Ends of Cylinder = (2) R 2 = 2 [( √2/2)R] 2 = R 2 # 1.00001.000000000 Deriving the VPP Cube Correction Scaling Factor 1/√[1/ R v 3 ] = R v 2 1 = √[1/ R v 3 ] R v 2 1 = [1/ R v 3 ] R v 4 1 = R v R v = R Volume Cube = R 3 Volume Rotating Cube = ( /2) R 3 Surface Area = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sides Rotating Cube = 2√2 R 2 ©WRHohenberger 1992-2014

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Type R Scaling Factor Compton Frequency Rot. VPP Cube 1.000000000000 1.0 Blue Rot. Octahedron 0.333333333333 3.0 Sphere 0.333333333333 3.0 Comparative Data for Various Polyhedrons ©WRHohenberger 1992-2014.5R.5R.5 R R c =. 707 R R R m =.5R

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Sphere Volume = (4/3) (Radius) 3 = (4/3) (R/2) 3 = (4/3) (1/8)R 3 = (1/3)(/2)R 3 Surface Area = 4 (Radius) 2 = 4 (1/4)R 2 = R 2 Rotating Octahedron (2 Cones) Volume = /3 (Radius) 2 (Height) = /3 (R/2) 2 R = /3 (1/4)R 2 R = (1/6)(/2)R 3 Surface Area = 2[ (Radius) (Side)] = 2 x (1/2)R x ( √2/2) R = ( √2/2) R 2 VPP Rotating Cube Volume = (Radius) 2 (Height) = (√2/2) 2 R 2 R = (1/2)R 2 R = (/2)R 3 Surface Area (2 Ends) = 2[ (Radius) 2 ] = 2[ x ( √2 /2) 2 R 2 ] = R 2 Comparative Data for Various Polyhedrons ©WRHohenberger 1992-2014.5 R R c =.70 7R R R m =.5 R

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Volume Sphere = 4/3(Radius) 3 = (4/3)(R/2) 3 = (4/3)(1/8)R 3 = [(3)](1/3)(/2)R 3 # 1.00001.0000 1/# 1.00001.0000 √1/# 1.00001.0000 Surface Area Sphere = 4 ( Radius) 2 = 4(R/2) 2 = R 2 # 1.00001.0000 Deriving the Triple Charged Sphere Correction Scaling Factor 1/√[1/R v 3 ] = R v 2 1 = √[1/R v 3 ] R v 2 1 = [1/R v 3 ] R v 4 1 = R v R v = R Volume Cube = R 3 Volume Rotating Cube = (/2) R 3 Surface Area = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sides Rotating Cube = 2√2 R 2 ©WRHohenberger 1992-2014

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Volume (Rotating Octahedron) = [(3)](1/6)(/2)R 3 #0.50000.50000 1/# 2.00002.00000 √1/# 1.41421.414213562373 Surface Area (Rotating Octahedron) = (√2/2)R 2 #.7071.7071067811865 Deriving the Triple Charged Octahedron Correction Scaling Factor 1/√[1/(1/2) R v 3 ] = (√2/2) R v 2 1/√[2/R v 3 ] = (√2/2) R v 2 1 = √[2/R v 3 ] (√2/2) R v 2 1 = [2/R v 3 ] (1/2) R v 4 1 = R v R v = R Volume Cube = R 3 Volume Rotating Cube = (/2) R 3 Surface Area = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sides Rotating Cube = 2√2 R 2 ©WRHohenberger 1992-2014

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Volume Rotating VPP Cube (Cylinder) [(3)][( √2/2)R] 2 R = [(3)]( /2) R 3 # 3.0000.111111111111 1/# 3.00009 √1/# 3.00003 Surface Area 6 Rotating Ends of Cylinder = (6) R 2 = 6 [( √2/2)R] 2 = 3 R 2 # 3.0000.333333333 Deriving the Triple Charged VPP Cube Correction Scaling Factor 1/√[1/3 R v 3 ] = 3 R v 2 1 = √[1/3 R v 3 ] 3 R v 2 1 = [1/3 R v 3 ] 9 R v 4 1/3 = R v R v = R/3 Volume Cube = R 3 Volume Rotating Cube = ( /2) R 3 Surface Area = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sides Rotating Cube = 2√2 R 2 ©WRHohenberger 1992-2014

