If I did this in 1734 I'd be World Famous

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  • เผยแพร่เมื่อ 24 ธ.ค. 2024

ความคิดเห็น • 488

  • @BriTheMathGuy
    @BriTheMathGuy  ปีที่แล้ว +12

    🎓Become a Math Master With My Intro To Proofs Course! (FREE ON TH-cam)
    th-cam.com/video/3czgfHULZCs/w-d-xo.html

  • @rogerkearns8094
    @rogerkearns8094 3 ปีที่แล้ว +2164

    If Euler proved something in 2021 he'd be even more famous.

    • @glumbortango7182
      @glumbortango7182 3 ปีที่แล้ว +91

      For a number of reasons in fact.

    • @dionysianapollomarx
      @dionysianapollomarx 3 ปีที่แล้ว +332

      @@glumbortango7182 including how he is still alive in 2021 to prove something

    • @rogerkearns8094
      @rogerkearns8094 3 ปีที่แล้ว +70

      @@dionysianapollomarx
      My point.

    • @oledakaajel
      @oledakaajel 3 ปีที่แล้ว +55

      Imagine Euler made some secret proof but hid it an it was only found hundreds of years later

    • @김노운-g4l
      @김노운-g4l 3 ปีที่แล้ว +25

      If Gauss or Euler still lived today, the history would be different

  • @ethanyap8680
    @ethanyap8680 3 ปีที่แล้ว +1317

    Cool fact: Euler actually approximated the sum to 16 decimal places and GUESSED that it was pi^2/6 before rigorously proving it

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว +222

      Woah! I did not know that, cool!

    • @karldavis7392
      @karldavis7392 3 ปีที่แล้ว +109

      16 digits is a whopping good approximation.

    • @Paul93Ye
      @Paul93Ye 3 ปีที่แล้ว +116

      I think if you know the result, how to prove it becomes easier with backwards engineering. Still impresive.

    • @karldavis7392
      @karldavis7392 3 ปีที่แล้ว +71

      @@Paul93Ye It definitely helps. I did well in math, but of course cannot compete with these guys. If somebody just gave me the number 1.644934 and asked what it was approximating, nothing in particular would come to mind. Maybe after a while I could figure it out, but I'm sure no competitor to Euler.

    • @karldavis7392
      @karldavis7392 3 ปีที่แล้ว +19

      How would you get 16 digits without a computer? You couldn't just add up terms, because it doesn't converge quickly enough. It would take over 100 million terms. Could it perhaps be done with calculus, finding the area of the smooth curve then estimating the error? I would need to see the method before being confident he actually had 16 digits.

  • @northernskies86
    @northernskies86 3 ปีที่แล้ว +335

    I proved this result using a Fourier series as one of my homework assignments for my math class but the way Euler did it is extremely elegant.

    • @Anteater23
      @Anteater23 3 ปีที่แล้ว +7

      Parseval’s identity?

    • @northernskies86
      @northernskies86 3 ปีที่แล้ว +13

      I did it slightly differently. I expanded x^2 in terms of an exponential Fourier series and evaluated the series at the boundary (x=1).

    • @jumbojimbo706
      @jumbojimbo706 3 ปีที่แล้ว +31

      Ok lad it’s youtube comments you ain’t gotta show off

    • @Untoldanimations
      @Untoldanimations 2 ปีที่แล้ว +2

      @@jumbojimbo706 it’s not showing off it’s a standard thing when you learn the Fourier series. We did the exact same thing plus a few other nice identities for homework

    • @adw1z
      @adw1z 2 ปีที่แล้ว

      Omg I recently proved a result on my example sheet on Fourier Series by accident to show the sum of the reciprocal fourth powers is pi^4/90, I believe if u take the FS of (1-x^2)^2 periodic on (-1,1) gives u this result. I was so fascinated by those, I did more research and managed to find a beautiful closed form solution for zeta(2n), so for n=2,4,6,…

  • @Mutual_Information
    @Mutual_Information 3 ปีที่แล้ว +498

    After watching this, I understand why the people of 1734 would make you famous. That was some serious deduction.

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว +54

      Ya gotta hand it to Euler!

    • @peterfireflylund
      @peterfireflylund 3 ปีที่แล้ว +11

      @@BriTheMathGuy he had a good eye for math, he really did!

