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arXiv · 1305.6851

Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach

Wolfgang Bertram
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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.

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Wolfgang Bertram. 2013-05-27. Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach. https://arxiv.org/abs/1305.6851

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