The intuition Behind Eulers Formula

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  • Опубликовано: 6 фев 2025

Комментарии • 149

  • @matercan5649
    @matercan5649 Месяц назад +230

    when i read the title my first thought was "which euler's formula" because euler literally made every formula in mathematics

    • @MAKiTHappen
      @MAKiTHappen  Месяц назад +187

      "Everything in mathematics is named after the second person who discovered it, because if it was named after the first, everything would just be called "euler""

    • @GD_EFFEHARDCORE
      @GD_EFFEHARDCORE Месяц назад +6

      @MAKiTHappen that is so true lol

    • @kaio0777
      @kaio0777 Месяц назад +3

      Man was truly thinking about the benfit of math.

    • @KingJAB_
      @KingJAB_ Месяц назад +1

      Second discoverer, so like the Fourier transform

    • @Illuminati_HD
      @Illuminati_HD Месяц назад

      @@MAKiTHappen Honestly id really like to subscribe to your channel but then my yt inbox will be constantly spammed with your livestreams, i fear this might be a porblem for multiple people. Have you thought about a seperate livestreaming channel?

  • @12Fakeaccount
    @12Fakeaccount Месяц назад +137

    This feels like 3Blue1Brown if Grant was learning this at the same time as us. I love this so much. Let me make a quick metaphor: top-down vs bottom-up. Grant explains top-down by showing how the components form a unified intuition, but you explain the foundations as a classmate who is one step ahead of us in understanding. I'm so excited to see you take off and become an influence in the community!

  • @jameshackney5438
    @jameshackney5438 Месяц назад +24

    Guys wake up, the new MAKiT vid just dropped
    Time to learn more in 20 minutes than in a semester of college physics

  • @satyamrajpro
    @satyamrajpro Месяц назад +38

    8:27 Ah yes, I love to learn about "Oiless Formula" in subtitles..

  • @KthW
    @KthW Месяц назад +34

    These are some of the best science videos i've seen,it is absolutely insane how little recognition you're getting... I hope you'll go viral

  • @Jonkuzon
    @Jonkuzon Месяц назад +7

    The segway from “ordinary” Taylor series to Euler’s formula was honestly kinda magical, well done!!

  • @vulpesaxis8494
    @vulpesaxis8494 Месяц назад +3

    It is amazing that you were able to explain all this content in just 20 minutes, AND do so clearly with neat and concise visuals and entertaining in a way that is just your own, I hope you more success in this platform and you earned a new subscriber

  • @maxe624
    @maxe624 Месяц назад +12

    I didnt realize you had so few subscribers until you mentioned it. I assumd these videos would be getting hundreds of thousands of views

  • @evefroggo4755
    @evefroggo4755 Месяц назад +5

    Finally caught one of these the day it released! I’ve loved your math videos, I hope you keep making them!

    • @N3rd-s1h
      @N3rd-s1h Месяц назад +1

      You can subscribe

  • @chonkychicken-zz4ks
    @chonkychicken-zz4ks Месяц назад

    I love this, it feels like a fun guided way to visualize things i learnt in uni 😭😭

  • @dasraffnix9471
    @dasraffnix9471 Месяц назад

    I'm really glad I've found your channel. My studies have started to suck all my passion for maths and physics out of me and channels like 3blue1brown and veritassium always make it seem so easy. They talk from an ivory tower ut you don't. You make things clear, don't hesitate to call out bullshit and you explain notation! You are amazing please keep doing what you're doing!

  • @georegio
    @georegio Месяц назад +36

    0:35 you already are broke

  • @Thaaa.PleaseBeAvailable
    @Thaaa.PleaseBeAvailable Месяц назад

    I absolutely love your videos and everything you do, the way you make understanding even the most complex of things intuitive is incredible. I’m so glad that I found your channel

  • @minsha_4290
    @minsha_4290 Месяц назад +7

    hey
    i absolutely love the videos!please keep em coming

  • @greg6400
    @greg6400 Месяц назад +7

    Absolutely insane how you are pumping out these videos every 10 days like how, also wishing for your success in full time yt
    5:38 14:57 15:01 15:18 18:45 18:49 18:52 18:56 best arrow

  • @leon9878
    @leon9878 23 дня назад

    the quality is always so high man, its amazing how you even make these in a week.

