Beautiful Proofs

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

• 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