The Pythagorean theorem, or Pythagoras theorem, illustrates the relationship between the three sides of a right-angled triangle. It is a basic relationship in Euclidean geometry.

According to Pythagoras’ theorem, if a triangle is right-angled (90 degrees), the square of the hypotenuse equals the sum of the squares of the other two sides.

Say, there exists a right angle with sides A,B, and C; and C being the hypotenuse or the longest side of the triangle. 

Then A² + B² = C². 

The theorem is named after the Greek philosopher Pythagoras, who lived about the year 570 BC. The theorem has been proven multiple times using various methods, maybe more than any other mathematical theorem. The proofs are varied, including geometric and algebraic proofs, School Analytics, and some date back several thousand years.