Beautiful Proofs
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A collection of the most beautiful proofs I found:

- Proof of the Pythagorean theorem. There are many ways to prove this. Prbably
  the simplest is a geometric proof, other cool ones in my opining are from
  Einstein_, and Leonardo da Vinci

.. _Einstein: https://www.youtube.com/watch?v=32zg2FGX4cA&t=434s

- Proof of the formula to find the roots of a parabola (geometric proof +
  algebra proof). Btw, a formula for finding roots of 5+ degrees is impossible!
  (Abel-Ruffini Theorem), so we are luck with parabolas. Also, imaginary numbers
  were invented to solve cubic equations.

- Proof that there are more real numbers than integer numbers

- Proof of the formula to calculate the Area of a sphere. Can be done with both
  Archimede_ and Cavalieri's Principle

.. _Archimede: https://www.youtube.com/watch?v=2IZh-KIAQLE