    • @theblinkingbrownie4654
      @theblinkingbrownie4654 3 ปีที่แล้ว +15

      @@peterfireflylund too bad he lost it

    • @Veritas47
      @Veritas47 3 ปีที่แล้ว +4

      But then your friend isnt doing harder problems than euler, because relatively euler was doing the most difficult problems of his time and even far ahead of them

    • @trongnghianguyen7133
      @trongnghianguyen7133 3 ปีที่แล้ว +2

      @Good Game i'm hopefully wanna see some tremendous achivement of your friend in the future

  • @eriktempelman2097
    @eriktempelman2097 3 ปีที่แล้ว +109

    Wow, super well done man! This isn't just math anymore, it's mathemagic.

  • @MatesMike
    @MatesMike 3 ปีที่แล้ว +236

    At some point your channel is gonna be Big! You make so easy explanations for difficult problems, and this is awesome!

    • @Kevin-14
      @Kevin-14 3 ปีที่แล้ว +12

      Pero bueno maik, que haces acá también jajajaja

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว +10

      I appreciate that! Thank you very much for watching and have a great day!!

    • @MatesMike
      @MatesMike 3 ปีที่แล้ว +4

      @@Kevin-14 estoy en todas partes jeje

    • @war_reimon8343
      @war_reimon8343 3 ปีที่แล้ว +1

      Maths Mike studying its competence. 😂 😂 😂
      La verdad, tras ver el video he pensado que esto es algo que encajaría en tu canal. ❤️

    • @mathhack8647
      @mathhack8647 2 ปีที่แล้ว

      I already recommended it for my kids . A talented teacher.

  • @tedsheridan8725
    @tedsheridan8725 3 ปีที่แล้ว +47

    My favorite proof of this is to look at a Fourier series of a sawtooth signal, say y = x from -pi to pi. Each sine term will have a 1/n factor. The power of the signal is just the integral of its square, so you end up getting the squares of all the individual sin terms in the series. Equating both sides (the original signal, and it's series) results in sum(1/n^2) on one side, and pi^2/6 on the other. I found this on my own and then learned it was well-known.

    • @karldavis7392
      @karldavis7392 3 ปีที่แล้ว +2

      That's cool, very impressive. I derived the focal length of a spherical section mirror when I was 16, and took the limit as the size gets small, and showed it around my high school. I couldn't get people to believe I didn't find it in some old book. (That was before the internet existed.) It took all the math I had taken up to then, which did not include calc.

    • @karldavis7392
      @karldavis7392 2 ปีที่แล้ว

      @@yahyabenhissoune Thanks. I'm not sure, I just moved and I probably can't find my old papers from high school but I'll look. That was 1986, time flies and details of memories fade, but the general idea was that I calculated the angle of reflection, then took the limit as the size of the mirror approached zero.

    • @gasun1274
      @gasun1274 2 ปีที่แล้ว

      @@karldavis7392 wow if i discovered that i'll proudly flaunt around with that result too

  • @Bodyknock
    @Bodyknock 3 ปีที่แล้ว +45

    Great explanation of this solution. 👍 I think my favorite video on the Basel Problem is the one 3Blue1Brown did where he showed geometrically where the “hidden circle” is in the equation by calculating the brightness of lanterns around a large circle and then looking at the limit as the circle’s radius approaches infinity.

    • @mike1024.
      @mike1024. 2 ปีที่แล้ว

      Yes, that's a great follow up to this video! Here's the link.
      th-cam.com/video/d-o3eB9sfls/w-d-xo.html

  • @kartashuvit4971
    @kartashuvit4971 3 ปีที่แล้ว +37

    I really enjoyed this derivation of the famous sum. The application of the fundamental theorem of algebra to solve this is genius.

    • @andreasxfjd4141
      @andreasxfjd4141 3 ปีที่แล้ว

      As this sum was solved (calculated), the fundamental theorem of algebra was not proved.

    • @kartashuvit4971
      @kartashuvit4971 3 ปีที่แล้ว

      @@andreasxfjd4141 Regardless... I'm sure Euler based his deductions on logical reasoning. It makes a lot of sense that a polynomial can be written as products of its roots, so he went with that. And on and on... until he arrived to a result, that when calculated, yields the exact values that you would get from brute force calculating 1 + 1/2! + 1/3! + ...
      Either it was a huge coincidence, or he stumbled on an important mathematical result

    • @angelmendez-rivera351
      @angelmendez-rivera351 3 ปีที่แล้ว +1

      @@andreasxfjd4141 The result is not based on the fundamental theorem of algebra, but on the Weierstrass factorization theorem, which extends the fundamental theorem of algebra from the integral domain of polynomial functions to the integral domain of entire functions.

