The Mechanism of the 2-Vectors 3-Poles and the Quadrature of the Two Conjugate Circles of Photons

Abstract From 40–The Special Problems of Euclidean Geometry 47 consist the, Moulds of Quantization, of E-Geometry in it, to become → Monad, through mould of Space – Anti-space in itself, which is the material dipole in inner monad Structure and which is identical with the Electromagnetic cycloidal field → Linearly through the mould of the Parallel Theorem 44-45, which are the equal distances between Points of Parallel and line → In Plane, through mould of Squaring the circle 46, where the two equal and Perpendicular monad-Vectors consist a Plane acquiring the common Plane-meter, π, → and in Space (volume) through mould of the Duplication of the Cube 46, where any two Unequal Perpendicular monads acquire the common Space-meter ³√2, to be twice each other, as analytically all methods are Proved and explained. 44-47 The Unification of → Space and Energy ← becomes through STPL Geometrical Mould Mechanism of Elements, the minimum Energy-Quanta, In monads → Particles, Anti-Particles, Bosons, Gravity – Force, Gravity – Field, Photons, Dark Matter, and Dark Energy, consisting the Material Dipoles in inner monad Structures i. e. , the innate Electromagnetic Cycloidal Field of monads ← 39-41 Euclid’s elements consist of assuming a small set of intuitively appealing axioms, Proving many other Propositions. Because no one until 9 succeeded to prove the Parallel Postulate by means of pure Geometric Logic, many self consistent non - Euclidean geometries have been discovered, based on Definitions, Axioms Postulates, in order that none of them contradicts any of the other Postulates. It was Proved 39, that the only Space - Energy Geometry is Euclidean, agreeing with the Physical reality, on unit AB ≡ Segment ≡ Vector which is The Electromagnetic field of the Quantized on AB Energy Space Vector of Angular Momentum = Spin, on the contrary to the General relativity of Space-time which is based on the rays of the non-Euclidean Geometries to the limited velocity of light in Planck’s cavity. Euclidean Geometry elucidated the definitions of its geometry-content, i. e. Point, Segment, Straight Line, Plane, Volume, Space [S, Anti-space AS, Sub-space SS, Cave, The Space-Anti-Space Mechanism of the Six-Triple-Points-Line, that Produces and transfers Points of Spaces, Anti-Spaces and Sub-Spaces in a Common Inertial Sub-Space, and a cylinder, in Gravity field MFMF Particles and describes the Space-Energy vacuum by Planck’s length level Gravity’s Length 3, 969·10⁻⁶² m, reaching the absolute Point = Lᵥ = ε (iNτh) ᵝ = 10⁻ᴺ = ∞ m, which is nothing, and the Absolute Primary Neutral Space PNS = cave r = 10⁻³⁵ ~ 10⁻⁶² m [43-46. In Mechanics, The Gravity-cave Energy Volume quantity | c̅ | = wr is doubled, and is Quantized in Planck’s cave Space quantity (h/2π) = The Spin = 2. wr³ → i. e. Energy Space quantity wr is Quantized, doubled, and becomes the Space quantity h/π following Euclidean Space-mould of Duplication of the cube, in Sphere volume V = (4π/3). wr³ and follows the Squaring of the circle π, and in Sub-Space-Sphere volume ³√2, as Trisection. In article 123, are given on the 2-Vectors, 3-Poles Rotating Squares Mechanism, such the Geometrical as the Mechanical Proof, by using the Conjugate circles of Polhode and Herpolhode which consist the Spin of Photons and which is their motion. The frequency needed for the velocity vector c̅ to rotate, is used the Kepler’s Unit of Time k = f²e a³, where a = λ / 2, and which is the clock measuring the changes of motions.