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
Pythagorean theorem the dot product of vectors. The dot product is called the "standard" inner product or the "Euclidean" inner product. However, other inner products are possible. The concept of length is replaced by the concept of the norm ||v|| of a vector v, defined as: In an inner-product space, the Pythagorean theorem states that for any two orthogonal vectors v and w we have Here the vectors v and w are akin to the sides of a right triangle with hypotenuse given by the vector sum v + w. This form of the Pythagorean theorem is a consequence of the properties