    • @mike1024.
      @mike1024. 2 ปีที่แล้ว

      Euler was indeed a genius!

  • @pragyaatiwarii
    @pragyaatiwarii 3 ปีที่แล้ว +13

    You explained this so easily wow .. Thank you so much. 💕

  • @Leptus87
    @Leptus87 2 ปีที่แล้ว +2

    As a student at Technical University - I had A grades from calculus and B+ from linear Algebra. I am also Math passionate from primary school, but my skills were boosted by very particular and demanding teacher in secondary school.You use a lot of tricks which are known for me, but some are really brillant and I see few of them first time! To proof equation mentioned in this video I use a bit different approach. I use Fourier series. To be more meaningfull - I use express function f(x) = ×^2 for x and then with help Dirichlet's conditions and with Fourier's series we can obtain pi^2/6. I am amazed with you calculus skills. Quite decent! You are doing it really great! When I see it, I am a bit claimer, that there are on earth Math passionates like me ;). Cheers!

  • @PunmasterSTP
    @PunmasterSTP 3 ปีที่แล้ว +5

    Wow, I am loving your videos! Sometimes people just launch into an explanation without taking a step back and giving a broader context, or discussing their approach. I really appreciate how you structure your videos, and how you explain the concepts inside of them. Keep up the great work!

  • @phamthehung2
    @phamthehung2 3 ปีที่แล้ว +4

    Your explanation is the best I've seen on ytube; concise and clear.

  • @angelmendez-rivera351
    @angelmendez-rivera351 3 ปีที่แล้ว +8

    For those who are curious about the manipulation that factored sin(x)/x into infinitely many monomials, this is made rigorous by the Weierstrass factorization theorem, which is a generalization of the fundamental theorem of algebra.

  • @p_square
    @p_square 3 ปีที่แล้ว +54

    You are already famous! 58k subs isn't a joke :)

    • @speedlunary797
      @speedlunary797 3 ปีที่แล้ว

      The title says world famous

    • @p_square
      @p_square 3 ปีที่แล้ว +4

      @@speedlunary797 Its not that people are watching him from only one country... People from many countries are watching him

    • @billcook4768
      @billcook4768 4 หลายเดือนก่อน

      Makes me wonder. In his lifetime did 58k people read Euler?

  • @BriTheMathGuy
    @BriTheMathGuy  3 ปีที่แล้ว +270

    What Famous result should we look at next?!

    • @bakhridinova6482
      @bakhridinova6482 3 ปีที่แล้ว +28

      1+2+3+...=-1/12 please

    • @danielmago4327
      @danielmago4327 3 ปีที่แล้ว +7

      gaussian integral

    • @MithicSpirit
      @MithicSpirit 3 ปีที่แล้ว +3

      @@bakhridinova6482 it's quite a nuanced topic to cover in Bri's short video style, I instead recommend Mathologer's video on it: th-cam.com/video/YuIIjLr6vUA/w-d-xo.html

    • @MithicSpirit
      @MithicSpirit 3 ปีที่แล้ว +2

      @@danielmago4327 already done th-cam.com/video/S79KPrIm_Gc/w-d-xo.html

    • @nubex2420
      @nubex2420 3 ปีที่แล้ว

      integral of sin(x)/x

  • @CarloPinciroli
    @CarloPinciroli 3 ปีที่แล้ว +7

    This was a really well made video.

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว

      Glad you thought so! Thanks for watching!

  • @gitanjalideb454
    @gitanjalideb454 ปีที่แล้ว +2

    And by curiosity i found that- Summation of 1/{(2n+1)^2} from n=0 to n=∞ is => π^2/8.

  • @crazyr303
    @crazyr303 3 ปีที่แล้ว +4

    Love your videos!

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว +1

      Thank you! Have a great day!

  • @mu.makbarzadeh2831
    @mu.makbarzadeh2831 3 ปีที่แล้ว +2

    I love this! Thank you!

  • @kalseru
    @kalseru 3 ปีที่แล้ว +2

    Amazing video, as always!

