Proof of Pythagoras' Identity

For all a and b in the real numbers, Pythagoras' identity states that a² + b² = c².

Proof:

1. We start by assuming a and b are positive real numbers.
2. We let c be the distance between the points (a, 0) and (0, b) in the plane.
3. By Euclidean geometry, c² = a² + b².
4. Therefore, a² + b² = c².

This is Pythagoras! He's a real legend.