Pythagorean theorem straightedge and compass. Pythagoras's theorem enables construction of incommensurable lengths because the hypotenuse of a triangle is related to the sides by the square root operation. The figure on the right shows how to construct line segments whose lengths are in the ratio of the square root of any positive integer. Each triangle has a side (labeled "1") that is the chosen unit for measurement. In each right triangle, Pythagoras's theorem establishes the length of the hypotenuse in terms of this unit. If a hypotenuse is related to the unit by the square root of a positive integer that is
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