Axiomathes 28 (2):155-180 (2018)

Authors
Boris Culina
University of Applied Sciences Velika Gorica, Croatia
Abstract
In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics.
Keywords Weyl’s axioms for Eucliedean geometry  A priority of Euclidean geometry  Philosophy of geometry  Elementary axioms for Euclidean geometry  Symmetries of Euclidean geometry
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DOI 10.1007/s10516-017-9358-y
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