  • @collin6526
    @collin6526 Месяц назад +1

    People we must support this man. His struggle is evident from the video. He was unable to polish the rough edges of the video because he cannot afford to take the proper time he needs. We cannot let this continue.

  • @j100j
    @j100j Месяц назад +4

    I've loved Euler's formula since I saw it back in middle school.

  • @johnstud1os
    @johnstud1os Месяц назад

    I LOVE this so much! The execution of this video is so satisfying and well done. Keep it up MAKiT!!

  • @MrBlaze2126
    @MrBlaze2126 Месяц назад

    Finally I got time to watch it! And I really appreciate that you explained the polar coordinates. I have been wondering what on earth it was.

  • @Lonschn.
    @Lonschn. Месяц назад

    You uploading is by far the best Christmas present this year

  • @mathpuppy314
    @mathpuppy314 Месяц назад +2

    Somehow this math guy has a better sense of humor than 99% of the world. Every video is such a pleasure to watch!
    11:53 seems good and efficient that you're also zooming out to show us the premier window, I'm sure that was just a copy and paste edit job.

  • @redmask6085
    @redmask6085 Месяц назад

    Great video, love your stuff. It's truly amazing how intuitve and fun you make those topics, like- and I really mean it, you're the best math channel on youtube I know

  • @Insuranceagentguy
    @Insuranceagentguy Месяц назад +1

    This is probably one of my favorite proofs in mathematics. Nicely explained!

  • @Bookie9477
    @Bookie9477 Месяц назад +1

    Great vid dude, I wish more schools would take the time to explain this stuff like you do instead of just jamming equations down students' throats.

  • @pugbloxgaming6397
    @pugbloxgaming6397 Месяц назад

    Great video I loved the graphics and the understandable way you explained it, besides the good jokes, ¡please keep on the amazing job! 😄👏

  • @alvinoceanohorsky6093
    @alvinoceanohorsky6093 Месяц назад

    Great video MAKiT as always. You must have spent a lot of time with these animations but it's just this that makes your videos special. Great job

  • @k4ktus1k50
    @k4ktus1k50 Месяц назад

    i’m in love with ur videos. Never stop making videos

  • @mega_mango
    @mega_mango Месяц назад

    I freaking love your channel dude

  • @synonys
    @synonys Месяц назад +4

    1:14 you just explained quadratic equations better in one picture than semesters of universities!!!

    • @akeebplazy1124
      @akeebplazy1124 Месяц назад +2

      I'm sorry but which place are u studying in that they teach u Quadratics in universities

    • @synonys
      @synonys Месяц назад

      @ it’s an exaggeration…

  • @mijailtoka9817
    @mijailtoka9817 Месяц назад

    Such a nice video!!
    One small thing I noticed, maybe it was intentional or not but in 10:35 to make the parentheses of the (1/2)^n look nicer in LaTeX, which im guessing you are using (maybe you are Manim or something to the effect which uses latex to write out equations), you could do \left(\frac{1}{2}
    ight)^n and that way the parentheses go up to de top of the 1 and the bottom of the 2.
    Keep it up, your vids are great!!

  • @joziahelliott1976
    @joziahelliott1976 Месяц назад +1

    This is literally perfect video i was just wondering were this came from

  • @gabrielribeiro222
    @gabrielribeiro222 Месяц назад +1

    Love ur vídeos.
    Hope your chanel grows a lot.

  • @thebeardman7533
    @thebeardman7533 Месяц назад +9

    Don't worry physicists won't mind putting infinity in functions only mathematicians would mind

    • @M_1024
      @M_1024 24 дня назад +1

      And engineers would just put 1*10¹² because that's big enough.

    • @infernoslayer5393
      @infernoslayer5393 23 дня назад

      ​@@M_1024well of course it is, 3.14159 is good enough unless ur making a massive circle for some reason, 10^12 is big enough for most anything

  • @ARKGAMING
    @ARKGAMING Месяц назад

    This is so entertaining
    I'm so glad RUclips recommended this to me

  • @Student-jd8vf
    @Student-jd8vf Месяц назад

    Your 3d cinematics are increasing exponentially!

