[AntonioLao]

If right triangles do not exist then Pythagorean Theorem is not provable. Without ideals, Fermat’s last theorem also is not provable. Since the domain of ideal numbers combined the real and the imaginary it spans the entire complex domain excluding of course real transcendental irrationals such as p and e. They provide algebraic solutions to infinite degrees polynomial equations.
In geometry, 180° are classified as a linear angle. It is the sum of the interior angles of an arbitrary triangle. A perpendicular bisector divides a line into two congruent angles, 90° each (actually, 4 angles making a full circular angle of 360°). Although it is trivial to bisect any arbitrary angle solely by geometric constructions, trisecting angles works exclusively for right triangles. Furthermore, pure geometric constructions can inscribe a regular pentagon within a unit circle simply by first constructing two 90° intersected diameters. Then bisect any of the four radii. Taking the line segment between the midpoint of the radius and the end of the diameter as a larger radius its arc intersect the first diameter at a point whose line segment joint to the end of the diameter gives the length for the side of a regular pentagon.
The power of orthogonal (90°) and linear (180°) symmetries allows the successful descriptions of elementary particle interactions using Feynman diagrams. However, Careful inspections reveal that no interaction angles are within the proximity of 90° and no straight line connects any vertices before and after each interaction. These necessarily invalidate the clockwise and counterclockwise space and time reflections and rotations while twisting all loops into concentric circles multiple of the unit radius. These are meaningless unless space-time quanta as squares of energy exist.