When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared distance between two points equals the sum of squares of the difference in each coordinate between the points.

Jun 28, 2025 · Pythagorean theorem, geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. Although the theorem has long been associated with the Greek mathematician Pythagoras, it is actually far older.

We also have a proof by adding up the areas. Historical Note: while we call it Pythagorean Theorem, it was also known by Indian, Greek, Chinese and Babylonian mathematicians well before he lived.

The Pythagorean Theorem guarantees that if we know the lengths of two sides of a right triangle, we can always determine the length of the third side. Here are the three variations of the Pythagorean Theorem formulas:

Dec 26, 2021 · Learn about the Pythagorean theorem in geometry. Get its definition, formula, and worked example math problems.

Jun 8, 2024 · The Pythagorean Theorem, also known as Pythagoras theorem is a mathematical relation between the 3 sides of a right triangle, a triangle in which one of 3 angles is 90°.

Dec 17, 2016 · Also known as Pythagoras' theorem, the Pythagorean theorem is a theorem in geometry that gives a relationship between the sides of a right-angled triangle. The Pythagorean theorem was evidently known before Pythagoras (6th century B.C.), but the proof in general form is ascribed to him.

The Pythagorean theorem states that if a triangle has one right angle, then the square of the longest side, called the hypotenuse, is equal to the sum of the squares of the lengths of the two shorter sides, called the legs.

Feb 22, 2019 · Collecting the terms results in the familiar formula, The Pythagorean Theorem. This means: "the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse."

Oct 24, 2022 · Today, nothing is known of Pythagoras’s writings, perhaps due to the secrecy and silence of the Pythagorean society. However, one of the most famous theorems in all of mathematics does bear his name, the Pythagorean Theorem.