<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body dir="auto">Hi Curve Fans,<div><br></div><div>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.</div><div><br></div><div>Having measured Edward's Curve one way or another, it's natural to wonder: how is this related to the plane pendulum?</div><div><br></div><div>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.</div><div><br></div><div>After many hours of heretical thought, discarding all normal forms, and surpassing a few failures of insight, Finally we arrive at the following animation:</div><div><br></div><div><a href="https://m.youtube.com/watch?v=7IqfauZ_9wQ">https://youtube.com/watch?v=7IqfauZ_9wQ</a></div><div><br></div><div>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.</div><div><br></div><div>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.</div><div><br></div><div>Hope you enjoy the new video,</div><div><br></div><div>Cheers,</div><div><br></div><div>Brad</div><div><br></div><div>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~</div><div><br></div><div>In some conceptions of the Force,</div><div>with geometric ground principles,</div><div>Spacetime harbors nothing more</div><div>than a variety of even manifolds,</div><div> Yet it does.</div><div>Decomposition reveals equal halves,</div><div> supposed equal halves,</div><div>related via an antisymmetric form.</div><div><br></div><div>"You know /what/ about the curves?"</div><div><br></div><div>Some of them go along the dark side</div><div> then along the light side</div><div>back along the dark side</div><div> never accomplishing any Work</div><div> just looking for action in the red.</div><div>Along others of the Curves,</div><div> every angle is terrifying,</div><div>All seeming to say,</div><div> "Abandon that adherent!</div><div> To consort dark side, alone."</div><div><br></div><div></div></body></html>