WITH A RULER AND A COMPASS AS THE RESTRICTIVE BASE - BECAME A REALITY: THE SOLUTION OF THE ANCIENT UNSOLVED GREEK PROBLEMS

2026-06-01T15:22:41+00:00

a... The Unsolvability of the Three famous Ancient Greek Problems—Doubling the Cube, Trisecting the Angle, and Squaring the Circle -- Stands on the Base justification of the Algebraic Field Theory (specifically GaloisTheory) and the Theory of Constructible Numbers, which were developed in the 19th century.

b... The Greeks often used other Techniques (like Conic sections orMechanical tools) to Solve these Problems, But their self-imposed "Euclidean" constraint, with a Ruler and a Compass ,(straightedge and compass) made these Specific Problems impossible to solve.

c... In the Published Articles [123],[124],[126] , it is clearly evident that the Solution of the Ancient , Unsolved Greek Problems, using a Ruler and a Compass , as the constraint has been set by Euclid], Has Become Possible, and is in the Critique of Both , Human Logic Thinking and , The Artificial Intelligence when it uses The Path of Knowledge to the Truths of Nature, and which is the Dialectic Logic of Euclidean Geometry.

d... From the Published Articles [123] , [124] , [126] , All Steps Follow the Restrictions set by Euclid which are < By A Ruler and a Compass >

In the New Article [125] the Proof is repeated , Both of the Squaring of the circle and the Doubling of the Cube using only a Ruler and a Compass , as well as the Bellow-motion of the Photon with The Photon`s Cloning Method.

GPH-International Journal of Mathematics

WITH A RULER AND A COMPASS AS THE RESTRICTIVE BASE - BECAME A REALITY: THE SOLUTION OF THE ANCIENT UNSOLVED GREEK PROBLEMS