Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach
History and Overview
2013-05-30 v1
Abstract
By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebra and elementary group theory), and (3) axiomatic geometry.
Cite
@article{arxiv.1305.6851,
title = {Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach},
author = {Wolfgang Bertram},
journal= {arXiv preprint arXiv:1305.6851},
year = {2013}
}
Comments
28 p., figures produced by using geogebra