The Squaring of the Circle Using < a Ruler and a Compass > & the Bellow Motion Used by the Photons

This article is a continuation of 123=VECTORS , and concerns The simplified But Rigorous Proof of this Problem, The Squaring of the Circle using a Ruler and a Compass, as it was first Posed by the Ancient Greeks. The Photons Square their, Energy circle ≡ the Herpolhode-SPIN, to equal an Energy Unit Square, which Unit-Square they Promote, either as the Speed of the Photon which is their Electric Field, or they store it perpendicularly to the motion in an equal area, The Anti-Square which is their Magnetic Field. Promotion is done at the angle of 45ᶱ, and thus The Bellow-motion is their Torsional motion. 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 or Postulates , in order that Non 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 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.{ [ for 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 beyond Plank´s length level [Gravity`s Length 3,969.10 ̄ 62 m] , reaching the absolute Point = Lv = ei (N2π) b=10 ͞ N= - ∞ m = 0 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.[wr]³ → i.e. Energy Space quantity [wr] is Quantized , doubled , and becomes the Space quantity h/π following Euclidean Space-moulds of Duplication of the cube, in Sphere volume V = (4π/3).[wr]³ 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 Rotation 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 ????̅ to rotate , is used the Kepler`s Unit of Time k = ????²???? ????????, where a = λ / 2 , and which is the clock measuring the changes of motions.