  • @paliophysical4481
    @paliophysical4481 Месяц назад

    Holy crao its the video i requested. Thanks makit. I love you man.

  • @aComedicPianist
    @aComedicPianist Месяц назад +1

    19:09 There are two i^(4n+3) equations, but one is obviously i^(4n+4), which I would say would probably be better written as i^(4n) as 4n+4 would be 4(n+1) which could just be set as 4(n), changing where you start, almost like the difference between 0123456789 and 1234567890.

    • @aComedicPianist
      @aComedicPianist Месяц назад

      Also, when the phone alarm started to ring, that’s the only time at the end of the video it’s not on the desk ironically.

  • @DDP-Gaming
    @DDP-Gaming Месяц назад +1

    amazing animations as always :)

  • @C8H13O5N
    @C8H13O5N Месяц назад +1

    Leaving a comment to boost the algorithm

  • @randigo9992
    @randigo9992 Месяц назад

    I recently was trying to think about the fundamentals of everything, the most fundamental rules of the universe and logic. It's like objects could be defined by their properties, you could define anything as an object and all objects have properties, math is made to describe those properties, so you could compare and operate that stuff, idk what else to add

  • @Unknow5622-b1g
    @Unknow5622-b1g Месяц назад +2

    How we will make a video about binomial theorem ? May be how to build up Taylor series ? (I haven't found a video that explains it so clearly yet)

  • @shobhitaagrawal
    @shobhitaagrawal Месяц назад

    You better explain the whole intuition behind every topic of maths before i die

  • @maestro3887
    @maestro3887 Месяц назад

    It's so sad that the "higher level" math (what I mean is math you need any background knowledge for, even if it's only things like Complex Numbers and basic integration knowledge) is not popular enough for your awesome work to be sustainable. Respect for still making those high quality videos!

  • @r3birth
    @r3birth Месяц назад +12

    comment for algorithm, love you makit!

  • @ddx5899
    @ddx5899 Месяц назад

    Keep going big guy, ull make it big

  • @kohlenoxyd
    @kohlenoxyd Месяц назад

    oh boy time to watch MAKiTs new vid like five times

  • @GoodBaleadaMusic
    @GoodBaleadaMusic Месяц назад

    Your content is is seriously awesome. The word inuition MADE ME CLICK Any low likes or views is because of volume. Dont be afraid to be loud. Be conscience of consistent highs and mids when you use vocal effects. Dont stop with the effects lol

  • @RishiVaish-ym1nr
    @RishiVaish-ym1nr 4 дня назад

    Great video 🌟

  • @potogen.0m0
    @potogen.0m0 Месяц назад +1

    14:26 why did the like get said 2 times there (in a demonic voice, i might add.)
    EDIT: Oh right, it's MAKiT's voice changer failing, his true voice is demonic because he is all powerful, our lord and savior MAKiT.

  • @SnakeOcelot
    @SnakeOcelot Месяц назад +10

    18:13 Hey, fantastic video! But I just want to point out a little mistake here: those are not the taylor series for sin e cos; instead, the first one is the one for cos (not sin) and the second one is for negative sin (not cos). I think you just got a little confused with the values of sin and cos, but except for that this is really an excellent video, so keep up the good work! 😊

  • @TheEliteMan723
    @TheEliteMan723 Месяц назад

    Great video as usual

  • @rubiscubesauvage9591
    @rubiscubesauvage9591 Месяц назад

    bro explain so well than understand (and i don't know the all the derivative part didn't study yet ) and English isn't my native language good continuation !

  • @tmodx
    @tmodx Месяц назад +1

    Banger

  • @benjaminmllebjerg8044
    @benjaminmllebjerg8044 Месяц назад

    That was a good video, well done.

