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
Fermat's right triangle theorem single Diophantine equation which can be simplified to Conversely, any solution to this equation could be factored to give a square congruum. (In particular, the squares formula_13, formula_14, and formula_15 form an arithmetic progression with congruum formula_16, which is a square itself.) Thus, the solvability of this equation is equivalent to the existence of a square congruum. But, if Fermat's last theorem were false for the exponent formula_17, then squaring one of the three numbers in any counterexample would also give three numbers that solve this equation. Therefore, Fermat's proof that no Pythagorean triangle has a square area implies that