What are continued fractions? How can they tell us what is the most irrational number? What are they good for and what unexpected properties do they possess? Where are they in the Universe and just what does chaos have to do with it?

John Barrow, Plus columnist and director of the Millennium Mathematics Project, is also the Gresham Professor of Geometry and he recently gave a lecture at Gresham College explaining how this particular way of writing numbers can reveal extraordinary patterns and symmetries. You can watch a video of his lecture and read his original Plus article Chaos in Numberland: the secret life of continued fractions.