But HOW did Euler do it?! A BEAUTIFUL Solution to the FAMOUS Basel Problem! 

Intuition drives innovation, but rigour keeps the system working

"They say that effort breeds success, but that's a complete lie; the world is not that accommodating. People with talent don't become talented, they're just born with their abilities right from the start".

Why do you say that..how can I have the intuition he had?

@@Sir_Isaac_Newton_ says who? How do you know that's true?

@@Sir_Isaac_Newton_ absolute bullcrap

fun fact: euler calculated the first 16 digits of pi^2/6, before developing his actual proof.

I must promote the chap I chatted with who really did what he said he did, just like me. A fucking genius. Pi IS 3,16 or 16/9. He finished the history of human astrological observation and fixed so many things we take as true. I am rewriting math and physics for RATIONALITY in both as well as language. Stay tuned, and as long as channel metrics decide truth, get ready for aliens.

@@dsm5d723 Pi is 3.141592653 and 16/9 is 1.78

@@ryanjagpal9457 It is his thing. i will give his screen name. He does have the perfect explanation of pre-literate astronomical observation. It is the obverse of my thing, Dimensional Gauge Symmetry. Three rational "irrational" gauges, e (c), sq2 and Pi. I was working with the ERRORS of modern math, and I did find them. Add the three numbers to the third decimal and the first 1 from the prime sequence and you get a mathematical model of a dynamic dipole, plusy dynamical friction embed in the Euclidean Plane. Math with out a dynamic explanation of physics is not measuring anything but math. 1+0.577+1.414+3.141=6.132 And I am working on the last bit of rationality in the modern paradigm, and it has to do with the resolution hidden in the "irrational" decimal expansion of these three numbers. Repeating is not understanding. I finished Einstein and Poincare with the Tesla Identity Matrix Determinant. gab.com/23andMe24andYou/posts/105477983888996278

@@ryanjagpal9457 DysonTorus Tesla Code is 3r 6r and 9r 5 days ago Ed leedskalnin. Coral castle π is 3.16r Tau is 6.3r Everything is out by 1.1 1.1s 66.6s 66.6m 22.2h 333.3days We are in 2222/3 Egyptians used 3.16 I recurred it and tested manually. If there's missing math then there's missing km2 of earth Eratosthenes was 10deg adrift lattitude as the magnetic equator is the real equator. DysonTorus Tesla Code is 3r 6r and 9r 4 days ago @DSM 5D best comment I've ever heard. Thanks buddy! Now find the sq root of 10. 3.16227766. That's just using my phone. 3.14159 is the error to hide 47m km2 in the south and is hidden in the north, or just missing full stop. 111.1 km as everything is a ratio of 1:1.1r mostly in my model. 10deg passed np from UK is let's say 111.1km, that offsets everything. Bit if there's 26666.66r km from true south to true north as 6666.66 is deci more than the famous 666 or 666r. It's all in plain site. The moon is the ruler. Look up first use of lunar calendar. It's way older than we've been worshipping the sun. Base the whole geo model onto the moonpole or monopol'y' as I call it. Gets really interesting. Please sub as all my videos are going into one amazing presentation noman has ever thought of since 4236BC DysonTorus Tesla Code is 3r 6r and 9r 3 days ago @DSM 5D Topman. I like Ur style. Babylonians. It's all about time line. 60 didn't fit in with lunar. Sumerians were 3000bc. Egyptians used lunar before 4236bc and Scotland found evidence of the lunar calendar 8000bc at least. So 60 base started 4236 by Egyptians. 365 calendar was 4236bc as well. I claim they could never figure it out. Without studying the world, they would have never have know the full path of the moon. We do. We should be using a 100 based system for time which is navigation. Because we don't, I have proven 10deg x 4 is missing at both poles. How did they hide 48m km2. Through assumption of 40000km. Well Magellan proved equator was way way shorter than 40000km. I proved it 100% in my day 2. It's all in plain sight. Nothing is hidden. We just aren't looking

@@ryanjagpal9457 DysonTorus Tesla Code is 3r 6r and 9r 3 days ago (edited) @DSM 5D I'm a cook with south African education. 86-94. 19/6 is 3.16r Manually 3.16r was bang on π was .08% out. I used a plate and tailors measure. I'm stuck on why perimetres change with shape change but not area? Given it a rest for day. Eric verlande talked of entrophic gravity. Will reply more later on. Thx bud. Heads going wild with numbers. What's these prizes? Clay math is who I emailed.

well this guy was once FAPPABLE maths if i recall correct you, so yeah Jens isn´t the guy with the best filter^^

@@Metalhammer1993 He is accurate, which is the most important thing. This IS pretty fucking dope :)

It's because he found a proof to get away with it.