  • @Mashrit
    @Mashrit Месяц назад +1

    18:07 that's the taylor series for cos
    18:20 that's the taylor series for -sin

  • @aravindakannank.s.
    @aravindakannank.s. Месяц назад

    Bro u r underated keep rocking bro

  • @NotHungarian
    @NotHungarian Месяц назад +1

    rigorous and intuitive is 3blue1browns's job

  • @joziahelliott1976
    @joziahelliott1976 Месяц назад +3

    There's a mistake at 18:02 it should be a minus sign after the x^4/24

  • @CT-sixes
    @CT-sixes Месяц назад

    Well, another MAKiT upload another banger where he lets his god complex out of control

  • @akshatrai9007
    @akshatrai9007 Месяц назад

    18:13 there's a silly mistake.
    Great video by the way ❤

  • @antoninnovak5074
    @antoninnovak5074 Месяц назад +1

    Hey MAKiT, I love your videos. Have you tried moving the streams for charity to a different channel? Just to try what is RUclips algorithm going to think about it. I think it could help your channel to be recommended more.

  • @calamitalcomputers
    @calamitalcomputers Месяц назад +1

    when i studied e^iπ, maclaurin and his expansions hard carried me

  • @no-ib2kr
    @no-ib2kr Месяц назад +1

    Makit please make a video on how intermolecular forces fit in the standard model and the four forces i feel like science will only make sense once I find out what it is

    • @MAKiTHappen
      @MAKiTHappen  Месяц назад +2

      Intermolecular forces ARE the four forces.
      It's electromagnetism to be exact if I'm not mistaken

    • @killianobrien2007
      @killianobrien2007 Месяц назад +1

      Electron charge makes each molecule a dipole

  • @Shadoxite
    @Shadoxite Месяц назад

    I understood none of that lmao but I am gonna watch it again
    EDIT: OMGG I AM A GENIUS NOW AND I HAVE A SECOND BRAIN GROWING

  • @Walter12347
    @Walter12347 Месяц назад +1

    18:04
    It looks like you found the taylor series for cosine then negative sine here.

  • @Rotbeam99
    @Rotbeam99 Месяц назад +1

    the fake greenscreen is a nice touch

  • @K0nam3Two
    @K0nam3Two Месяц назад +3

    Can you make a video about the other euler formula?

    • @MAKiTHappen
      @MAKiTHappen  Месяц назад +6

      Yeah, I have it scheduled right in between the eulers constant, and the other other eulers formula

  • @mylesvmiles7571
    @mylesvmiles7571 Месяц назад

    Just wanted to say i was around when he was at 10k subs

  • @the33rdguy
    @the33rdguy Месяц назад

    Bro keep going. The algorithm will notice!!! Trust!

  • @mo-dodo4224
    @mo-dodo4224 Месяц назад

    Great Video!
    btw whats the music used it's so smooth

  • @moozcode6882
    @moozcode6882 Месяц назад

    Great video :]

  • @leciniminis144
    @leciniminis144 Месяц назад +1

    13:24 the third derivative can be called “aberrancy”

  • @RalphScott-wu8ei
    @RalphScott-wu8ei Месяц назад

    The derivative is parallel. The fourth derivative is the same number you started off with; if e^(a*0) is always 1, then the only possible function is a rotation left by a from 1.

  • @Epoch11
    @Epoch11 Месяц назад +1

    I just turned 46 and when I think back to my time in high school from 92 to 96, I can picture how much I absolutely hated mathematics with a passion. I flunked algebra and trigonometry. Fast forward to my Community College days and I am forced to take the class again as I am trying to get my degree in engineering. This time however I have a great teacher. And does my grade improve to a D or even a C? Nope, I got an A. All because I had a competent teacher who would do things like this and show us where things came from. It seems like half the teachers in America don't really understand mathematics and are ill-equipped to teach it.

  • @advikdutta
    @advikdutta 13 дней назад

    We have to submit to Makit for he is a GOD

  • @Sng4
    @Sng4 Месяц назад

    Once again, leaving a comment for the algorithm :D

  • @mani_mincraft
    @mani_mincraft Месяц назад

    Damn your videos are really good and you make me laugh every time.