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Calculating Octahedron Electron Charge Js = 5.97441869080294 x 10 -16 Vol Ratio TOcta = [.5000000000000 ]Vol. Vol TOcta = 4.522611238033755 x 10 -38 Pe = 7.9205820273672 x 10 -30 E = 5.46252995411794 x 10 16 D = 4.836626616974897 x 10 5 SA = L2 [.7071067811865 ] SA = 3.31259080730198x 10 -25 e = 1.60217648697431 x 10 -19 ©WRHohenberger 1992-2014

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1 st Generation Electron DBQ Octahedron Mass Structure with Briddell’s Field Structure Lines of Force ©WRHohenberger 1992-2014

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Part 4 Fractal Mass Scaling Ratios ©WRHohenberger 1992-2014

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Top or Frontal View of an Octahedral Electron ©WRHohenberger 1992-2014 North South WestEast

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Counting Edge Energy Cells for an Octahedral Electron ©WRHohenberger 1992-2014 4.941361E+15

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Counting Face Energy Cells for an Octahedral Electron ©WRHohenberger 1992-2014 4.941361E+15

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Counting Quadrant Energy Cells for an Ocatahedron Electron ©WRHohenberger 1992-2014 4.941361E+15

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Deriving Octahedral Scaling Ratios ©WRHohenberger 1992-2014 4.941361E+15

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Periodic Table for the Hexagonal Fractal (Scaling Ratio =.5 or 2 ) ©WRHohenberger 1992-2014

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Deriving the Icosahedral Scaling Ratios ©WRHohenberger 1992-2014

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Comparing Various Proton & Neutron to Triangular & Cubic Energy Cell Electron Mass Scaling Ratios Quarks = Vectors = Field Structures Red / Blue / Green = X, Y, Z Coordinates Gluons = Captured Energy Cells = Aetherons = Quark Balls = Mass Quantum Foam = Particle Structures = Polyhedra, Tori, Spheres ©WRHohenberger 1992-2014

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Fundamental Three Dimensional Shapes Platonic Solids Archimedian Solids Sphere Torus Catalan Solids Catalan Solids

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Triangular (3) Energy Cells versus Square (4) Energy Cells ©WRHohenberger 1992-2014

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Lockyer’s VPP and the Electromagnetic Wave ©WRHohenberger 1992-2014

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Particle Spins ½ Spin 3/2 Spin ©WRHohenberger 1992-2014

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Calculating the Rotating Octahedral Scaling Constant ©WRHohenberger 1992-2014 X Y Z

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Calculating the Rotating Octahedral Scaling Constant ©WRHohenberger 1992-2014

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Electromagnetic Wave Saturation Point ©WRHohenberger 1992-2014

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Part 5 Charge Scaling Ratios ©WRHohenberger 1992-2014

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Comparing Sphere & Torus Correction Scaling Factors 4 2 r t 2 R t = (/6)R 3 R t = R 3 /24r t 2 4 2 r t R t = R 2 R t = R 2 /4r t R 3 /24r t 2 = R 2 /4r t R = 6r t r t = (1/6)R R t = R 2 /4r t R t = R 2 /4(R/6) R t = ( 3 / 2 )R Volume Cube = R 3 where R/2 = R s = R ro = R t Volume Rotating Cube = (/2) R 3 Volume Sphere = 4 / 3 R s 3 = (/6)R 3 = ( 1 / 3 )(/2)R 3 Volume Rotating Octahedron = (2 /3)R ro 3 = ( 1 / 6 )( /2)R 3 Volume Torus = 4 2 r t 2 R t = ( r t 2 R t /R s 3 )(/2)R 3 Surface Area Cube = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sphere = 4R s 2 or R 2 Surface Area Rotating Octahedron = 2√2R ro 2 = (√2/2)R 2 Surface Area Torus = 4 2 r t R t = (r t R t /R s 2 )R 2 4 2 r t 2 R t =( 4 / 3 )R s 3 R t = R s 3 /3r t 2 4 2 r t R t = 4R s 2 R t = R s 2 /r t R s 3 /3r t 2 = R s 2 /r t R s = 3r t Let R s = ( 1 / 2 )R R t = ( 3 / 2 )R r t = ( 1 / 6 )R ©WRHohenberger 1992-2014

