Take any two rational numbers whose product is 2, and add 2 to each. The results are the legs of a right triangle with rational sides.

For example, 13/17 × 34/13 = 2. If we add 2 to each of these we get 47/17 and 60/13 or, clearing fractions, 611 and 1020. The hypotenuse is 1189.

Because (*z* + 2)^{2} + [(2/*z*) + 2]^{2} = [*z* + 2 + (2/*z*)]^{2}, if *z* is rational, so are all three sides.

(R.S. Williamson, “A Formula for Rational Right-Angle Triangles,” *Mathematical Gazette* 37:322 [December 1953], 289-290, via Claudi Alsina and Roger B. Nelsen, *Icons of Mathematics*, 2011.)