First Fourier Series: The Eight Note [Music] First Fourier Series, 10x Zoom First Fourier Series, 100x Zoom End of First Fourier Series,

Start of Second Fourier Series Second Fourier Series: The Sigma/Sum Symbol End of Second Fourier Series,

Start of Third Fourier Series Third Fourier Series: England, United Kingdom End of Third Fourier Series,

Start of Fourth Fourier Series Fourth Fourier Series: Joseph Fourier End of Fourth Fourier Series,

Start of Fifth Fourier Series Fifth Fourier Series: Nail and Gear End of Fifth Fourier Series,

Start of Sixth Fourier Series Sixth Fourier Series: A Treble Clef End of Sixth Fourier Series,

Start of Seventh Fourier Series Seventh Fourier Series: Hilbert’s Curve End of Sixth Fourier Series,

Start of Eighth/Final Fourier Series Eighth/Final Fourier Series: Seattle, Washington,

United States of America End of Eighth/Final and Every Fourier Series.

After the Fourier series video, I was left with a lot of "extra footage", and much of it is so mesmerizing that it really felt like a shame not to put it out there in some form.

At about 5:18 in the video when the animation zooms out and shows the outline of the man; if you look closely it almost seems as if Batman is hidden within his mustache!

Next up: imagine doing this in 3D using spheres…

All those vectors movement look more complex than the shape they draw.

Visual ASMR.

That music makes this all the more enjoyable.

But…. what does it sound like?!

Each vector is a life

All life exists along a single strand with its own intrinsic ebb and flow

어캐했노

This video is perfect! ♥!

Can someone please refer to a tutorial about how to parse svg files to obtain coordinates of arbitrary shapes?

Really hope someone makes a website where you can just draw a picture and see the circles try to draw what you drew.

For each element, is the number of rotations per drawing cycle a whole number?

음악 보고싶은데 영어 고자라..

So when do you go 3D?

You could make these with gears couldnt you?

Stop with the clickbait titles…

Thank you for putting the vector counts in the description

How does one do this so smoothly in python

But how do you decide the relative speed of drawing each line segments? I suppose drawing a circle with uniform speed and varying speed requires some different Fourier series, as the latter would not be a simple sine function when I plot the x-t graph

i'd love to see/hear the vectors turned into audible frequencies. could be a new synthesizer concept!

so we finally know the length of the coast of great britain!

Now we wait for the future programs that constructs these animations out of any drawing 👀

Thanks youtube for giving us like button, though it is not sufficient as this video proves that we need a love/heart button

I love the dynamics of these animations, especially the last one. The way the chain of vectors goes from gentle spirals to lightning-fast whips to frenetic chaos and back, it's absolutely mesmerizing.

Or… how to single out a single note from a guitar chord (or any other instrument). And then move it to another register.

My friend: don't fall for the wrong guy again.

Me: 0:30

My friend: OH MY GOD

한국인 있나요…

Time to announce 3Blue1Brown as the final boss of fourier series

Why so many arms? Isn't it just x/y?

I wonder if one could design clockwork that works that way, by using the fourier series to find the radii of many cogwheels… steampunk stuff. Wait, is that how mechanical analog computers work?

It boggles my mind that all of this can be summarized in the equation Σ(Ae^[nti])…. Just What?!

Làm ơn có tiếng việt để tôi hiểu đi

Is there any software I can use to test & generate such shapes?

Is it possible to make a circle with more than 10 circles that have different size?

I had no concept of the incredible power of Fourier's work. Thank you for the enlightenment.

Now I want to make a mechanical model…

Hey grant

Big fan

Which software do you use to animate this?

It will be helpful for me to understanding higher math.