  • @jacobmobin978
    @jacobmobin978 3 ปีที่แล้ว +2

    Hard enough to solve the damn problem, let alone Edit in all the graphics, key frames, lighting effects, and scripting to make it as simple to understand,
    Good job man! :D

  • @sayantansinha2735
    @sayantansinha2735 3 ปีที่แล้ว +11

    How man?? How with such ease?? Hats off 🙏♥

  • @war_reimon8343
    @war_reimon8343 3 ปีที่แล้ว +1

    Loved the video and the development. 👌

  • @nadavkopit
    @nadavkopit 8 หลายเดือนก่อน

    Great video. A minor (yet important) correction : in timestamp 1:56 , in the last line, the "greenish" zero should be inside curly braces, since "backslash" subtraction is defined between two sets ( it is undefined between a set and an element.)

  • @joelchristophr3741
    @joelchristophr3741 ปีที่แล้ว

    You're knowledge! Hats off 💫👑

  • @stevenp7991
    @stevenp7991 6 หลายเดือนก่อน

    excellent explanation. thank you

  • @Arriyad1
    @Arriyad1 6 หลายเดือนก่อน

    You deserve to be famous as you managed to explain this in 4 minutes

  • @div_07
    @div_07 2 ปีที่แล้ว +2

    Yeah I totally understood all that.

  • @yuvalmaharshak5566
    @yuvalmaharshak5566 3 ปีที่แล้ว +2

    WOW, I didn't understand most of it but it seem that for someone with math knowledge bigger than first semester you will teach him great

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว

      Glad to hear that! Thanks for watching!

  • @derkach7907
    @derkach7907 3 ปีที่แล้ว +1

    And I was sitting here 95% of the time thinking the answer must be 2...

  • @kikilolo6771
    @kikilolo6771 6 หลายเดือนก่อน

    And there are still people out there saying Euler isn't a physicist

  • @adw1z
    @adw1z 2 ปีที่แล้ว +1

    U should do a video extending this formula to zeta(2n), I would love that! Recently did a talk on it using a very similar method which uses the weierstrass infinite product for sinh rather than sine, to generalise it for n = 2,4,6,…

  • @hydrochloricacid2146
    @hydrochloricacid2146 2 ปีที่แล้ว +1

    We were TRICKED into proving this in Signal processing class (in a slightly backwards way of course)

  • @Vivek_Yadav1143
    @Vivek_Yadav1143 5 หลายเดือนก่อน

    Beautiful!

  • @BenBen-bb7bb
    @BenBen-bb7bb 3 ปีที่แล้ว +6

    Yea I’m in algebra 2 and trigonometry I have no clue what’s going on right now

    • @pogclippers4098
      @pogclippers4098 3 ปีที่แล้ว

      the taylor series is the difficult part. The rest is basic I would say. The more impressive is how he connected the dots. And the sheer algebraic parkour he went through

  • @haydenmartin1197
    @haydenmartin1197 3 ปีที่แล้ว +1

    this channel is awesome

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว

      Glad you think so! Have a great day!

  • @Nole2701
    @Nole2701 3 ปีที่แล้ว +5

    If I proved that the sum of the squares of the 2 sides of a right angled triangle equaled the square of the hypotenuse in 2000 BC, I'd be world famous.

    • @GodbornNoven
      @GodbornNoven 2 ปีที่แล้ว

      haha.

    • @Eye-vp5de
      @Eye-vp5de 11 หลายเดือนก่อน

      If I was born in 100000 BC I'd be world famous

  • @RafaxDRufus
    @RafaxDRufus 3 ปีที่แล้ว +4

    3:40 Sum body once told me...

  • @yb3604
    @yb3604 9 หลายเดือนก่อน

    that is ABSOLUTELY brilliant!!!!!!!!!!!!!!

  • @dibyojyotibhattacherjee897
    @dibyojyotibhattacherjee897 2 ปีที่แล้ว

    Awesome solution man.

  • @ASingMusic
    @ASingMusic 9 หลายเดือนก่อน +1

    Class 11th student watching this❤

  • @JoelPlay
    @JoelPlay 2 ปีที่แล้ว +1

    Me at night watching this before I go to bed:
    "Yeah I think I get it"

  • @RazorM97
    @RazorM97 3 ปีที่แล้ว

    Petition to send this back in time.

  • @Felipe-sw8wp
    @Felipe-sw8wp 2 ปีที่แล้ว

    “Read Euler, read Euler, he is the master of us all.” -- Laplace

  • @KevinBravo1993
    @KevinBravo1993 3 ปีที่แล้ว +4

    This video just brought joy to me.

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว +1

      Very happy to hear it! Have a wonderful day!

