Pythagorean Fraction

Given a Pythagorean Triple $(a, b, c)$, the fractions $a/b$ and $b/a$ are called Pythagorean fractions. Diophantus showed that the Pythagorean fractions consist precisely of fractions of the form $(p^2-q^2)/(2pq)$.

References

Conway, J. H. and Guy, R. K. ``Pythagorean Fractions.'' In The Book of Numbers. New York: Springer-Verlag, pp. 171-173, 1996.