[curves] Transformations of Edward's Curve

[bradklee at gmail.com]

Hi Curve Fans,

According to the archives you sometimes have topics with an educational bent. This post is to share one critical calculation, which seems otherwise to be missing from the literature.

Having measured Edward's Curve one way or another, it's natural to wonder: how is this related to the plane pendulum?

Many creative people will not be satisfied by a rote explanation in terms of the Latin elliptic functions, "Sinus Amplitudinis" and "Cosinus Amplitudinis". In fact many of us did not grow up with a good education in Latin, which makes old manuals all the more difficult to read.

After many hours of heretical thought, discarding all normal forms, and surpassing a few failures of insight, Finally we arrive at the following animation:

https://youtube.com/watch?v=7IqfauZ_9wQ

The curvature flows utilize a Fourier series approximation, which converges over 99% of the interior region. I don't think it's even possible to do much better, because the critical points along the boundary contain irremovable divergences, i.e. cannot be completely smoothed.

In an upcoming work, this calculation will be described in all detail. I'm trying to make it easy enough to understand, even for people with only a background in discrete mathematics or computer science. The idea is that this effort could help to put the common person on equal footing with Kaiser Friedrich Wilhelm IV crowd.

Hope you enjoy the new video,

Cheers,

Brad

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In some conceptions of the Force,
with geometric ground principles,
Spacetime harbors nothing more
than a variety of even manifolds,
             Yet it does.
Decomposition reveals equal halves,
            supposed equal halves,
related via an antisymmetric form.

"You know /what/ about the curves?"

Some of them go along the dark side
            then along the light side
back along the dark side
          never accomplishing any Work
          just looking for action in the red.
Along others of the Curves,
          every angle is terrifying,
All seeming to say,
          "Abandon that adherent!
          To consort dark side, alone."

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