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Volume (Torus) = [(3)]4 2 r t 2 R t = (12 2 r t 2 R t )R 3 /(2R s ) 3 24r t 2 R t /8R s 3 (/2)R 3 = 3r t 2 R t /R s 3 (/2)R 3 # 1.01.0 1/# 1.01.0 √1/# 1.0 1.0 Surface Area (Torus) = 4 2 r t R t = 4(r t R t /4R s 2 )R 2 = (r t R t /R s 2 ) R 2 # 1.01.0 Deriving the Sphere Triple Charged Torus Correction Scaling Factor 1/√(3r t 2 R t /R s 3 )= (r t R t /R s 2 ) 1= √(3r t 2 R t /R s 3 )((r t R t /R s 2 )) 1 = (3r t 2 R t /R s 3 )( 2 r t 2 R t 2 /R s 4 ) 1 = (3 3 r t 4 R t 3 )/R s 7 r t = 4 √(R s 7 /(3 3 R t 3 )) Let R s = R/2 & R t = 3R/(2) r t = 4 √(1/128/(3(27/8)) = 4 √1/1296 =1/6 R t + r t = 3/(2) +1/6 = (9+)/6 R t + r t =.64413149R Volume Cube = R 3 Volume Rotating Cube = (/2) R 3 Surface Area = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sides Rotating Cube = 2√2 R 2 ©WRHohenberger 1992-2014

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Plotting the Sphere Triple Charged Torus Correction Scaling Factor ©WRHohenberger 1992-2014

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Deriving the Sphere Triple Charged Spindle Torus Proton ©WRHohenberger 1992-2014 Spindle Torus N = 5.165

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Comparing Octahedron & Torus Correction Scaling Factors 4 2 r t 2 R t = ( /12)R 3 R t = R 3 /48 r t 2 4 2 r t R t = (√2 /2)R 2 R t = √2 R 2 /8 r t R 3 /48 r t 2 = √2 R 2 /8 r t R 3 / √2 R 2 = 48 r t 2 /8 r t R/ √2 = 6r t r t = R/6 √2 R t = R 3 /48 ( R/6 √2 ) 2 R t = 3R/2 Let R ro = ( 1 / 2 )R R t = ( 3 / 2 )R r t = ( 1 / 6 √2 )R Volume Cube = R 3 where R/2 = R s = R ro = R t Volume Rotating Cube = (/2) R 3 Volume Sphere = 4 / 3 R s 3 = ( /6)R 3 = ( 1 / 3 )( /2)R 3 Volume Rotating Octahedron = (2 /3)R ro 3 = ( 1 / 6 )( /2)R 3 Volume Torus = 4 2 r t 2 R t = ( r t 2 R t /R s 3 )( /2)R 3 Surface Area Cube = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sphere = 4R s 2 or R 2 Surface Area Rotating Octahedron = 2√2R ro 2 = (√2/2)R 2 Surface Area Torus = 4 2 r t R t = (r t R t /R s 2 )R 2 4 2 r t 2 R t = (2 /3)R ro 3 R t = R ro 3 /6 r t 2 4 2 r t R t = 2 √2 R ro 2 R t = √2 R ro 2 /2 r t R ro 3 /6 r t 2 = √2 R ro 2 /2 r t R ro 3 / √2 R ro 2 = 6 r t 2 /2 r t R ro / √2 = 3r t r t = R ro /3 √2 R t = R ro 3 /6 ( R o /3 √2 ) 2 R t = 3R ro / Let R ro = ( 1 / 2 )R R t = ( 3 / 2 )R r t = ( 1 / 6 √2 )R ©WRHohenberger 1992-2014

