Electronic Proceedings of the Thirteenth Annual International Conference on Technology in Collegiate MathematicsAtlanta, Georgia, November 1619, 2000Paper C035
Quaternions and Rotations in 3Space, With the TI83 
Guy T. Hogan
Norfolk State University
Norfolk, VA 23504
USA
Phone: (757) 8239562
Fax: (757) 8238427
gthogan@nsu.edu

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The Complex Numbers, and the Quaternions are the only possible
associative division algebras over the reals. The Complex Numbers can be
viewed as a 2dimensional vector space over the reals, while the Quaternions
are a 4dimensional 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 3space. This paper offers a short program,
written for the TI83, 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, TI83