Geometric Algebra with Conzilla: Building a Conceptual Web of Mathematics (2002)
| Venue: | MASTER THESIS IN MATHEMATICS, DEPARTMENT OF MATHEMATICS |
| Citations: | 2 - 2 self |
BibTeX
@INPROCEEDINGS{Nilsson02geometricalgebra,
author = {Mikael Nilsson},
title = {Geometric Algebra with Conzilla: Building a Conceptual Web of Mathematics},
booktitle = {MASTER THESIS IN MATHEMATICS, DEPARTMENT OF MATHEMATICS},
year = {2002},
publisher = {}
}
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Abstract
In this paper, the technique of conceptual modeling using the Unified Modeling Language (UML), is applied to the mathematical field known as Geometric Algebra for probably the first time. Geometric Algebra is a unified language for analyzing the full range of geometric concepts in mathematics and physics, first developed by H. Grassmann and W. K. Clifford, and later revitalized by D. Hestenes. A thorough introduction to the field of Geometric Algebra is given, with accompanying conceptual models. Examples of the technique of multiple narration, where the same model is used to tell different stories, are analyzed. The specific problems and advantages of using UML as a visual language for a conceptually rich mathematical communication are discussed. Using the conceptual browser Conzilla, the conceptual models have been made available for online browsing within a virtual mathematics exploratorium being developed by the research group led by Ambjörn Naeve, mathematician and senior researcher at CID, Center for user-oriented IT-design at the Royal Institute of Technology in Stockholm. The specific advantages of using interactive models are discussed.
