UM ESPAÇO DE RANDERS ESPECIAL COMO MODELO CONCRETO DE GEOMETRIA NÃO EUCLIDIANA PLANA: AXIOMA DA RÉGUA INFINITA DE RANDERS

Abstract

In this work we study a specific model of non-Euclidean geometry, where the Cartesian plane is endowed with a special Randers metric. The way of measuring distances in this new geometry is not symmetric. Here the geodesics continue to be straight lines and due to the non-symmetry of this perturbed metric, we obtain two notions of the infinite ruler axiom.

Keywords: Ruler Axiom, Randers Metric, Plane Geometry.