The ensuing description to serve as a possible path to a mathematical proof.
For scaling to any size, a ratio of side a to b (a:b) is employed. Side b is maintained constant between the limits 1:4 and 4:1 for any base right triangle. Therefore, the radius of the cylinder with b as its axis is constant.
Point D1 is defined as the apex of the evolved oblique triangular pyramid as per the prior conjecture: PYTHAGOREAN THEOREM GENERALIZATION as CONSEQUENCE of THREE-DIMENSIONS
As point D1 exists in the locus of points of the two intersecting perpendicular cylinders whose axes are sides a and b, then all D1’s must exist on the surface of the constant cylinder with the axis of side b.
A plot of ALL D1’s on the cylinder surface yields a three-dimensional space curve. If the 3D curve is unwrapped from the cylinder into a plane, a two-dimensional function may exist, possibly sinusoidal in shape.
Thus, conceptually – a curve, of yet to be determined function, is cylindrically mapped to reveal a locus of points where all D1’s exist.
