What Is the Pythagorean Theorem

The Formula

a² + b² = c² where c is always the hypotenuse (longest side, opposite the 90° angle).

Example

Legs of 3 and 4: 9 + 16 = 25 → hypotenuse = 5. Common triples: 3-4-5, 5-12-13, 8-15-17.

Real-World Uses

• Construction: 3-4-5 rule verifies right angles
• Navigation: Shortest distance between points
• Computer graphics: Distance calculations in 2D/3D
• GPS: Trilateration uses extended form

History

Babylonians used it c. 1800 BC. Ancient Indian, Chinese, and Egyptian mathematicians discovered it independently. Pythagoras credited with first known proof.