[ #InternationalMathematicsDay Special]

So, here's collection of my favorite mathematical proofs. Hope y'all find those interesting. In case you wish to extend this, feel free to do so.

PS - Feel free to add citations/credits in case they are unknown.

(1) Visual Proof of Pythagoras Theorem (By unknown):

(2) Visual Proof of Binomial Theorem (Wiki Media):

(3) Proof of Infinitude of Primes (Northsheild, Sam):

(4) Interesting Case of Euler's Identity:

(5) Proving Euler's Identity [1/2] (By Unknown):

(6) Proving Euler's Identity [2/2] :

(7) Proof that 22/7 > pi ( https://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_%CF%80)

(8) A simple proof that π is irrational
Niven, Ivan. A simple proof that $\\pi$ is irrational. Bull. Amer. Math. Soc. 53 (1947), no. 6, 509. https://projecteuclid.org/euclid.bams/1183510788

(9) Fundamental theorem of algebra (Liouville):

From: https://www.ndsu.edu/pubweb/~novozhil/Teaching/452%20Data/12.pdf

Via Liouville's theorem:

(10) Proof of Bertrand's Postulate (Via: Wiki):

From: https://en.wikipedia.org/wiki/Proof_of_Bertrand%27s_postulate

(11) Buffon's needle problem (via: Wiki):
Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?
https://en.wikipedia.org/wiki/Buffon%27s_needle_problem
Answer:

(12) Proving Basel Problem using Fourier Series (unknown):

From: https://en.wikipedia.org/wiki/Basel_problem

(13) Christoffel's Symbol using Euler Lagrangian Eqn: (Unknown)

From: Tong, David (Lectures of GR)

*- Note this is a special case of n-d flat manifold!

Help extending the list! :-)