What is a Fourier Series? (Explained by drawing circles) - Smarter Every Day 205

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Doga's a super smart dude who writes a Turkish blog "Bi Lim Ne Güzel Lan" that roughly translates roughly to "Science is Awesome Dude". We had a lot of fun working on this together. He would really appreciate it if you checked out his blog. The fun thing is that most of his articles transcend language.

Doga’s Blog (written in Turkish):

Doga’s original Fourier Series blog article that blew my mind:

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Brady’s Video “Optical Tweezers and the 2018 Nobel Prize in Physics - Sixty Symbols”
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Ambiance and musicy things by: Gordon McGladdery did the outro music the video.
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Warm Regards,

Destin

[lbmetei]

Big fan of Mr. Fourier. He made my life very difficult.

[TheCodingTrain]

Well, I guess I know what I'm going to try to program on this Friday's live stream!

[smartereveryday]

"It looks like a whip".... (Starts studying whips)

[AsianBrozGaming]

1:53 "sine ways are probably the simplest kind of waves right? the second most some kind of wave is..."
me: cosine waves
him: a square wave.
me: oh

[lauraleeane]

As a grad student who uses Fourier transforms daily, it is incredibly valuable to watch well made videos like this that take a step back and see the beauty behind the math. Often in the classroom we focus to much on the answer and not enough on the beauty behind the math to get the answer.

[EAHowe]

I had Dr. Doga for my Physics I and II classes my freshman year. Crazy to see him on this channel.

[sunscream]

YouTube should recommend these types of videos to everyone.

[akuljamwal]

Dr. Doga hasn't looked happy since his pronunciation of GIF was corrected

[Hardzinho_Yay]

In Physics we have a saying: If you have one problem needs to be solved with fourier series, then you have 2 problems.

[SpaceSnaxxx]

4:23 "I made this amazing art tool and you're correcting my pronunciation?"

[domainofscience]

That is such and awesome visualisation of the Fourier series! It also makes me wonder what your logo sounds like. You could play each of these circle bundles as a musical note that is made of all of the sine waves, so your logo is a chord of 4 notes. I wonder if it would sound nice?

[jerrygundecker]

I like the part where you asked him to explain it. You can see him stop,
(momentary exasperation) and rethink it to put it into words. We actually saw his brain change gears. Loved it.

[jima]

His reaction to your correction of how to pronounce "gif" was perfect lol

[sef]

Doga (Doğa, more correctly) means "nature" in Turkish. So "nature" tries to understand "nature" by using math :) proud of him!

[naonao]

Leaning about the harmonic series rn. learning that not only can you make just about any sound just by adding simple sign waves together but you can also draw by adding sign waves is absolutely blowing my mind.

[jaidenboucher]

I have never left one of your videos without a smile on my face and this is no exception. Thank you so much for doing what you do.

[Freizeitflugsphaere]

This is what kills me at university at the moment...

[Hexanitrobenzene]

"...let's challenge him !"
Destin shows a logo of SmarterEveryDay. I'm like, "Come on, man, you can't approximate that with Fourier series. That's a multi-valued function!"
Doga constructs a graph with 4 parametric functions, each approximated with Fourier series. I'm like "Oh... o_0
I stand corrected." :D

[Rujenz]

Welcome to the comment section, where we have:

90% about the GIF pronunciation
10% regarding the Fourier series

[DrTWG]

I'm no mathematician or coder (MD by trade) but managed to get a square wave going - much like the one above with all the circles whipping around - using Javascript & p5 library. It was actually easy . The series is basically sin(wt) + sin(3wt)/3 + sin(5wt)/5 t is your time step, w = freq . The more terms the squarer. Getting the graphics looking good & moving was the tricky bit.