If You Only Have Time For One Video, Make It This One

Ahhh HSC

Same

im rewatching some old avgn episodes rn and this part consistently makes me lose my shit no matter how many times i see it

Finally found it, I think about this post more often then I would like to admit

Surely this has to be staged, surely

A short note on how to interpret Fourier Series animations

When one searches for Fourier series animations online, these amazing gifs are what they stumble upon.

They are absolutely remarkable to look at. But what are the circles actually doing here?

Vector Addition

Your objective is to represent a square wave by combining many sine waves. As you know, the trajectory traced by a particle moving along a circle is a sinusoid:

This kind of looks like a square wave but we can do better by adding another harmonic.

We note that the position of the particle in the two harmonics can be represented as a vector that constantly changes with time like so:

And being vector quantities, instead of representing them separately, we can add them by the rules of vector addition and represent them a single entity i.e:

                                                  Source

The trajectory traced by the resultant of these vectors gives us our waveform. 

And as promised by the Fourier series, adding in more and more harmonics reduces the error in the waveform obtained.

        Have a good one!

**More amazing Fourier series gifs can be found here.

This is deep, even coming from the simpsons

I just absolutely lost it,

But thank goodness for the subtitles otherwise I would never have known what that seal was saying

my favorite seal is that one that just goes “uuunhh. eggs” and makes fart sounds with his mouth