Norman Wildberger (University of New South Wales)

Friday 1st September, 12.05-12.55pm, Carslaw 373

Geometry for algebraists

Metrical geometry usually involves a Riemannian metric, or perhaps some alternative such as a Lorentzian metric. However it turns out that Euclidean, elliptic and hyperbolic geometries can be formulated entirely algebraically using ideas from rational trigonometry.

This unifies Euclidean and non-Euclidean geometries, clarifies the distinction between the affine and projective situations, and makes the theory more general, accurate and simple. Computations often use integer arithmetic instead of floating point, and allow generalization to an arbitrary field, any dimension, and remarkably any quadratic form. This approach gives a new direction for algebraic geometry, exploiting the natural metrical structure of projective space.

This talk will be at a general level, and requires no familiarity with trigonometry, classical or otherwise.