Pythagorean theorem Pythagorean theorem In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides "a", "b" and "c", often called the "Pythagorean equation": where "c" represents the length of the hypotenuse and "a" and "b" the lengths of the triangle's other two sides. Although it is
Legendre's three-square theorem Legendre's three-square theorem In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers if and only if is not of the form formula_2 for integers and . The first numbers that cannot be expressed as the sum of three squares (i.e. numbers that can be expressed as formula_2) are Pierre de Fermat gave a criterion for numbers of the form 3"a" + 1 to be a sum of three squares essentially equivalent to Legendre's theorem, but did not provide a proof. N. Beguelin noticed in 1774 that every positive