History of mathematical notation back to any school or period before that of the Ionian Greeks, but the subsequent history may be divided into periods, the distinctions between which are tolerably well marked. Greek mathematics, which originated with the study of geometry, tended from its commencement to be deductive and scientific. Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of
Fermat's right triangle theorem is, by the Pythagorean theorem, they would form two integer-sided right triangles in which the pair formula_10 gives one leg and the hypotenuse of the smaller triangle and the same pair also forms the two legs of the larger triangle. But if (as Fibonacci asserted) no square congruum can exist, then there can be no two integer right triangles that share two sides in this way. Because the congrua are exactly the numbers that are four times the area of a Pythagorean triangle, and multiplication by four does not change whether a number is square, the existence of a square