  • @K_V-S
    @K_V-S 6 หลายเดือนก่อน

    Majestic Euler clicked it 🗿

  • @nishantkumartiwari1202
    @nishantkumartiwari1202 3 ปีที่แล้ว

    Calculating (-1/2)! by a method adopted by myself -
    Let's calculate C(n,1), of course it is n . Put n=1/2 so C(1/2,1) is equal to 1/2
    apply formula of combination C(1/2,1)= (1/2)!/{1!(-1/2)!} . Now knowing 1/2! as √π/2 , equate both equations and hence we get value of (-1/2)! as √π . Incredible .
    Similarly we can calculate some more negative and fractional factorials .
    If you know this trick already, then this trick has been already discovered, but if no one knows this trick then I am the first to use this .

  • @yatharthgupta6468
    @yatharthgupta6468 3 ปีที่แล้ว +2

    Wow just brilliant 😍

  • @yousef1354
    @yousef1354 2 ปีที่แล้ว

    I didn't understand most of this and it make want to learn more of It.

  • @Handelsbilanzdefizit
    @Handelsbilanzdefizit 3 ปีที่แล้ว +3

    The volume of a 4dimensional sphere with radius 1 is: π²/2.
    So the basel problem is a third of that. Maybe you could prove it with 4-spheres.

  • @MathZoneKH
    @MathZoneKH 3 ปีที่แล้ว

    That’s great video

  • @ERRORRubiksZeraBrand
    @ERRORRubiksZeraBrand ปีที่แล้ว

    When i was using a n infinite series calculator, i accidently put in this and i remembered what 3b1b said .

  • @magicmike1122
    @magicmike1122 8 หลายเดือนก่อน

    I have a question. If you had the product of a Power Series’ roots, like we did in this problem (1+x/π)(1-x/π)•••
    How can you then find the power series for that?
    In other words, the product of the roots in this video also happens to be the product of the roots for Tan(x)/x so how do we know the power series isn’t this, but it’s sinx/x

  • @adityadharpal5879
    @adityadharpal5879 8 หลายเดือนก่อน +1

    I have a doubt if we write in the sinx/x =(1-x²/π)............
    We can also write log(x) =(1-x) but reality is not correct

  • @TheAwesomeJordy
    @TheAwesomeJordy 3 ปีที่แล้ว

    Brilliant!

  • @potatoesandducks958
    @potatoesandducks958 3 ปีที่แล้ว

    Woah woah I just found this channel and
    What do you mean such quality content isn't made by a million sub channel?

  • @mathhack8647
    @mathhack8647 3 ปีที่แล้ว +1

    B
    R
    A
    V
    O
    This is well presented for the mere mortals.

  • @joshuajoshua46
    @joshuajoshua46 3 ปีที่แล้ว

    The probability that any two random numbers are Coprime is 6/pi^(2).

  • @我妻由乃-v5q
    @我妻由乃-v5q 3 ปีที่แล้ว

    I love it!

  • @akankshasharma7498
    @akankshasharma7498 3 ปีที่แล้ว +88

    To be famous in 1734:
    1) know all results from high school
    2) be observant
    To be famous now:
    1) tiktok 😑

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว +11

      😂

    • @Reports.
      @Reports. 3 ปีที่แล้ว +7

      Well not everyone likes Tiktolk I personally cring when watching it. Once I cringed so hard to the point where I just couldn't watch people try to act/be funny, and we all know that people mostly watch Tiktok to laugh/disconnect from reality.

    • @grubbygeorge2117
      @grubbygeorge2117 3 ปีที่แล้ว +1

      @@Reports. Just because you and some others (including myself) do not watch the tiktoks doesn't mean that it is not a way to fame and some great money, though!

    • @Reports.
      @Reports. 3 ปีที่แล้ว +3

      @@grubbygeorge2117 I never claimed that it is not, I'm just mentioning that it is not something everyone likes because of all the simps, attention seekers, psychos, and ''girl power movement/man-hating''. Given there are actually funny people there but the majority are the states above.

    • @grubbygeorge2117
      @grubbygeorge2117 3 ปีที่แล้ว +1

      @@Reports. none of the things you listed are specific to the platform though

  • @aashsyed1277
    @aashsyed1277 3 ปีที่แล้ว

    0:57 but i dont see how sinx has that product representation. i graphed it and it was not even close.

