Electronic Proceedings of the Thirteenth Annual International Conference on Technology in Collegiate Mathematics

Atlanta, Georgia, November 16-19, 2000

Paper C035

Quaternions and Rotations in 3-Space, With the TI-83

Guy T. Hogan

Norfolk State University
Norfolk, VA 23504
Phone: (757) 823-9562
Fax: (757) 823-8427

Click to access this paper: paper.pdf


The Complex Numbers, and the Quaternions are the only possible associative division algebras over the reals. The Complex Numbers can be viewed as a 2-dimensional vector space over the reals, while the Quaternions are a 4-dimensional real vector space. Multiplication by a unimodular complex number is, essentially, rotation (in the plane) through the angle (amplitude) of the unimodular complex multiplier. And, by analogy, there is a multiplication, with a twist, operation by unimodular quaternions which accomplishes a rotation in 3-space. This paper offers a short program, written for the TI-83, making use of a matrix representation, in order to get around the lack of symbolic manipulation capability with this calculator.

Keyword(s): complex variables, abstract algebra, linear algebra, TI-83