### 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

E-mail: gthogan@nsu.edu

#### ABSTRACT

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.