Episode two of Five Numbers, the BBC radio series presented by Simon Singh.

Most people’s first slice of Pi is at school where it is generally made palatable as either 3.14 or the fraction 3 1/7. The memory of this number may be fuzzy for those propelled through their Maths GCSE by the power of Casio (where Pi was reduced to a button on the bottom row of the calculator), but the likelihood is they still recall that romanticised notion of a number whose decimal places randomly go on forever. At its simplest, Pi is the ratio of the circumference of a circle to its diameter. At its most complex, it is an irrational number that cannot be expressed as the ratio of two whole numbers and has an apparently random decimal string of infinite length.