Cauchy's Proof of the Basel Problem | Pi Squared Over Six (3blue1brown SoME1 Entry) // If you're looking for challenging or tricky math problems, you found the right video. The Basel Problem was one of the most challenging math questions that stumped many great mathematicians, including the famed Bernoulli brothers.

The first proof was provided by the great Leonhard Euler in 1734. The solution is pi squared over six - a surprising "pi formula" which gets the exact sum of the reciprocals of the squares of all the natural numbers from one to infinity. Whereas Euler's proof requires elements of calculus, the proof by Cauchy, which we explore in this video, only requires advanced precalculus. Some necessary ingredients to complete the proof include the binomial theorem (expansion), De Moivre's formula, the squeeze theorem, and Vieta's formula. Plus a lot of trigonometry (grade 12), trigonometric identities, and algebra.

Other mathematical proofs also exist and we need look no further than our fellow math channel friends on YouTube for their awesome explanations. A geometric proof of the Basel Problem is given by 3b1b and an awesome calculus based proof in the complex domain is given by Black Pen Red Pen. Mathologer shows the original proof by Euler himself. I want to thank 3blue1brown (3b1b) for hosting the Summer of Math Exposition contest (SoME1).

Time Stamps:
0:00 Intro
1:20 Act 1: Setting up the Trig Squeeze
3:09 Act 2: Putting Limits on the Squeeze
4:44 Act 3: De Moivre Becomes Imaginary
6:18 Act 4: Converting to a Polynomial
7:50 Act 5: Vieta Seals the Deal
9:34 Grand Finale and Outro

Still reading this? Then write "I love the Basel Problem!" in the comments below!

#3b1b #SoME1 #risetotheequation

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