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 formula_196. The area of the fundamental parallelogram (in this case a rectangle) of the lattice is formula_82. The area of the open disk, formula_198, of radius formula_199 centered around the origin is formula_200. Furthermore, formula_198 is convex and symmetrical about the origin. Therefore, by Minkowski's theorem there exists a nonzero vector formula_196 such that formula_203. Both formula_204 and formula_205 so formula_206. Hence formula_82 is the sum of the squares of the components of formula_208. Let formula_209 be prime, let formula_210 denote the natural numbers (with or without zero), and consider the finite set formula_211 of triples of numbers. Then formula_212