Introduction A less well-known features of Twitter is that, outside of all the angry shouting, occasionally an interesting mathematical discussion breaks out. One of these was started by asking the simple question `is there a geometric interpretation of complex eigenvalues?’. … Continued
Image showing a motor orbit. Code available at enkimute.github.io. If you prefer, you can download a PDF version of this article, slightly expanded with better typesetting. Introduction Geometric algebra is a very natural language for describing concepts in Euclidean geometry, … Continued
A number of different groups have produced implementations of Geometric Algebra in symbolic algebra packages. These include: A Mathematica notebook created by Terje Vold. Clifford Algebra with Mathematica, by Aragon-Camarasa, et al. arXiv:0810.2412 A GA module for SymPy. SymPy is a … Continued
This book is available from CUP and Amazon. Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with … Continued
Motivated by conventional gauge theories, we consider a theory of gravity in which the Einstein-Hilbert action is replaced by a term that is quadratic in the Riemann tensor. We focus on cosmological solutions to the field equations in flat, open … Continued
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of Kerr-Schild fields, the stress-energy tensor can be regarded as a total divergence in Minkowski spacetime. If one assumes … Continued
Blending schemes based on circles provide smooth `fair’ interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity can be achieved by … Continued
Stationary vacuum solutions of Kerr-Schild type are analysed within the framework of gauge-theory gravity. The complex structure at the heart of these fields is shown to have a clear geometric origin, with the role of the unit imaginary fulfilled by … Continued
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of a gauge-theoretic formulation of gravity. This formulation employs the spacetime algebra (the Clifford algebra of spacetime), which offers a number of novel insights into the nature of … Continued