E.M.S. Hitzer

Poster presented at the *Pukyong National University -
Fukui University International Symposium 2001 for Promotion of Research
Cooperation*, 23 Nov. 2001, Pukyong National University, Busan, Korea.

**Abstract:**
Geometric Calculus
has developped into a universal, unified common language for
all areas of mathematics, science and engineering.
Since "Wittgenstein believed ... that our understanding comes in the area of
our imagination"[1] this presentation aims at visualizing the fundamental
concepts of Geometric Calculus.
The technical means of visualization are
1) GABLE
- A Matlab Geometric Algebra Tutorial and
2) Vector Field Design 1.0
- a Geometric Calculus based two-dimensional
interactive vector field software.
The basics of GABLE are
briefly reviewed
and then a number of demo routines used to show the inner
product and (Grassmann's)
outer product of vectors. Both are then unified in
(Grassmann's and Clifford's)
geometric product of vectors. Then the
usefulness of this new type of product is
shown for projection, rejection,
vector division, rotations and rotational
interpolations. In the second part
we skip through the easy to use interactive
features of Vector Field Design
1.0 and demonstrate the real time design and
modification features for some
relevant vector fields.

[1] Paul Yonggi Cho, **The 4th Dimension**, Vol. **2**, Ben Publishing,
Secunderabad, 2000.

[Postscript] 1091k, gzip compressed

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