@@Metalhammer1993 Well that name isn't wrong. This shit gives math boners.

@@thomasrad6296 Don't you mean he found a "proof way" to get away with it? Just a math puns!

Haha

x is a perfectly fine approximation of sin(x) for values of x close enough to zero.

Sionae 😂😂😂😂

I had to stop and rewind to 15:35. My brain was automatically rounding. It took me more than a few seconds to shift gears.

Well, for a sufficient small enough interval of x values around x=0, you can replace the "=" sign with a "~" sign

1:04 hoyristically

*You* ler? Nah... *We* ler? Perfection *_ussr intensify_*

@@arnavanand8037 Oil er USA intensifies

Lmaoo

LMAO

"If two polynomial functions have the same zeros, then they are basically the same, if and only if their coefficients and degrees are the same."

@@kuronekonova3698 actually, if two polynomials have the same zeros and their degree is the same, they are the same polynomial, hehe

@@ernestomamedaliev4253 not necessarily cuz you can multiply any polynomial by a constant to get a new polynomial with the same degree, same zeroes, yet different. I think if two polynomials have the same degree and (complex) zeroes, they are proportional to each other by some constant.

@@snootiermoon yeah, thinking abou that, I guess you are right. We need to specify that the coefficient of the maximum degree term is 1 in order to establish what I said earlier. Thank you for the correction! 😉

Variables vary too much, so unreliable.

LMAO this made me laugh harder than what I thought

n, k, all much the same just letter placeholders for some variable. Get used to it, or you'll end up exploding in flames in your life.

Easy... Good that he didn’t use x or y instead of k, then n to solve it😂😂😂

K

Or you can use papa fourier's series.

You can still compare but the results require further insight to get. Try.

Wait what is zeta?

@@ryanjagpal9457 C'mon, every body knows the zeta function! Even a 3rd grader!

@@jkstudyroom How can a third grader know that? Pretty sure they should be learning how to write by then Idk where you go to?

I said, "you're shitting me?!" My 9 year old says, "Dad, where did you think he was headed?"

BISS

When you’re Euler, you tell both the steak and the eater what’s up.

Pretty much, ever heard about renormalization? Essentially you just "hide away" some term that blows up to infinity and the leftover is your answer :D

Luigi T. Sousa In the words of Andrew Dotson: Ree-normielization

@@MessedUpSystem Yeah! We use this idea of renormalization in Asymptotic Methods, one of my modules. More specifically, finding solutions to small perturbations of Duffing's equation in which a straightforward expansion ansatz gives rise to a non-uniform solution.

Euler 'used' the "sinc-function" 'quite often' , e.g. : cos (na) + i * sin (na) = [ cos(a) + i*sin(a) ]^n --> set here a = x/n , with a fixed & real x --> cos(x) + i*sin(x) = [cos(x/n) + i*sin(x/n]^n --->> sin(x/n) / (x/n) --> 1 , for x/n --> 0 , i.e. for n --> inf --->> so asymtotically 'we' have sin(x/n) ~ x/n , moreover 'we' see / "know" that cos(x/n) ~ 1= cos(0) , for large n --->>> ; so it's "plausible" to write : cos(x) + i*sin(x) = lim [ 1 + ix/n]^n , for n --> inf , thus 'we' get a 'definition' for the exponential function [ on which the "Euler method" for solving ODE's numerically is based ! ] : e^x = lim [ 1 + x/n ]^n , n --> inf , according to the last "well known" limit ... !!! { exercise : show that lim [ 1 + x/n ]^n = sum(k = 0 to inf) x^k/k! , n --> inf }

Was that some math joke that my dumbass producer mind won't get

@@williamrichmond814 Taylor series expansion

could you send me that article please?

@@eliaschavez364 Glad to, it is "Quelques conséquences surprenantes de la cohomologie de 𝑆𝐿_2(ℤ)" by Don Zagier.

;_;

:)

I recommended this video to friends cause of it xD

:)

Germany switzerland

Nah that would be impossible to understand it at that degree and plus how are they gonna reach the blackboard

I solved it in 10-th form at school

@@firi4737 is that basically year 10?

Pretty late, but I‘m from switzerland and in 11th grade... that stuff‘s pretty simple

:)