Science Forums 2

[FrankM]

What I was hoping to do when posting the "Mathematically Perfect Triangle" was to elicit aid in defining the underlying mathematical relationships of the geometric structure that produced the symmetry. The process to produce the symmetry requires one element of the right triangle be "constrained" and I choose the vertical leg for the constrained element in my example, and it will always be equal to one.

The use of the linear and angular notation associated with transverse waveforms is "unconventional" but it results in geometric/mathematical relationships that have unusual scope. You can translate (rotate) the angle to 45 degrees and still get symmetry, but you have recognize what is and is not a variable, which is discussed in the Universal.pdf article.

I suggest that the process that produced the symmetry is another variant of the geometric/trigonometric forms, which are plane, spherical and hyperbolic geometry, and their associated plane, spherical and hyperbolic trigonometry.