  • @mcmann7149
    @mcmann7149 Месяц назад

    Very interesting video. Obviously, you're not going to be perfect in everything, but I would be willing to wait longer for explanations for certain analytical functions such as the radius of divergence.

  • @ElusiveEel
    @ElusiveEel Месяц назад

    but the picture you're drawing is not "the reason why" 2:11 is so, combinatorics is. there's one way to choose x^3, there's 3 ways to choose x^2y, there's 6 ways to choose xyz etc.
    that also doesn't generalise to higher dimensions. try visualising the 5D hypercube cut up by (x+y+z)^5

  • @CosmicHase
    @CosmicHase Месяц назад

    This is exactly how I'd teach my bro maths.
    I have no idea what you are saying tho.

  • @jpase
    @jpase Месяц назад

    Guys don't worry about his fridge, his mask doesn't have a mouth and therefore he doesn't need to eat. He is a god afterall, right?

  • @lucascsrs2581
    @lucascsrs2581 12 дней назад

    If 3blue1brown was a zoomer LOL
    Keep the amazing work bro!

  • @henricobarbosa7634
    @henricobarbosa7634 Месяц назад

    Loved it 😂

  • @mavinu4845
    @mavinu4845 Месяц назад

    commenting for a future filled fridge

  • @rubiscubesauvage9591
    @rubiscubesauvage9591 Месяц назад

    keep going

  • @denorangebanan
    @denorangebanan Месяц назад +1

    my autism loves this

  • @ibi_DoesAlot
    @ibi_DoesAlot Месяц назад +1

    for the algorithm

  • @georgecop9538
    @georgecop9538 Месяц назад +1

    6:04 I guess no one cares about rotation matrices. Sad

  • @SayandipRoy-n7j
    @SayandipRoy-n7j Месяц назад

    So underrated !!!! 😢😢

  • @vincehomoki1612
    @vincehomoki1612 Месяц назад +1

    What is wrong with you, RUclips???

  • @prernabhatt1952
    @prernabhatt1952 Месяц назад

    great :)

  • @Nerdiest_nerd
    @Nerdiest_nerd Месяц назад

    At 1:56 shouldn't (x+y)³ be x³+y³+3x²y+3y²x, i think u accidentally missed that,apart for that good video😊

    • @MAKiTHappen
      @MAKiTHappen  Месяц назад

      Well... I can't really argue about math with the nerdiest nerd

  • @ineedabettername1
    @ineedabettername1 21 день назад

    Nice

  • @wajihkassraoui96
    @wajihkassraoui96 Месяц назад +1

    If you read my comment then I'm lucky I'm searching for => in frensh (devlopment limité)
    Like
    exp(x)=1+x+x²/x+ø(x²)
    This DL2 where lim x->0 ø(x²) =0
    Ther is some other formulas
    And I need to understand from where they come and ther applications

  • @turbulance1720
    @turbulance1720 Месяц назад

    I'm mad now because he didn't say MAKiT happen! Grr!

  • @BrokenBreaking
    @BrokenBreaking Месяц назад

    Omg could it really be!!

  • @Caeleb-rw4hl
    @Caeleb-rw4hl Месяц назад

    Am I losing it or is this dude in the current Fortnite battle pass

  • @theebefuddled
    @theebefuddled Месяц назад

    Form Voltron with another channel(s) and save Us all ...

  • @elliotthedoge9456
    @elliotthedoge9456 Месяц назад +1

    Why is there the Taylor series in the image

    • @MAKiTHappen
      @MAKiTHappen  Месяц назад +4

      You will not believe what sum I'll use to prove eulers in the video

    • @elliotthedoge9456
      @elliotthedoge9456 Месяц назад

      I am outraged that you said the radius of convergence was boring, fucking Abel was a genius that some mf called Cauchy did not review their manuscript

    • @elliotthedoge9456
      @elliotthedoge9456 Месяц назад

      "The rigorous side" proceeds to forget to mention all fucking conditions for anything you've done

    • @elliotthedoge9456
      @elliotthedoge9456 Месяц назад

      NO WAY MAXWELL EQUATIONS TEASER
      I CAN'T STOP rot(B) = μj + dE / dt