Epicycles, complex Fourier series and Homer Simpson's orbit

now mathologer is more about the simpsons than about math:(

Eugh, you should reupload this video without showing donald trump. He has caused so much hurt and misery.

Excelente informação sobre as epiclicóides, das séries de Fourier. A aplicação de tudo isso nas neurociências fará, certamente, que nos aproximemos cada vez mais do constructo da consciência!

JUST WOW! GREAT! AWESOME! WONDERFUL!!!

because universe is fractal in nature and composition, a same volume of space can carry multiple waves at the same time, due each wave is transported at a different level of the fractality, and being the universe fractality like any fractality, infinite, infinite are the amount of waves matter can have, proving that light speed is infinite ... in the only way the energy of a place in the universe is limited, is in its maximum fractal density, even when in the universe as a whole there is not maximum for its maximal densities through its odes, and that is why for a given celestial body and medium, its absorption, transmission and emission are from infinite light speed to their maximum fractal density possible waves, making every material able to carry, before its fractal density disintegrates, or deliver, infinite amount of energy when we master down it fractally

WooW great job, just a note Naseer Aldeen Altousy, was Arabic Muslim scholar, you can even see that his scriptures was written in Arabic languge, I can even read it now

Wow, somehow I have never completely understood why the inverse Fourier Transformation is calculated as it is .. thanks to this video now I know.

I am truly amazed

Fantastic!

Meh did 5 minutes and no Homer. Gay

It is great. By the way i tried to convert the notebook from mathematica to maple.. Got extremely weird stuff.. Does anyone could have done it ?👌

I wish I could like this video an infinite number of times.

Ehegh

a mini moon.... right... today we call it a satelite sending GPS signals... we coud doe the same for the moon placing stationairy satelites into orbit with the moon. as we do with earth...

The epicycles were discovered by Indian astronomers prior to surya siddhanta treatise.

Beautiful

Fascinating. I'm glad you did this one that is so much like one or two I saw about square orbits by "All things physics", only with more maths details on Fourier series. I bet they saw your video first! I can't do animations but just formulae on Excel - and have one set up to make spirograph patterns and can just change some figures at the top of some columns to change the shape, number of points, etc. It's based on the toy version with its limited cog number ratios - but on Excel you can input any numbers. The problem with trying to make the square orbit was if you make the 'hole distance' on the small wheel further out towards the edge of the wheel the orbit corners are too pointy and sides too curved and if you put the 'hole' closer to the centre the square sides are straighter but the corners more rounded, and at some point there is a compromise between square corners and straight sides.
Anyway that other video inspired me to get the Spirograph out and draw loads more patterns, and my Mum's cousin appreciated a card covered in them for his birthday! I also printed out some computer generated patterns and left them at church for children to colour in when they are bored or have nothing better to do...! At least that is kind of educational for them if it gets them thinking about such mathematical patterns.
It would be nice to see pictures of Fourier transforms of the sounds that various musical instruments make. Wouldn't they just be spiky plots of the distruibution of frequencies / harmonics. Some sounds look fascinating on audio files (I use Wavepad aduio editing) and sometimes I look at the Fourier transform time plot which shows how the proportions of each frequency change over time. (Maybe because I want to find out the frequency of an annoying background whistle or hum!)

Thank you for the video, I like it.
Do you know in Nepal we follow a lunar calendar. After 3 years there is an extra month added to balance the solar and lunar year - the "mala maas". At that time there were no any mathematics to show such things but they calculated the same idea accurately.

u r simply the best!!
🤸🤸🤸💕💕💕💕🙏🙌🧘

The name of the persian mathematician is: نصیرالدین طوسی ✌️ copy this in google translation and listen to the pronunciation

I've gotta learn to use Geogrebra better. I like to make these simulations myself, but as of now I'm stuck using Algodoo. Which is better suited for physics, but it does the job for stuff like this, too. Taking a few operational quirks into account. Still a great program, though.

just wanna say that the mathematician you mentioned as Persian is actually Arab, and the text on that paper is also Arabic.

You have to do another video on Fourier Analysis! Truly awesome

Does this mean, that when we draw Homer Simpson, somewhere in our heads, epicycles are occurring?

What's the music we keep hearing during the animations ?

This video had so many 7-gun salute moments, I ran out of ammo... hats off.. zen master!!!!

Most of these possible moon orbits have the moon way further from planet then is actually possible.

Really? Homer Simpson has orbit? Cause it's means that the're something of close-or-bigger mass to Homer's

Really, trump?

Can anyone provide the co-ordinates of the Homer Simpson image in the video in .mat format ?🙂🙂

thank you for making this

This is the kind of problem you have when you are using a router…

The basis for the toy of the late 60s, the Spirograph --- epicycles going back a 1000 years or more. If not a toy, a representation for some sorts of mechanical engineering. My parents wanted me to be an engineer, by way of a hint they got me that toy for Christmas. I wanted to be a scientist, a Chemist. I found it more interesting. I also got a degree in math. Turns out that most people find engineers easier to relate too. Most folks find that engineering, while hard, is more relatable as they can follow along if they too run through the hard tedious math for themselves. The math that most engineers typical use is well known and not cutting edge. The same can't be said for science. Science tends to be cutting edge, watch PBS' NOVA. Folks tend to have real problems with cutting edge.

How do generalized Fourier series fare for drawing.

"Mathematicians don't have to worry about reality"

Basically electrical engineering in a heart beat...

If the universe if infinite, that means there is a tiny moon, out there somewhere, tracing out the path of homer simpson...

Just beautiful. I've seen this video many times along the years enjoying it always.

My favorite identity is e^ipi + 1 = 0. There are all what is needed to start complex plane 0, 1, i, e and pi.

me: oh so that time is a solar eclipse

Thank you for putting LIFE into FOURIER SERIES!

380'000/150/10⁶=2,5*10-³Вот поэтому и орбита выглядит как округленный 12-угольник.

It's the toosie slide