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

  • Published: 10 December 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):

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

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Comments • 4 255

  • Ben Schofield
    Ben Schofield  11 months back

    Holy cow, Destin how are you today?

    • onafixedincome
      onafixedincome  6 months back

      @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 back

      @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  7 months back

      One of my favorites, well done!

    • Thomas Leligado
      Thomas Leligado  7 months back

      @SmarterEveryDay I really appreciate your videos, and you as a person. It's sometimes hard for people to see YouTube 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  9 months back

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

  • Ricardo Pesenti
    Ricardo Pesenti  2 days back

    No it's .gif destin... not .jif...
    But this is the best visualisation of a fourier series i have ever seen.

    • MEndeavour
      MEndeavour  2 days back

      Probably Writing one of the last comments on this video, as the comments section will be removed by YouTube (as per COPPA) :( :( :(

      • Dan Mart
        Dan Mart  2 days back


        • robert lee
          robert lee  3 days back

          Do you have promo codes for kiwico?

          • Daniel Avila
            Daniel Avila  3 days back

            Buen trabajo. Saludos desde Panamá canal.

            • likyishi
              likyishi  4 days back

              와 이게 뭐지.....엄청나다

              • Jin Shikami
                Jin Shikami  4 days back

                Simulate some circuits! Type: androidcircuitsolver/app.html

                • Ethan O
                  Ethan O  6 days back

                  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  1 weeks back

                    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  2 weeks back

                      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  2 weeks back

                        What tie knot is that?

                        • roladun
                          roladun  2 weeks back

                          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  3 weeks back

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

                            • hareti
                              hareti  3 weeks back

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

                              • marlontrujillo1080
                                marlontrujillo1080  3 weeks back

                                Doha seems like a really d1k...

                                • Alan Lenisa
                                  Alan Lenisa  3 weeks back

                                  nice point of view

                                  • Kevin Gilkey-Graham
                                    Kevin Gilkey-Graham  3 weeks back

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

                                    • sankar r
                                      sankar r  3 weeks back

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

                                      • norm colbert
                                        norm colbert  3 weeks back

                                        its time

                                        • Mu's
                                          Mu's  4 weeks back

                                          As bayraklari As 🇹🇷🇹🇷🇹🇷

                                          • Amit Shende
                                            Amit Shende  4 weeks back

                                            please share Matlab code for drawing any shape with Fourier transform

                                            • Constant Rohmer
                                              Constant Rohmer  4 weeks back

                                              How did he converted the brain-drawing into functions ?

                                              • Subhash Chowdhury
                                                Subhash Chowdhury  4 weeks back

                                                Please do it for Fourier Transformation

                                                • Subhash Chowdhury
                                                  Subhash Chowdhury  4 weeks back


                                                  • LYNDONisHERE
                                                    LYNDONisHERE  4 weeks back

                                                    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  4 weeks back


                                                      • 0n. GUVEN
                                                        0n. GUVEN  1 months back

                                                        Can we use this in a 3d printerss i wonderr

                                                        • Joseph Madratz
                                                          Joseph Madratz  1 months back

                                                          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  1 months back

                                                            That circle is very wonky

                                                            • Udo Matthias drums
                                                              Udo Matthias drums  1 months back

                                                              chaos pendel!!

                                                              • Udo Matthias drums
                                                                Udo Matthias drums  1 months back

                                                                love it!!

                                                                • Ruchir Rawat
                                                                  Ruchir Rawat  1 months back

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

                                                                  • Bart Burkhardt
                                                                    Bart Burkhardt  1 months back

                                                                    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  1 months back

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

                                                                      • Kanishka Wijayananda
                                                                        Kanishka Wijayananda  1 months back

                                                                        Amazing work guys keep on going

                                                                        • James Bonanno
                                                                          James Bonanno  1 months back

                                                                          Wow that was absolutely amazing! I haven't seen something on YouTube that caught my interest so well in a long time. I subscribed and I hit the Bell.

                                                                          • Nothing\
                                                                            Nothing\  1 months back

                                                                            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  1 months back

                                                                              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  1 months back

                                                                                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  1 months back

                                                                                  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  1 months back


                                                                                • stevecytfme
                                                                                  stevecytfme  1 months back

                                                                                  Ok. I'm out. Over my head.

                                                                                  • Papa Rob
                                                                                    Papa Rob  1 months back

                                                                                    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
                                                                                      Samwisegamgee The Brave  1 months back

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

                                                                                      • Sherwin Imperial
                                                                                        Sherwin Imperial  1 months back


                                                                                        • Marc Paul
                                                                                          Marc Paul  1 months back

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

                                                                                          • Anderson Pyaban
                                                                                            Anderson Pyaban  1 months back

                                                                                            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  1 months back

                                                                                              Süpeerrrr.Türk birini görmek ne güzel.
                                                                                              Supeerrrr.Very nice to see a turkish guy.