Professor Stewart's Incredible Numbers by Ian Stewart

Positive and negative, real and imaginary, rational and irrational, big and small - all kinds of special numbers reveal their astonishing properties in this tour from zero to infinity. You'll discover the secrets of sudoku, Rubik's cubes, fractals and musical scales, as well as learning how numbers evolve through time and that you live in eleven-dimensional space. The companion iOS app Incredible Numbers allows you to explore the subject further (£4.99 from iTunes).