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

The Basel Problem solution is one of the most well known in the mathematical world - but do you know the Basel Problem history? Leonhard Euler was the first to solve the Basel Problem and became famous for it!

Here will will go through the approach to the Basel Problem Euler Proof. I hope you enjoy it!

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#math #brithemathguy #Euler

Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

[BriTheMathGuy]

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[rogerkearns]

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

[ethanyap]

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

[northernskies]

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.

[Mutual_Information]

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

[MatesMike]

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

[eriktempelman]

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

[kartashuvit]

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

[Bodyknock]

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.

[tedsheridan]

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.

[p_square]

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

[pragyaatiwarii]

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

[BriTheMathGuy]

What Famous result should we look at next?!

[gitanjalideb]

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

[sayantansinha]

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

[PunmasterSTP]

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!

[phamthehung]

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

[angelmendez-rivera]

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.

[BenBen-bbbb]

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

[Leptus]

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 <-pi, pi> 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!