Visualizing More Quaternions

Visualizing More Quaternions is a sequel to Dr. Andrew J. Hanson's first book, Visualizing Quaternions, which appeared in 2006. This new volume develops and extends concepts that have attracted the author's attention in the intervening 18 years, providing new insights into existing scholarship, and detailing results from Dr. Hanson's own published and unpublished investigations relating to quaternion applications. Among the topics covered are the introduction of new approaches to depicting quaternions and their properties, applications of quaternion methods to cloud matching, including both orthographic and perspective projection problems, and orientation feature analysis for proteomics and bioinformatics. The quaternion adjugate variables are introduced to embody the nontrivial quaternion topology on the three-sphere and incorporate it into machine learning tasks. Other subjects include quaternion applications to a wide variety of problems in physics, including quantum computing, complexified quaternions in special relativity, a detailed study of the Kleinian "ADE" discrete groups of the ordinary two-sphere, and the incorporation of quaternion geometry into the isometric embedding of the Eguchi-Hanson gravitational instanton that corresponds to the k=1 Kleinian cyclic group. Visualizing More Quaternions endeavors to explore novel ways of thinking about challenging problems that are relevant to a broad audience involved in a wide variety of scientific disciplines.