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@ne_ochen_horosho835

4 ай бұрын

❤

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

@glumbortango7182

3 жыл бұрын

For a number of reasons in fact.

@dionysianapollomarx

3 жыл бұрын

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

@rogerkearns8094

3 жыл бұрын

@@dionysianapollomarx My point.

@oledakaajel

3 жыл бұрын

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

@user-kf5gp2yj9i

3 жыл бұрын

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

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

@BriTheMathGuy

3 жыл бұрын

Woah! I did not know that, cool!

@karldavis7392

3 жыл бұрын

16 digits is a whopping good approximation.

@Paul93Ye

3 жыл бұрын

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

@karldavis7392

3 жыл бұрын

@@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

3 жыл бұрын

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.

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

3 жыл бұрын

Parseval’s identity?

@northernskies86

3 жыл бұрын

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

3 жыл бұрын

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

@Untoldanimations

2 жыл бұрын

@@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

Жыл бұрын

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,…

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

@BriTheMathGuy

3 жыл бұрын

Ya gotta hand it to Euler!

@peterfireflylund

3 жыл бұрын

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

@theblinkingbrownie4654

3 жыл бұрын

@@peterfireflylund too bad he lost it

@Veritas47

3 жыл бұрын

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

3 жыл бұрын

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

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

@BriTheMathGuy

3 жыл бұрын

Very glad you enjoyed it!

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

@Kevin-14

3 жыл бұрын

Pero bueno maik, que haces acá también jajajaja

@BriTheMathGuy

3 жыл бұрын

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

@MatesMike

3 жыл бұрын

@@Kevin-14 estoy en todas partes jeje

@war_reimon8343

3 жыл бұрын

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

@mathhack8647

2 жыл бұрын

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

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.

2 жыл бұрын

Yes, that's a great follow up to this video! Here's the link. kzread.info/dash/bejne/lmGjlcd7adbMnNY.html

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

3 жыл бұрын

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

2 жыл бұрын

@@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

2 жыл бұрын

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

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!

@BriTheMathGuy

2 жыл бұрын

Thanks so much!

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

@andreasxfjd4141

3 жыл бұрын

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

@kartashuvit4971

3 жыл бұрын

@@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

3 жыл бұрын

@@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.

2 жыл бұрын

Euler was indeed a genius!

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

@BriTheMathGuy

3 жыл бұрын

You're so welcome!

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

@BriTheMathGuy

2 жыл бұрын

Glad you liked it!

You're knowledge! Hats off 💫👑

I love this! Thank you!

@BriTheMathGuy

3 жыл бұрын

You're so welcome!

Loved the video and the development. 👌

@BriTheMathGuy

3 жыл бұрын

Glad you enjoyed it!

Love your videos!

@BriTheMathGuy

3 жыл бұрын

Thank you! Have a great day!

Amazing video, as always!

@BriTheMathGuy

3 жыл бұрын

You're the best!

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

@speedlunary797

3 жыл бұрын

The title says world famous

@p_square

3 жыл бұрын

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

I love the black background! It's soothing to the eyes on an amoled screen

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

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

This was a really well made video.

@BriTheMathGuy

3 жыл бұрын

Glad you thought so! Thanks for watching!

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,…

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

@BriTheMathGuy

3 жыл бұрын

Thank you! Cheers!

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!

Awesome solution man.

@BriTheMathGuy

2 жыл бұрын

Glad you think so!

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.

Brilliant!

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.)

Nice explain!

@BriTheMathGuy

3 жыл бұрын

Glad you think so!

I love it!

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

3 жыл бұрын

Glad to hear that! Thanks for watching!

this channel is awesome

@BriTheMathGuy

3 жыл бұрын

Glad you think so! Have a great day!

That’s great video

Wow just brilliant 😍

@BriTheMathGuy

3 жыл бұрын

Glad you like it!

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

Yeah I totally understood all that.

What Famous result should we look at next?!

@bakhridinova6482

3 жыл бұрын

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

@danielmago4327

3 жыл бұрын

gaussian integral

@MithicSpirit

3 жыл бұрын

@@bakhridinova6482 it's quite a nuanced topic to cover in Bri's short video style, I instead recommend Mathologer's video on it: kzread.info/dash/bejne/i6l9q8yFopnchaQ.html

@MithicSpirit

3 жыл бұрын

@@danielmago4327 already done kzread.info/dash/bejne/hWttrbKredDFd8Y.html

@nubex2420

3 жыл бұрын

integral of sin(x)/x

wonderful ❤

@BriTheMathGuy

3 жыл бұрын

Thank you! Cheers!

