On May 1, 7:02 pm, 1treePetrifiedForestLane <Space...@hotmail.com> wrote: > hint: three of the dihedrals are "right" (or left). > > > > > > > > > the direct application to tetrahedronometry follows > > from the special angular configuration > > of the right or left trigonum on the diameter, > > the circumdiameter. > > > often ...
Basically the conservation of ratio and angle in the triangle or 3-gon has then sine and cosine as orthogonal functions.
An idea is to generalize that to n-gons with families of n-1 many "orthogonal" functions, then as to the development of extensions of Fourier series for analysis, and other general simple, tractable results. These constructs simply already have these features, they're not well-explored where trigonometry is well-developed over time and used throughout geometry and analysis. One might see this with potential applications for spectrum analysis, n-D systems, and approximation of n-many periodic components in extensions of the two dimensions of planar analysis in Fourier series.
Another generalization then is as to each n-gon and variations in the evolutions of points swept given isotropies and anisotropies of the "(un-)rolling square" or here triangle. Then these would offer (more) simply parameterized solutions, given the generalized framework, to differential equations and etcetera.
Rolling squares and recycled triangles: Avenues for progress.