Commutative and non-commutative parallelogram geometry: en experimental approach

Wolfgang Bertram (1)

1 IECL - Institut Élie Cartan de Lorraine

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.

Mots clés: lattice; Desargues theorem; associativity; torsor; projective geometr; group; geogebra

Domaines: Mathématiques générales [math.GM]; Théorie des groupes [math.GR]

Wolfgang Bertram. Commutative and non-commutative parallelogram geometry: en experimental approach. 2013. ⟨hal-00826566⟩