  • @AvivCMusic
    @AvivCMusic ปีที่แล้ว

    That Euler dude is pretty smart NGL

  • @duckyoutube6318
    @duckyoutube6318 5 หลายเดือนก่อน

    Huh...
    I was thinking using the sum of squares formula for the bottom
    So that.
    Sum of x^2=(x+1)(2x+1)/6
    And so the sum would be 1 over that. 1/S(x^2)

    • @undecorateur
      @undecorateur 4 หลายเดือนก่อน +1

      It didn't work since 1/(x+y) ≠ 1/x + 1/y for all reals x and y

  • @bizoitz86
    @bizoitz86 ปีที่แล้ว +2

    @BriTheMathGuy I tried something similar with exp(x) - 1 instead of sin(x) and got a different result. Is there a reason why? Did I do math incorrectly?

    • @Colded-h1m
      @Colded-h1m 8 หลายเดือนก่อน

      Hlo

  • @R-OHAN
    @R-OHAN 3 ปีที่แล้ว +1

    Solution: a time machine

  • @alienbroccoli8296
    @alienbroccoli8296 3 ปีที่แล้ว +1

    You should team up with Mathologer

  • @ahmadsrour9802
    @ahmadsrour9802 3 ปีที่แล้ว

    Fucking euler is in every mathematical class i take

    • @someguy650
      @someguy650 3 ปีที่แล้ว

      Take a chill pill

  • @Kdd160
    @Kdd160 3 ปีที่แล้ว

    Nice explain!

  • @arielbrito33
    @arielbrito33 3 ปีที่แล้ว +1

    Great video :)
    . i have a question, why do the x^2 gets the value x=1 at the end?

  • @diywithreza
    @diywithreza 3 ปีที่แล้ว

    i'm a viewer from Iran

  • @sylph2689
    @sylph2689 3 ปีที่แล้ว +2

    That's interesting!

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว +1

      Glad you thought so! Have a great day!

  • @rubenvela44
    @rubenvela44 3 ปีที่แล้ว

    They are trying to take my 3rd tier proof I think I need your help

  • @masminerk9843
    @masminerk9843 3 ปีที่แล้ว +1

    shouldn't the roots be n(pi) -1? as the constant term is 1, one of the factors may be 0 when n(pi) - 1.
    (i think)

  • @byfrax2371
    @byfrax2371 3 ปีที่แล้ว +7

    but pi² = g = 10 so pi²/6 = 1.67

    • @jeaneude9380
      @jeaneude9380 3 ปีที่แล้ว +3

      Pi squared isn't equal to 10

    • @Eye-vp5de
      @Eye-vp5de 11 หลายเดือนก่อน

      ​@@jeaneude9380fundamental theorem of engineering

    • @CURIOUS_FLAIR
      @CURIOUS_FLAIR 8 หลายเดือนก่อน +1

      This guy is on the moon

    • @SteveOmnipotent
      @SteveOmnipotent 6 หลายเดือนก่อน +2

      Engineer moment

  • @bakhridinova6482
    @bakhridinova6482 3 ปีที่แล้ว +2

    wonderful ❤

  • @ramone.chacon5084
    @ramone.chacon5084 3 ปีที่แล้ว

    Excuseme sir, what did you do here at 2:56 I don't understand that factorization 😢

    • @tyler-iy4jk
      @tyler-iy4jk 5 หลายเดือนก่อน

      We just are considering the terms with x^2 in them after distributing out the whole thing. Just look at the first few: -x^2/pi^2 *1, we’re multiplying by 1 for all of those terms so all the terms with x^2 in them stay the same and are added up to get the final coefficient for x^2, then we just factor out x^2

  • @Z7youtube
    @Z7youtube 2 ปีที่แล้ว

    0:31 what exactly does calc 2 contain? cuz we take this representation of sin in high school

    • @wavez4224
      @wavez4224 2 ปีที่แล้ว

      You got an interesting high school then. In my high school we only really took the derivative of functions and did optimization problems.

    • @Z7youtube
      @Z7youtube 2 ปีที่แล้ว

      @@wavez4224
      well, we just took this representation of (sin) and (cos) and (e) to know how did Euler’s formula come, so we don’t actually use those representations in our questions

    • @Z7youtube
      @Z7youtube 2 ปีที่แล้ว

      @@wavez4224
      but yea overall i’m having fun with my math study of high school :) most ppl here don’t because they only rely on what we learn from school or whatever, which is mostly boring and not taught in the best way, but i dig inside the meanings of what i learn throw youtube and have a deeper perspective about it

    • @wavez4224
      @wavez4224 2 ปีที่แล้ว

      @@Z7youtube yea I also felt the same in high school. It felt like we weren’t being taught the full version because most people only take the course to get the credit. I’m now studying computer science in university but considering a switch to math major
      I’m guessing you already know about him but 3blue1brown posts phenomenal videos about math topics. You should check out his videos if you haven’t already.