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Volume (Torus) = [(3)]4 2 r t 2 R t = (12 2 (r t 2 /4R ro 2 )(R t /R ro )R 3 24r t 2 R t /4R ro 3 (/2)R 3 =6r t 2 R t /R ro 3 (/2)R 3 # 1.01.0 1/# 1.01.0 √1/# 1.0 1.0 Surface Area (Torus) = 4 2 r t R t = 4(r t /2R ro )(R t / √ 2R ro )R 2 = √ 2(r t R t /R ro 2 ) R 2 # 1.01.0 Deriving the Octahedron Triple Charged Torus Correction Scaling Factor 1/√(6r t 2 R t /R ro 3 )= √ 2(r t R t /R ro 2 ) 1= √(6r t 2 R t /R ro 3 )( √ 2(r t R t /R ro 2 )) 1 = (6r t 2 R t /R ro 3 )(2 2 r t 2 R t 2 /R ro 4 ) 1 = (12 3 r t 4 R t 3 )/R ro 7 r t = 4 √(R ro 7 /(12 3 R t 3 )) Let R ro = R/2 & R t = 3R/(2) r t = 4 √(1/128/(12(27/8)) = 4 √1/(1296)(4) =1/6 √2 R t + r t = 3/(2) +1/6 √2 R t + r t =.595315959473R Volume Cube = R 3 Volume Rotating Cube = (/2) R 3 Surface Area = 6R 2 Surface Area 2 Ends Rotating Cube = R 2 Surface Area Sides Rotating Cube = 2√2 R 2 ©WRHohenberger 1992-2014

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Plotting the Octahedron Triple Charged Torus Correction Scaling Factor ©WRHohenberger 1992-2014

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Deriving the Octahedron Triple Charged Spindle Torus Proton Spindle Torus N = 5.165 ©WRHohenberger 1992-2014

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The Triple Charged Spindle Torus Proton Ratios ©WRHohenberger 1992-2014

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Part 6 Future Research ©WRHohenberger 1992-2014

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Intenral Proton Structure ©WRHohenberger 1992-2014

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The Triple Charged Torus Neutron, Nucleon & Atomic Structure ©WRHohenberger 1992-2014

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Fine Structure Constant Is there a Non-Uniformity to the Structure due to Angular Momentum? ©WRHohenberger 1992-2014

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Pion & Delta to Electron Mass Ratios - Octahedron Chart ©WRHohenberger 1992-2014 2187.183 + 243.018 – 18.001 = 2412.2

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rtrt RtRt Triple Charged Torus Fractal Structures Ring Torus N = 6+ Horn Torus N = 6 Spindle Torus N = 5 Spindle Torus N= 4 Spindle Torus N = 3 ©WRHohenberger 1992-2014

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Triple Charged Torus Fractal Structure Equations ©WRHohenberger 1992-2014

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Color Electrodynamics & Energy Cells ©WRHohenberger 1992-2014

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Energy Cells, Aetherons & Gluons Color Singlet States Eight Gluon Colors ©WRHohenberger 1992-2014

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Minimum Resolution of the Aether ©WRHohenberger 1992-2014

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The Polygon & Variable Pi ©WRHohenberger 1992-2014

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Overview of the Electromagnetic Wave Spectrum ©WRHohenberger 1992-2014

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Overview of the Electromagnetic Wave Spectrum ©WRHohenberger 1992-2014

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Michelson-Morley Experiment Gravity – Solar & Planetary Vortexes ©WRHohenberger 1992-2014 Does the Michelson-Morley Experiment prove that there is no aether, or that the aether is in orbit around the Earth and the Sun? Aether Drag Does the Earth drag the Aether, or does the Aether cause the Earth to Rotate

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Infinity versus a Finite Universe ©WRHohenberger 1992-2014

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