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
Fermat's right triangle theorem Fermat's right triangle theorem Fermat's right triangle theorem is a non-existence proof in number theory, the only complete proof left by Pierre de Fermat. It has several equivalent formulations: An immediate consequence of the last of these formulations is that Fermat's last theorem is true for the exponent formula_3 and hence for any multiple of 4. In 1225, Fibonacci was challenged to find a construction for triples of square numbers that are equally spaced from each other, forming an arithmetic progression, and for the spacing between these numbers, which he called a congruum. One way of describing Fibonacci's solution is