Pythagorean theorem three sides in place of squares (squares are a special case, of course). The upper figure shows that for a scalene triangle, the area of the parallelogram on the longest side is the sum of the areas of the parallelograms on the other two sides, provided the parallelogram on the long side is constructed as indicated (the dimensions labeled with arrows are the same, and determine the sides of the bottom parallelogram). This replacement of squares with parallelograms bears a clear resemblance to the original Pythagoras's theorem, and was considered a generalization by Pappus of Alexandria in 4 AD The
Nonhypotenuse number Nonhypotenuse number In mathematics, a nonhypotenuse number is a natural number whose square "cannot" be written as the sum of two nonzero squares. The name stems from the fact that an edge of length equal to a nonhypotenuse number "cannot" form the hypotenuse of a right angle triangle with integer sides. The numbers 1, 2, 3 and 4 are all nonhypotenuse numbers. The number 5, however, is "not" a nonhypotenuse number as 5 equals 3 + 4. The first fifty nonhypotenuse numbers are: Although nonhypotenuse numbers are common among small integers, they become more-and-more sparse for larger numbers. Yet, there