[DayLateDon]

Hello ...

Inspired by this video of Moebius transformations ...

Moebius transformations revealed

... I would like to create an animation of one of my favorite insights, a "Calculus-free" development of the derivatives of sine and cosine functions.

A write-up of the idea appears here:

Calculus-Free Derivatives of Sine and Cosine (PDF)

An interactive Mathematica-based Demonstration is here:

Calculus-Free Derivatives of Sine and Cosine - Wolfram Demonstration Project

(The Demonstration can be viewed in the free Mathematica Player, available via a link on that page.)

Both the write-up and the Demonstration seem overly complicated. I believe that the concept can be presented in an elegant animation --with a few explanatory sub-titles-- but I am not skilled enough in POV-Ray and such to create compelling visuals. Given that the point is to help students wrap their minds around the concepts here, the slicker the graphics, the better.

Would anyone be interested in collaborating on such a project?


Thanks and regards,

Day Late Don

[Oisín]

Wow.

I understood absolutely nothing of that. Post or links.

*blinks stupidly*




Good luck on the project, though—I’m sure there are plenty of people here who are smarter than me and some kind of idea what on earth you’re talking about.

[loki74]

Aha... I get it. Wrap the square around a cylinder, and the diagonals will make a spiral. Project that spiral onto a plane, and you get a trig function. Clever...

Animating it isn't terribly complicated, once you get the square wrapped around the cylinder... that's a little bit tough for an amateur like me, but I imagine it could be nicely done using morph targets, or even bones. I just might give it a try....



The video you linked was very nice too, excellent explanation! Although, I'd be very interested if such a thing existed for Fourier transformation... I never could wrap my head around that one. Quaternion rotations are also a bit confusing. Well, going between them and Euler rotations, anyway. Then again, Calc For Business is the extent of my math schooling so.... <_< ;;