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Pythagorean Theorem

Elementary

Definition

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides. Mathematics' most famous theorem.

a² + b² = c²

Pythagorean Theorem (c is hypotenuse)

c = √a² + b²

Hypotenuse length

Example 1

Find the hypotenuse of a right triangle with sides 3 and 4.

Example 2

If hypotenuse is 13 and one side is 5, find the other side.

Discovered by: Pythagoras (or earlier) (c. 6th century BCE)

Proved by Pythagorean school, but known earlier in Babylon and India.

Right angle verification, distance

GPS, distance measurement

Vector distance calculation