The Cayley-Menger determinant, quadrances and spreads in higher dimensions

Abstract:

The Cayley-Menger determinant, also known previously to Euler and Tartaglia, is a key tool for us in defining metrical quantities in higher-dimensional rational trigonometry. In this talk, we look at its classical origins and see how we can generalise this to our rational trigonometry framework, with specific mentions to defining quadrances and spreads in higher dimensions.