Extending trigonometry to higher dimensions using linear algebra

Abstract:

Wildberger's framework of rational trigonometry (2005) presents a new way of orienting the study of geometry and trigonometry towards a more logical foundation; its algebraic nature allows us to extend our study naturally to higher dimensions and to more general fields and dot product geometries. In this talk, I present the ways in which we deal with trigonometry in higher dimensions. We will see how to formalise basic concepts like quadrance and spread (replacements of distance and angle for rational trigonometry), as well as their higher-dimensional counterparts.