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

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- Published on Dec 10, 2018
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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):

bilimneguzellan.net/

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

bilimneguzellan.net/fuyye-serisi/

Click here to tweet him "thanks" for bilimneguzellan

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GET SMARTER SECTION

mathworld.wolfram.com/FourierSeries.html

Brady’s Video “Optical Tweezers and the 2018 Nobel Prize in Physics - Sixty Symbols”

ru-clip.com/video/XjXLJMUrNBo/video.html

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Warm Regards,

Destin

Ben Schofield11 months ago^{+1841}Holy cow, Destin how are you today?

onafixedincome5 months ago@SmarterEveryDay I'm always a bit shy of addressing you Prominent Busy People...you've a lot better things to do than put up with nosy folk like me.

I plan to keep waving at my screen and yelling "HI DESTIN!" every time I see you pop up? Does that count?

Ps....Anyone who hustles you for more uploads, etc, should have to wait an extra week to see the next one. :P

Eli Spizzichino6 months ago^{+1}@SmarterEveryDay Destin4president! I've loved your podcast (and I'm not an American). China's social ranking system is really scaring and the world is going straight in that direction. I agree on the nose-dive problem (that could be addressed by a weighting algorithm) but I think the core problem is that we're getting used to the idea that machines can be better then humans in judging humans. I'm not saying that AI has no good potential in this field (there are many example of this already), I'm saying that we're inherently superior to do so, it's built in our brain for example we have entire set of neurons just dedicated to judge mouth and facial muscles movements to get an intuitive "feeling" of the other person/animal intention/truthiness. The smell test you were speaking about, it came by evolution.

The dystopian future is reaching our present time faster then one might think, and is very important to speak about this stuff to hopefully prevent the inevitable nefarious outcome these issues presents.

Gordy Cucullu6 months agoOne of my favorites, well done!

Thomas Leligado7 months ago@SmarterEveryDay I really appreciate your videos, and you as a person. It's sometimes hard for people to see RU-clip creators as people and not robots, getting mad when you don't upload on time. Thank you so much for all the work you do, I love this channel and all the work you do for it. Please don't feel like you need to do all this as people say you need to, you are a person and this is strenuous work! That isn't to say I don't appreciate seeing and learning from these videos. I really hope you see this, because you have helped me get through some really rough times and I wish you the very best in everything.

Anon543878 months ago@SmarterEveryDay The link to the Sixty Symbols video does nothing. Perhaps add a link in the description.

Ethan O3 hours agoEl tipo cree que él puede hacer interesante a las series de Fourier, cuando en realidad es delrevés, de los 8 minutos, 2 son lo que lo hace interesante con el tema de Fourier, el resto es bosta de la opinión del tipo que se quiere lucir con Fourier!, deslike!

arjun periDay agoGo to a top 10 university and 0 of my professors have been able to explain the underlying concepts of Fourier series this well.

Arno Claassens4 days agoGreat addition to this video is 3blue1brown's video on it. Both give different ways to understand the topic and in conjunction they give a great intuition.

Sergiu Muresan5 days agoWhat tie knot is that?

roladun10 days agoPerfectly said order out of chaos that came to my mind when I first watch this on 3Blue1Brown channel on Fourier Series/DE, I recommend all to watch that.

Eufalesio12 days agoit’s not pronounced “gif”, it’s pronounced “gif”

hareti13 days ago^{+1}I want to see the list of sine waves that makes up the neon sign.

marlontrujillo108013 days agoDoha seems like a really d1k...

Alan Lenisa14 days agonice point of view

Kevin Gilkey-Graham15 days agoReminds me of something that would be used by the mechanics of the automata

sankar r15 days agoThis is the best posdible explanation for fourier series.

Thanks a million.

norm colbert16 days agoits time

Mu's18 days agoAs bayraklari As 🇹🇷🇹🇷🇹🇷

Amit Shende18 days agoplease share Matlab code for drawing any shape with Fourier transform

Constant Rohmer20 days agoHow did he converted the brain-drawing into functions ?

Subhash Chowdhury20 days agoPlease do it for Fourier Transformation

Subhash Chowdhury20 days agoExcellent

LYNDONisHERE22 days agoIm in an intro to quantum class and this has honestly been pretty helpful considering how mentally in debt I fell towards the class. Cheers Mate :)

Girish Garg22 days ago3b1b

0n. GUVEN24 days agoCan we use this in a 3d printerss i wonderr

Joseph Madratz24 days agoWhat is different between this method vs finite fourier series method taught in college math courses. Is this just a way to visualize what’s happening when sine and cosine terms are added via the Fourier series or is it a different technique.

C R26 days agoThat circle is very wonky

Udo Matthias drums27 days agochaos pendel!!

Udo Matthias drums27 days agolove it!!

Ruchir Rawat29 days agoDestin : you know what are gifs ?

Doga : am i a joke to you?

