E.M.S. Hitzer, L. Redaelli

*Advances in Applied Clifford Algebras*,
**13**(2) pp. 157-181 (2003).

**Abstract:**
Conventional illustrations of the rich elementary relations and physical applications of geometric algebra are helpful,
but restricted in communicating full generality and time dependence. The main restrictions are one special perspective
in each graph and the static character of such illustrations. Several attempts have been made to overcome such
restrictions. But up till now very little animated and fully interactive, free, instant access, online material is available.

This report presents therefore a set of over 90 newly developed
(freely online
accessible)
JAVA applets. These applets range from the elementary concepts of vector,
bivector, outer product and rotations to triangle relationships, oscillations
and polarized waves. A special group of 21 applets illustrates three
geometrically different approaches to the representation of conics; and even
more ways to describe ellipses. Next Clifford's famous circle chain theorem
is illustrated. Finally geometric applications important for crystallography
and structural mechanics give a glimpse of the vast potential for applied
mathematics. The interactive geometry software
Cinderella was
used for creating these applets. The interactive features of many of the
applets invite the user to freely explore by a few mouse clicks as many
different special cases and perspectives as he likes. This is of great help in
"visualizing" geometry encoded by geometric algebra.

[Postscript] 1606k gzip compressed, [PDF] 565k

[Geometric Calculus Japan index]