    • @TelepathShield
      @TelepathShield 3 หลายเดือนก่อน

      I’m in AP calc now, and I’ve gone ahead and learned stuff like this even though we’re just now mentioning derivatives in class, I wish they offered BC

  • @HAHALOSAH
    @HAHALOSAH 2 ปีที่แล้ว

    1:56 sounds cut lmao

  • @StyleMann
    @StyleMann 3 ปีที่แล้ว

    Got this video recommended and have no clue whats going on lmfaoo

  • @xiaoyang1519
    @xiaoyang1519 3 ปีที่แล้ว +1

    It is kinda annoying and highly nontrivial, though, to justify the factorization which was proven much later and is known as Weierstrasse factorization theorem.

  • @JockyJazz
    @JockyJazz 3 ปีที่แล้ว

    Well, you are famous even now.

  • @colecharb
    @colecharb 3 ปีที่แล้ว +1

    Really enjoyed this! We can do this sort of infinite-term manipulation provided that the series converges absolutely, correct?

    • @showmikbiswas4272
      @showmikbiswas4272 3 ปีที่แล้ว

      Yes.

    • @angelmendez-rivera351
      @angelmendez-rivera351 3 ปีที่แล้ว

      Absolute convergence is not sufficient, actually. You also need the series to have an infinite radius of convergence.

    • @lyrimetacurl0
      @lyrimetacurl0 2 ปีที่แล้ว

      Thought he would do sum of 2^n equals -1 😁

  • @ranjitsarkar3126
    @ranjitsarkar3126 3 ปีที่แล้ว +1

    I will challenge you to make a 10 minute video on fermat's last theorem where you will show the proof.

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว

      I would fail that challenge!!

  • @3la5t1c81rdy
    @3la5t1c81rdy 3 ปีที่แล้ว +1

    Real challenge: be world famous in 2021

  • @Thankmel8r
    @Thankmel8r 3 ปีที่แล้ว

    You can still be world famous, if you prove the P/NP conjecture.

  • @drcoungrations
    @drcoungrations 3 ปีที่แล้ว +3

    To solve this strictly without proofing, that INFINITE polynomial may be factorizated, we can consider the function (sin πx)/πx
    In the first of all, let's express this function in the Maclaurin series:
    (sin πx)/πx=1-π²x²/3!+π⁴x⁴/5!...
    On other side, we have Fourier series of piecewise-defined function f(x)=cos αx, where x∈[-π;π] and α∉Z:
    cos αx=((sin πα)/π)(1/α+∑{n=1, to ∞}((-1)ⁿ(2α/(α²-n²))cos nx))
    Put α=t and x=π. Divide by (sin πα)/π and... We get inf. sum for π cot πt into aliquot fractions:
    π cot πt=1/t+∑{n=1, to ∞}((-1)ⁿ(2t/(α²-n²))), where t∉Z
    Subtract from the both parts of equality 1/t, integrate it from 0 to x and use one of rules of log (if logarithms equal, their arguments equal too), we get infinite multiplication for (sin πx)/πx:
    (sin πx)/πx=∏{n=1, to ∞}(1-x²/n²)=(1-x²)(1-x²/4)(1-x²/9)(1-x²/16)..., x∈(-1;1)
    (omg, I'm tired)
    From equal of Maclaurin and Fourier series we have:
    1-π²x²/3!+π⁴x⁴/5!-...=(1-x²)(1-x²/4)(1-x²/9)(1-x²/16)...
    -x²(π²/6)=-x²ζ(2), ζ(x) - dzeta-function. (In 2 it equale infinite sum of n¯². And that's what we need)
    Divide by -x² and finally get:
    ζ(2)=π²/6
    I found this beautiful modification of First Euler's method of solving Basel's Problem absolutely accidentally, when I decided to integrate infinite sum expression of π cot πt to practice XD
    I'm sorry for grammar and lexical mistakes, if I did them. I don't speak English very well :c

    • @drcoungrations
      @drcoungrations 3 ปีที่แล้ว

      By the way, we can very easy solve Basel Problem by Fourier series of x²))

    • @angelmendez-rivera351
      @angelmendez-rivera351 3 ปีที่แล้ว

      You said this is a strict calculation without "proofing" (?), but what you wrote is an alternative proof anyway

    • @drcoungrations
      @drcoungrations 3 ปีที่แล้ว

      @@angelmendez-rivera351, yes... But I wrote "...without proofing, that INFINITE polynomial may be factorizated...". Factorization of infinite polynomials isn't obvious. I proofed calculation with a little other idea)

    • @drcoungrations
      @drcoungrations 3 ปีที่แล้ว

      @@angelmendez-rivera351 I think, that I just did grammar mistake in that sentence) Isn't it?

