E.M.S. Hitzer

*Mem. Fac. Eng. Fukui Univ.* **50**(1) (2002).

**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 21st 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 of geometric calculus for the engineering sciences
three representative examples are looked at in some detail: elasticity, image
geometry and pose estimation. **Next a current snapshot survey of geometric
calculus software is provided.** Finally the value of geometric calculus for
teaching, research and development is commented.

[Postscript] 828k, gzip compressed

[Geometric Calculus Japan index]