Electronic Proceedings of the Thirteenth Annual International Conference on Technology in Collegiate MathematicsAtlanta, Georgia, November 16-19, 2000Paper C035Quaternions and Rotations in 3-Space, With the TI-83 |
Guy T. HoganNorfolk State University Norfolk, VA 23504 USA Phone: (757) 823-9562 Fax: (757) 823-8427 gthogan@nsu.edu |
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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.Keyword(s): complex variables, abstract algebra, linear algebra, TI-83