Pythagorean theorem

American  

noun

Geometry.

1. the theorem that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

---

Pythagorean theorem Scientific  

/ pĭ-thăg′ə-rē′ən /

1. A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides. It is mathematically stated as c ² = a ² + b ², where c is the length of the hypotenuse and a and b the lengths of the other two sides.

---

Etymology

Origin of Pythagorean theorem

First recorded in 1905–10

Example Sentences

We still use the Pythagorean theorem and euclidean principles.

From Slate • Sep. 26, 2025

If verified, Johnson and Jackson’s proof would contradict mathematician and educator Elisha Loomis, who stated in his 1927 book The Pythagorean Proposition that no trigonometric proof of the Pythagorean theorem could be correct.

From Scientific American • Apr. 10, 2023

The Pythagorean theorem is therefore equivalent to the equation sin2 x + cos2 x = 1.

From Scientific American • Apr. 10, 2023

Fortunately, there’s a much easier way to use the Pythagorean theorem on a job site.

From Seattle Times • Dec. 12, 2022

The misery began when I moved beyond the Pythagorean theorem to sine, cosine and tangent.

From "Educated" by Tara Westover