Algebra and geometry of Hamilton's quaternions
History and Overview
2016-06-13 v1 History and Philosophy of Physics
Abstract
Inspired by the relation between the algebra of complex numbers and plane geometry, William Rowan Hamilton sought an algebra of triples for application to three dimensional geometry. Unable to multiply and divide triples, he invented a non-commutative division algebra of quadruples, in what he considered his most significant work, generalizing the real and complex number systems. We give a motivated introduction to quaternions and discuss how they are related to Pauli matrices, rotations in three dimensions, the three sphere, the group SU(2) and the celebrated Hopf fibrations.
Keywords
Cite
@article{arxiv.1606.03315,
title = {Algebra and geometry of Hamilton's quaternions},
author = {Govind S. Krishnaswami and Sonakshi Sachdev},
journal= {arXiv preprint arXiv:1606.03315},
year = {2016}
}
Comments
11 pages, 4 figures