  • @jayxone
    @jayxone ปีที่แล้ว

    Bro I did this when I was 9 when I was dreaming of infinity

  • @igorkarlic2297
    @igorkarlic2297 3 ปีที่แล้ว

    If I had done it in 1734 I'd have been famous. Grammar police!

  • @mfadhilal-fatih1427
    @mfadhilal-fatih1427 3 ปีที่แล้ว

    Being famous by telling others idea sucks, it felt like doing evil thing

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว

      😈

    • @mfadhilal-fatih1427
      @mfadhilal-fatih1427 3 ปีที่แล้ว

      @@BriTheMathGuy hahaha im sorry, i dont mean to give hate messages or something like that. Im just being sarcastic

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว

      @@mfadhilal-fatih1427 not at all! Have a great day!

  • @antoine2571
    @antoine2571 2 ปีที่แล้ว

    Amazing

  • @Logicallymath
    @Logicallymath 3 ปีที่แล้ว

    my head hurts now

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว +1

      I'm sorry but I hope you have a great day anyhow!

    • @Logicallymath
      @Logicallymath 3 ปีที่แล้ว

      @@BriTheMathGuy thank you
      also can you too a video on what it means to take a number say x to the hyperpower of a fraction I've been curious

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว

      @@Logicallymath I don't know the answer currently but that sounds interesting!

    • @Logicallymath
      @Logicallymath 3 ปีที่แล้ว

      @@BriTheMathGuy Even Bri the math guy doesn't know! OH NO thanks for your time

  • @henning4070
    @henning4070 3 ปีที่แล้ว

    You only use the location of the roots of the function and the fact that the zeroth order of the Taylor series is 1. What would happen if you would take another function with these properties,for example (0.7*sin(x)+0.1*sin(3x))/x? This is another function with a different Taylor series, but the product representation with the roots is the same. Isn't this a contradiction?

  • @kathanshah8305
    @kathanshah8305 3 ปีที่แล้ว +2

    I hope he will cross 500k by end of this year

  • @kabsantoor3251
    @kabsantoor3251 3 ปีที่แล้ว +1

    This is beautiful but how do we know that the rules which hold for polynomials with finite number of terms will also hold for an infinite polynomial (or a power series whatever you call it? ) Like matching terms with same power of x.

    • @thijsdekok798
      @thijsdekok798 3 ปีที่แล้ว

      Matching terms is correct for power series. You could see a powerseries as a vector in the infinite dimensional vector space P(R). Since it is an vector, it has a unique representation in terms of the basis, which are all positive integer powers of x. Therefore two representations of the same vector (the power series) must have the same coefficients.

    • @angelmendez-rivera351
      @angelmendez-rivera351 3 ปีที่แล้ว

      @@thijsdekok798 What you said is not quite correct, and it is a well-known fact that this factorization only works if the series has an infinite radius of convergence, which it does in the case of sinc(x).

    • @angelmendez-rivera351
      @angelmendez-rivera351 3 ปีที่แล้ว

      We know these rules are valid thanks to the Weierstrass factorization theorem.

    • @thijsdekok798
      @thijsdekok798 3 ปีที่แล้ว

      Angel Mendez-Rivera I know, but I wasn’t talking about the factorization, solely about the matching coefficients

  • @muhammadaryasaputra6754
    @muhammadaryasaputra6754 3 ปีที่แล้ว

    I KNEW IT!

    • @BriTheMathGuy
      @BriTheMathGuy  3 ปีที่แล้ว

      Great! Have a wonderful day!

  • @bl_q
    @bl_q ปีที่แล้ว

    oiler 💀

  • @aakashkhamaru9403
    @aakashkhamaru9403 ปีที่แล้ว

    "oiler"

  • @aram8832
    @aram8832 3 ปีที่แล้ว +1

    Wow!