Fourier Series (Sawtooth Approximation)

[@rt]

Hi Guys

Could someone explain why there are two different circular animations about YouTube for Fourier Series Sawtooth animation?

Here’s one example where every second circle is rotating clockwise:


Yet the Wikipedia example here is different:


Wouldn’t these be two entirely different formulas?
At the very least I think theta would alternate positive and negative for the first example only.
I put this in projects section because it is a software project. I have been making my own.
Cheers, Brek.

[T3sl4co1l]

Probably, because cos(-x) = cos(x)?  For even harmonics, the direction of rotation doesn't matter, because they always have the same vertical component relative to the rest.

Tim

[@rt]

Lol can we forget the whole thing and make this thread go away?

There must be an issue with my rotation.
When I reproduce the second animation, as the iterations get near 200 or so,
the sawtooth becomes as good resolution as infinite is going to get on a limited resolution screen.
I can explain and fix the jittery points (it’s because I’m only connecting every third sample).



When I reproduce the first one it’s great except there’s a little kink in the middle of the diagonal part of the wave.
That is not uploaded though... I’ll look into it again :O