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

  • 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.
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Comments • 4 246

  • Ben Schofield
    Ben Schofield 11 months ago +1841

    Holy cow, Destin how are you today?

    • onafixedincome
      onafixedincome 5 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 Spizzichino
      Eli Spizzichino 6 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 Cucullu
      Gordy Cucullu 6 months ago

      One of my favorites, well done!

    • Thomas Leligado
      Thomas Leligado 7 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.

    • Anon54387
      Anon54387 8 months ago

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

  • Ethan O
    Ethan O 3 hours ago

    El 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 peri
    arjun peri Day ago

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

  • Arno Claassens
    Arno Claassens 4 days ago

    Great 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 Muresan
    Sergiu Muresan 5 days ago

    What tie knot is that?

  • roladun
    roladun 10 days ago

    Perfectly 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.

  • Eufalesio
    Eufalesio 12 days ago

    it’s not pronounced “gif”, it’s pronounced “gif”

  • hareti
    hareti 13 days ago +1

    I want to see the list of sine waves that makes up the neon sign.

  • marlontrujillo1080
    marlontrujillo1080 13 days ago

    Doha seems like a really d1k...

  • Alan Lenisa
    Alan Lenisa 14 days ago

    nice point of view

  • Kevin Gilkey-Graham
    Kevin Gilkey-Graham 15 days ago

    Reminds me of something that would be used by the mechanics of the automata

  • sankar r
    sankar r 15 days ago

    This is the best posdible explanation for fourier series.
    Thanks a million.

  • norm colbert
    norm colbert 16 days ago

    its time

  • Mu's
    Mu's 18 days ago

    As bayraklari As 🇹🇷🇹🇷🇹🇷

  • Amit Shende
    Amit Shende 18 days ago

    please share Matlab code for drawing any shape with Fourier transform

  • Constant Rohmer
    Constant Rohmer 20 days ago

    How did he converted the brain-drawing into functions ?

  • Subhash Chowdhury
    Subhash Chowdhury 20 days ago

    Please do it for Fourier Transformation

  • Subhash Chowdhury
    Subhash Chowdhury 20 days ago


    LYNDONisHERE 22 days ago

    Im 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 Garg
    Girish Garg 22 days ago


  • 0n. GUVEN
    0n. GUVEN 24 days ago

    Can we use this in a 3d printerss i wonderr

  • Joseph Madratz
    Joseph Madratz 24 days ago

    What 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 R
    C R 26 days ago

    That circle is very wonky

  • Udo Matthias drums
    Udo Matthias drums 27 days ago

    chaos pendel!!

  • Udo Matthias drums
    Udo Matthias drums 27 days ago

    love it!!

  • Ruchir Rawat
    Ruchir Rawat 29 days ago

    Destin : you know what are gifs ?
    Doga : am i a joke to you?

  • Bart Burkhardt
    Bart Burkhardt Month ago

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

  • gbob99
    gbob99 Month ago

    Is "The Roots of Unity" concept considered a Fourier Transform?

  • Kanishka Wijayananda

    Amazing work guys keep on going

  • James Bonanno
    James Bonanno Month 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\
    Nothing\ Month ago

    You 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.

  • VPXM
    VPXM Month ago

    Gifs 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 macdonald
    daker macdonald Month 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.

    • VPXM
      VPXM Month ago

      You 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...

  • stevecytfme
    stevecytfme Month ago


  • stevecytfme
    stevecytfme Month ago

    Ok. I'm out. Over my head.

  • Papa Rob
    Papa Rob Month ago

    Smarter 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 Brave

    Thats elegant. Im a caveman so what do I know but I'll be damned if that is not elegant.

  • Sherwin Imperial
    Sherwin Imperial Month ago


  • Marc Paul
    Marc Paul Month ago +1

    Finally, thanks to you, Destin, and Doga, I can visualize additive functions with a Fourier series! Thank you!

  • Anderson Pyaban
    Anderson Pyaban Month 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 Zahid
    Seyfullah Zahid Month ago

    Süpeerrrr.Türk birini görmek ne güzel.

    Supeerrrr.Very nice to see a turkish guy.

  • Nico Brits
    Nico Brits Month ago

    I 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 Tirkey

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

  • jak frost
    jak frost Month ago

    First time I wished I could like a video more than once

  • Manie de Bruin
    Manie de Bruin Month ago

    I am now drunk

  • Loris Lewandoski
    Loris Lewandoski Month ago +1

    Fourier transforms, fourier series, cosine transforms, k-l transforms, etc is what i've been learnin these years.

    TPHBLIB Month 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.

    TPHBLIB Month 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 YALÇIN
    Giray YALÇIN Month ago

    did you study EE?

  • blanca roca
    blanca roca Month ago

    Beatiful 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 Hashmi
    Shahzad Hashmi Month ago

    Wonderful video

  • Jim Moriarty
    Jim Moriarty Month ago

    Sorry, but it's pronounced as gif not gif

  • chaos
    chaos Month ago

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

  • Aristo Teles
    Aristo Teles Month ago

    Congratulations doğa from Turkey

  • Aristo Teles
    Aristo Teles Month ago

    Congratulations doğa from Turkey

  • Aristo Teles
    Aristo Teles Month ago

    I have expected thousands of Turkish comments

    EALHAM AL MUSABBIR Month ago +1

    Thats simply mind-blowing facts you've just shown....

  • Venkatesh Iyer
    Venkatesh Iyer Month ago

    Dude you're awesome

  • Leo3ABP gaming
    Leo3ABP gaming Month ago +1

    Thumb up if you also store your old university notebooks :)

  • David Hunt
    David Hunt Month ago

    No, 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.