Bart BurkhardtMonth agoI am curious why he was showing the fractal at 4:27, what was that? does it have a relation to the fourier series?

gbob99Month agoIs "The Roots of Unity" concept considered a Fourier Transform?

Kanishka WijayanandaMonth agoAmazing work guys keep on going

James BonannoMonth ago^{+1}Wow that was absolutely amazing! I haven't seen something on RU-clip that caught my interest so well in a long time. I subscribed and I hit the Bell.

Nothing\Month agoYou don't need Mathematica to do this. Unless you have a Raspberry Pi, it'll set you back a couple hundred bucks. I've done fourier series in Geogebra, which has a standalone or web based version. Or Desmos, which is a bit easier to learn and runs in a browser. I've also made simulations of electronic circuits which can approximate fourier series.

VPXMMonth agoGifs are not pronounced Jifs. It's not peanut butter, or somebody's name. You can add to a language, but you cannot start changing pronunciations... otherwise pretty soon everyone would be speaking "jibberish". I've been around long enough, to study beginning techniques of gifs. Get with the program dude.

daker macdonaldMonth ago^{+1}I don't believe that math is the language which describes the physical world. It's more so a translation of observation. Approximating the visual observation to a language that can be recorded, studied and shared. Like, a relative map for future studies.

VPXMMonth agoYou are correct. It is present, best approximation technique, that they use.

Otherwise, we'd already have "formulas" for dreaming, falling in love, FTL states, the black goo between universes, etc...

stevecytfmeMonth agoDerpy?

stevecytfmeMonth agoOk. I'm out. Over my head.

Papa RobMonth agoSmarter you may be Gustin, but you don't dis your guests in some perverted form of humor. Especially if you are wrong! It's not Jif as in peanut butter. Gif as in Humility.

Samwisegamgee The BraveMonth agoThats elegant. Im a caveman so what do I know but I'll be damned if that is not elegant.

Sherwin ImperialMonth agoimpressive!

Marc PaulMonth ago^{+1}Finally, thanks to you, Destin, and Doga, I can visualize additive functions with a Fourier series! Thank you!

Anderson PyabanMonth ago^{+1}cool. I did this in my Engineering mathematics but never had the chance to visualize the behaviour of the equations this way

Seyfullah ZahidMonth agoSüpeerrrr.Türk birini görmek ne güzel.

Supeerrrr.Very nice to see a turkish guy.

Nico BritsMonth agoI hated Fourier when I did engineering Maths, back in Noahs class. I think, for the first time, I now understand why. You kids, you thing your so smart.... ;-)

Nishant Celestine TirkeyMonth agoInteresting thing in this video is that you are wearing the same shirt I had in my 11th or 12th grade. LOL

jak frostMonth agoFirst time I wished I could like a video more than once

Manie de BruinMonth agoI am now drunk

Loris LewandoskiMonth ago^{+1}Fourier transforms, fourier series, cosine transforms, k-l transforms, etc is what i've been learnin these years.

TPHBLIBMonth ago@UC6107grRI4m0o2-emgoDnAA why n=1, or 3 or 5 ...in short why only ODD numbers are used, when the fact of the matter is that there are two wipers used for n=3 and 3 used for n=5? Please respond.

TPHBLIBMonth ago@UC6107grRI4m0o2-emgoDnAA why n=1, or 3 or 5 ...in short why only ODD numbers are used, when the fact of the matter is that there are two wipers used for n=3 and 3 used for n=5? Please respond.

Giray YALÇINMonth agodid you study EE?

blanca rocaMonth agoBeatiful visualisations animations graphics.. Wish I had them when i was a kid. Fourier derived formula for getting the amplitude and phase of the oscillations which build up the resulting function you want. However it has certain limits on discontinuous functions etc and we see this very nicely as including more and more components gets better BUT around 2:58 and 3:33 there we see an overshoot which doesnt seem to be going away anytime and in fact was all predicted hundreds of years ago by these great mathematicians who kind of saw these graphics in their heads apparently.

Shahzad HashmiMonth agoWonderful video

Jim MoriartyMonth agoSorry, but it's pronounced as gif not gif

chaosMonth agoWow! I have a degree in acoustics, and it still blows my mind to see it presented like this.

Aristo TelesMonth agoCongratulations doğa from Turkey

Aristo TelesMonth agoCongratulations doğa from Turkey

Aristo TelesMonth agoI have expected thousands of Turkish comments

EALHAM AL MUSABBIRMonth ago^{+1}Thats simply mind-blowing facts you've just shown....

Venkatesh IyerMonth agoDude you're awesome

Leo3ABP gamingMonth ago^{+1}Thumb up if you also store your old university notebooks :)

David HuntMonth agoNo, that is not illuminating. The addition of waves is an addition of waves and nothing else. BTY he pronounced giv correctly it is Giga that is pronounce with a J. You have the swagger but not the punch.