[math-fun] Origamic Number Theory

To my surprise there actually is another cheerful fact about the square of the hypotenuse. A Pythagorean triple is any integer solution of x^2+y^2=z^2 and, as we know, one gets all solutions by choosing any integers n>m. and defining T(m,n) by, x=n^2-m^2n, y=2mn, z=m^2+n^2. (T stands for triple and/or triangle) CHEERFUL FACT To see a given solution lay an mxn sheet of paper on the desk A_____ m ____ B n n C_____m_____D Fold and crease so that corner D falls on corner A. The triangle bounded by AB and the image of BD is (up to similarity) T(m,n). The proof is an exercise in 9th grade algebra. Surely this must have been noticed before, but where? Happy Holidays DG