THE UNIVERSITY OF NEW SOUTH WALES DEPARTMENT OF PURE MATHEMATICS _________________DEPARTMENTAL SEMINAR__________________ Speaker: A. Prof. Norman Wildberger (UNSW) Title: Hyperbolic geometry: past and future Date: Tuesday, 26 August 2008 Time: 12:00 noon Venue: RC-3084, The Red Centre, UNSW Abstract: Non-Euclidean geometry was one of the great developments of nineteenth century mathematics. This talk will give a historical introduction to hyperbolic geometry, and then introduce a simpler and more elegant direction for the subject, based on extending the ideas of rational trigonometry and universal geometry. We begin by mentioning the initial developments of Gauss, Bolyai and Lobachevski, the current models associated due to Beltrami and Poincare relying on the approach to geometry advocated by Riemann, and then moving to a somewhat forgotten chapter--- the projective model associated to Cayley, Beltrami and Klein. This is the jumping off point to our new approach, which we will only have time to briefly discuss. This talk will be very low on formulas and high on pictures, and should be easily accessible to undergraduates. Enquiries to Jonathan Kress, 9385 7078, j.kress@unsw.edu.au