Project Mathematics! video modules were created between 1988 and 2000. Another two modules, "Teachers Workshop" and "Project MATHEMATICS! Contest", were created in 1991 for teachers and are only available on videotape. The content of the nine educational modules follows below. In 1988, "The Theorem of Pythagoras" was the first video produced by the series and reviews the Pythagorean theorem. For all right triangles, the square of the hypotenuse is equal to the sum of the squares of the other two sides ( a + b = c ). The theorem is named after Pythagoras of ancient Greece. Pythagorean triples occur when all
Proofs of Fermat's theorem on sums of two squares has two involutions: an obvious one formula_213 whose fixed points formula_214 correspond to representations of formula_82 as a sum of two squares, and a more complicated one, which has exactly one fixed point formula_217. Two involutions over the same finite set must have sets of fixed points with the same parity, and since the second involution has an odd number of fixed points, so does the first. Zero is even, so the first involution has a nonzero number of fixed points, any one of which gives a representation of formula_82 as a sum of two squares. This proof, due to