Given a Pythagorean Triple , the fractions and are called Pythagorean fractions. Diophantus showed that the Pythagorean fractions consist precisely of fractions of the form .
References
Conway, J. H. and Guy, R. K. ``Pythagorean Fractions.'' In The Book of Numbers. New York: Springer-Verlag,
pp. 171-173, 1996.