Friday 21st October, 2011 16:00-17:00 Mathematics Building, room 516
The construction of complex numbers as pairs of real numbers is well-known. In the 19th century the Irish mathematician William Rowan Hamilton tried to produce similar number systems in higher dimensions. Although he was unsuccessful with triples of numbers, he did discover the 'quaternions'. Shortly afterwards the 'octonions' were discovered by Hamilton's friend John T. Graves. We will discuss these hypercomplex numbers, the ways in which they deviate from familiar properties of R and C, and the, somewhat surprising, fact that these four - dimensions 1, 2, 4 and 8 - exhaust the possibilites for 'normed division algebras'.