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
Proofs of Fermat's theorem on sums of two squares of which is a sum of two squares, is itself a sum of two squares." 2. "If a number which is a sum of two squares is divisible by a prime which is a sum of two squares, then the quotient is a sum of two squares." (This is Euler's first Proposition). 3. "If a number which can be written as a sum of two squares is divisible by a number which is not a sum of two squares, then the quotient has a factor which is not a sum of two squares." (This is Euler's second Proposition). 4. "If