E.M.S. Hitzer

*Proc. of the Pukyong National University -
Fukui University International Symposium 2001 for Promotion of Research
Cooperation*, Pukyong National University, Busan, Korea, 59
(2001).

**Abstract:**
This paper treats important questions at
the interface of mathematics and the engineering sciences. It starts off with a
quick quotation tour through 2300 years of mathematical history. At the beginning
of the 21^{st} century, technology has developed beyond every
expectation. But do we also learn and practice an adequately modern form of
mathematics? The paper argues that this role is very likely to be played by
(universal) *geometric calculus*. The fundamental *geometric product*
of vectors is introduced. This gives a quick-and-easy description of rotations
as well as the ultimate geometric interpretation of the famous quaternions of
Sir W.R. Hamilton. Then follows a one page review of the historical roots of
geometric calculus. In order to exemplify the role geometric calculus for the
engineering sciences three representative examples are looked at in some
detail: elasticity, image geometry and pose estimation. Finally the value of
geometric calculus for teaching, research and development and its worldwide
impact are commented.

[Postscript]
974k, gzip compressed.

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[Postscript]
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