This circle has the equation x2 + y2 = 25, and it contains rational points, like (0, 5) and (3, 4), as well as other points, like (2, \sqrt {21}) and (\sqrt {11}, - \sqrt {14}). But knowing just one ...

This is equivalent to the following result: If all critical points of a rational function lie on a circle in the Riemann sphere (for example, on the real line), then the function maps this circle into ...