Pythagorean Theorem
A fundamental relation between the three sides of a right triangle in Euclidean geometry.
4 min readUpdated July 19, 2026
Statement
In any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c².
History
Though named after the Greek mathematician Pythagoras (c. 570–495 BCE), the relationship was known to Babylonian and Indian mathematicians centuries earlier. Hundreds of proofs exist today.
Applications
The theorem underpins distance calculations in coordinate geometry, navigation, architecture, computer graphics, and machine learning.