Posts tagged 'pythagorean-triples'

F.33 Euclidean (m, n) Generators

For integers m > n >= 1, Euclid’s quadratic generators a = m^2 - n^2, b = 2 m n, and c = m^2 + n^2 satisfy a^2 + b^2 = c^2 and inradius r = n(m - n).

F.42 Altitude of a Pythagorean Triple Triangle

In a right triangle with legs a, b and hypotenuse c, the altitude h_c = a b / c satisfies the Inverse Pythagorean Theorem 1/h_c^2 = 1/a^2 + 1/b^2 and divides the hypotenuse into projections u = b^2/c and y = a^2/c with h_c^2 = u y.