Medieval philosophers believed that certain numbers had magical properties and, in a sense, they were right. This program explores irrational, negative, prime, and imaginary numbers and the surprising ways they manifest throughout the physical world. Professor Marcus de Sautoy explains key concepts about pi and other numbers by using examples such as the harmonious design of Chartres Cathedral; the ratios that govern both music and the distress cries of animals; the evolutionary advantage gained by cicadas that hatch only during prime-number years; and the practical application of imaginary numbers by air traffic controllers tracking planes. Produced by the Open University. Part of the series The Math Code. (60 minutes)