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Topic: N-gonometry
Replies: 24   Last Post: May 5, 2013 2:55 PM

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ross.finlayson@gmail.com

Posts: 1,203
Registered: 2/15/09
Re: N-gonometry
Posted: May 4, 2013 11:39 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

Regards,

Ross Finlayson



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