Affine and projective universal geometry: uniting spherical and hyperbolic geometries
by Associate Professor N J Wildberger
Abstract: Universal geometry is a generalization of Euclidean geometry that extends not only to arbitrary fields, but also to general quadratic forms. There is both an affine and a projective version. The former extends the ideas of rational trigonometry, namely quadrance and spread. The latter involves deformations of the basic laws of rational trigonometry to give algebraic reformulations of Napier's rules and laws etc.
This dramatically simplifies both spherical and hyperbolic geometries, and I'll show some pictures to illustrate the many new opportunities for metrical geometry and algebraic geometry that are opened up.
For More Information: Lawrence Reeves email: L.Reeves@ms.unimelb.edu.au