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

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

That's interesting!

@BriTheMathGuy

3 жыл бұрын

Glad you thought so! Have a great day!

I seem to recall that there is a decent easy formula for the series 1 / n^2k for positive integers k. I'm guessing many people have thought about this already, but it seems like some sort of similar manipulation could get us the odd powers too?

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

@pogclippers4098

3 жыл бұрын

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

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

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

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

@showmikbiswas4272

3 жыл бұрын

Yes.

@angelmendez-rivera351

3 жыл бұрын

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

@lyrimetacurl0

2 жыл бұрын

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

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

Amazing

@BriTheMathGuy

2 жыл бұрын

You are!

Sir please make a video on this question next Integral from 0 to 2pi(1/(3+2sin(x))dx Using contour integrals

This video just brought joy to me.

@BriTheMathGuy

3 жыл бұрын

Very happy to hear it! Have a wonderful day!

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

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)

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

Petition to send this back in time.

co-efficient

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.

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

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?

Cool 👌🏼

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

Wow!

@BriTheMathGuy

3 жыл бұрын

🤯

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

3 жыл бұрын

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

3 жыл бұрын

@@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

3 жыл бұрын

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

@thijsdekok798

3 жыл бұрын

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

Great

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

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 .

I like your funny words funny man

So from this method we can also determine the sum of the first fourth powers and sixth and eighth etc. ? Cool!

tres interessant

The probability that any two random numbers are Coprime is 6/pi^(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?

@user-qb5gv3pi1l

Ай бұрын

Hlo

Class 11th student watching this❤

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

2 жыл бұрын

haha.

@Eye-vp5de

4 ай бұрын

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

This Is purely beautiful

@BriTheMathGuy

3 жыл бұрын

Glad you think so! Have a great day!

What is the difference? sqrt((-1)^2) and sqrt((-1))^2 ?

the fundamental theorem of algebra applies to polynomials of finite order. How does it work for an infinite order polynomial such as the one in the video?

@angelmendez-rivera351

3 жыл бұрын

Weierstrass factorization theorem.

@bastiana.n.4277

3 жыл бұрын

@@angelmendez-rivera351 Thanks! I haven't taken a complex analysis course yet :(

You should team up with Mathologer

@firstname9845

3 жыл бұрын

Mathologer is my lecturer

@BriTheMathGuy

3 жыл бұрын

I'd love to!

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

@BriTheMathGuy

3 жыл бұрын

😂

@Reports.

3 жыл бұрын

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

3 жыл бұрын

@@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.

3 жыл бұрын

@@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

3 жыл бұрын

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

Does anyone have english subtitles for this?

i'm a viewer from Iran

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

but pi² = g = 10 so pi²/6 = 1.67

@jeaneude9380

3 жыл бұрын

Pi squared isn't equal to 10

@Eye-vp5de

4 ай бұрын

​@@jeaneude9380fundamental theorem of engineering

@CURIOUS_FLAIR

Ай бұрын

This guy is on the moon

3:40 Sum body once told me...

@BriTheMathGuy

3 жыл бұрын

😂

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

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

I can see this channel will grow with more than 5 million subscribers... I just want to say, thank you for your very amazing videos 👍👍👍 and.... I hope you will not forget me when you've achieved that amount of subscribers 😁

Can't we do this with cos and gain values for odd zeta.

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

Solve jee advanced problems those are really interesting

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

@BriTheMathGuy

3 жыл бұрын

I would fail that challenge!!

That Euler dude is pretty smart NGL

😱😱😱😱😭😭😭 AWESOME

This is also written as zeta(2)

@BriTheMathGuy

3 жыл бұрын

True!

1:56 sounds cut lmao

i think you ment bezout theorm not fundamental theorm of algebra

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

@wavez4224

Жыл бұрын

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

@Z7youtube

Жыл бұрын

@@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

Жыл бұрын

@@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

Жыл бұрын

@@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.

I KNEW IT!

@BriTheMathGuy

3 жыл бұрын

Great! Have a wonderful day!

Would that mean that this sum *6 and then taking the sqrt on both sides would be an approximation for pi?

@Avighna

Жыл бұрын

A very slowly converging approximation but yea

"oiler"