Astronomy has generated much mathematics; we review some history.

 Small rational numbers appear in relations between orbital periods of planets and moons, and between other astronomical quantities.  A  structure underlying the appearance of  these numbers is the Farey tree, acousin to the series of Farey fractions.  Circles also encode arithmetic. The Farey fractions  are encoded by Ford circles.  They are useful in classifying approximations of real numbers by rationals and also  have  a subtle relation to the Riemann hypothesis.