Journal for Geometry and Graphics 15 (2011), No. 2, 129--139
Copyright Heldermann Verlag 2011
Axiomatizing Perpendicularity and Parallelism
Pentti Haukkanen
School of Information Sciences, 33014 University of Tampere, Finland
pentti.haukkanen@uta.fi
Jorma K. Merikoski
School of Information Sciences, 33014 University of Tampere, Finland
jorma.merikoski@uta.fi
Timo Tossavainen
School of Applied Educational Science and Teacher Education, University of Eastern Finland, P. O. Box 86, 57101 Savonlinna, Finland
timo.tossavainen@ uef.fi
We establish a framework in which one can study perpendicularity and parallelism axiomatically. The lines of the Euclidean plane provide an admissible model of our axiom system but various other models exist, too. Focusing only on these two relations, our approach is more elementary and, thus, more suitable for the teaching of deductive geometry in the upper secondary schools and in mathematics teacher education than other existing axiomatizations of the Euclidean plane geometry.
Keywords: Euclidean geometry, mathematics education, parallelism, perpendicularity.
MSC: 51-01; 97G99, 51F99
[ Fulltext-pdf (152 KB)] for subscribers only.