(pĭ-thāg'ə-rē'ən) 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.

Note: The theorem is often expressed a2 + b2 = c2.

Note: The simplest whole number expression of this theorem is called the 3, 4, 5 triangle. In a right triangle, if one side measures three units, and the second side measures four units, the hypotenuse must measure five units because 32 + 42 = 52; that is, 9 + 16 = 25.