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A proposal for a variation on the axioms of classical geometry
Authors:Bjorn Schellenberg
Institution:1. Department of Mathematics , College of Mount Saint Vincent , 6301 Riverdale Avenue, Riverdale, NY 10471, USA bjoern.schellenberg@mountsaintvincent.edu
Abstract:A set of axioms for classical absolute geometry is proposed that is accessible to students new to axioms. The metric axioms adopted are the ruler axiom, triangle inequality and the bisector axiom. Angle measure is derived from distance, and all properties needed to establish a consistent system are derived. In particular, the SAS congruence theorem is proved. The proofs are broken into many small steps suitable for the target audience. Some explorations with geometry drawing programmes are shown.
Keywords:geometry  axiom  metric  triangle inequality  bisector theorem  SAS congruence
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