TABLE OF CONTENTS:

0:00 Eighth note

1:23 Capital Sigma

2:27 Great Britain

4:03 Fourier's portrait

6:04 Nail and Gear

7:43 Treble clef

8:56 Approximation of Hilbert curve

10:24 Seattle outline from Frasier

For the description the 8th note is formally known as the quaver

Please correct me if I'm wrong

How to be talented like you…?

i like it

GOOD

never visualized Fourier series this way….amazing

Could this kind of stuff theorically works in higher dimensions as well? Say, 3D sculpture for instance?

Is there a connection between these animations and quantum field theory? If everything is excitations in some all-permeating field, that seems to imply that the universe is just a really fancy 3d analog of these waves/rotations. Someone correct me if my intuition is way off.

Hey Grant, I was wondering watching music theory videos about music intervals. Is it true that a music interval is a superposition of two different frequency sinus waves? If so, I became curious if the intervals like the perfect 5th or a major chord that are more apealing to our ears are also more appealing to our eyes if they were visualized? And the opposite is as well interesting for me if a tritone looks “ugly”. Are u interested to check that?

This is the closest event to understand what mathematicians means when they "the beauty of Mathematics"!!.

At hindsight and at my age I never thought that I went to see something like this. The only idea that comes to my mind is simply AMAZING

Hey, are the magnitudes and phases of the harmonics being changed throughout the drawing? Or do they remain the same throughout?

Please upload visual theory and applications of laurant and machlaren series.

Can you provide us the svg files used to create those animation? I've always wanted to code to do this.

Do you suppose a Saturn rocket could be evolve-morphed into a really cool looking flying saucer from the big leagues?

This must be a pain to animate lol

one of the coolest things I've ever seen!

IT'S JUST ROTATING STICKS

This is incredible. Love this channel so much! 🙂

What a super cool animation!!

Is it possible to say now many NP hard problems could be modeled by fourier.

VERY GOOD

Most beautiful dance I have ever seen

@3blue1Brown: Can you make a video explaining just how you made this? I would really love to be able to do something like this in, for example, MATLAB ;)!

The smaller arrows reminds me of brownian motion.

How do people derive the functions to graph these…?

Now I want someone to look at this an tell me that math isn't beautiful

Math is beautiful

7:15 Reminds me of CGP Grey

That title screamed clickbait, but this is still a 3B1B video, which warrants at least a single view from me.

Thanks 🙏🙇 to Buddh:ha, he taught to believe in our power of BUDDHAHOOD. removing the gap between humanity and GOD 😇🙏👼.

7:38 3BLUE1BROWN IS A COMRADE ❤️❤️❤️

Sometimes I wish these great physicists and mathematicians could see what they really made

I mean, when Maxwell introduced displacement current into Ampère's law it paved the way for modern physics

Fourier would be amazed at how beautiful a visual representation of his work could be or how it could be applied to explain a lot of things

And to think that nothing of this would exist or take much longer to come to reality if Newton and Leibniz didn't decide to play around with geometry

Is this fractal ?

I just found my favourite video to fall asleep to. Subscribed.

Thanks for giving Rubinetti some extra attention in this video. His music is really breathtaking.

Edit: I'm a professional composer.

YES…

I can now show make people understand why I love math

YES

YES

YES YES YES

Goose bump!

please try 3b1b eye.

Who else watch this for sleep?

I hope it can be translated to Chinese,I am Taiwan ,i love your Video very mich,Thanks!

Ahh yes, enslaved chaos

It's so telling and awesome that the straight lines are not perfectly straight 🙂

Simply breathtaking.

Serious question, is this an efficient way to compress such vector drawings?

The space needle!! Wow! Long back I had tried generating the random waveforms on the Oscilloscope using the DAC and a microcontroller. I could not even do a small curve. I can guess the efforts you put behind your videos.

So is this like porn for us maths people?

springy bois, thats what this should have been called

Quien vino por crespo? avdhdjjwdj

Beautiful!

Check out the coding train on how to Code that.

Salute to Animator

Almost cried !

Ok , I cried !

an elegant caricature that portrays what life is.. thank you for such a mesmerizing work