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
Incircle and excircles of a triangle has area formula_39. Similarly, formula_40 has area formula_41 and formula_42 has area formula_43. Since these three triangles decompose formula_35, we see that the area formula_45 is: where formula_48 is the area of formula_35 and formula_50 is its semiperimeter. For an alternative formula, consider formula_51. This is a right-angled triangle with one side equal to "r" and the other side equal to formula_52. The same is true for formula_53. The large triangle is composed of 6 such triangles and the total area is: The Gergonne triangle (of "ABC") is defined by the 3 touchpoints of the incircle on the 3 sides.