Sobre circunferências e pontos médios na geometria da epsilon-métrica da soma

In this work, the authors perturb the metric of addition by adding a linear map that depends on a perturbation parameter epsilon, with 0 <= epsilon < 1. This new way of measuring distances in the Cartesian plane is called the epsilon-metric of addition. It is shown that the epsilon-metric of addition is non-negative and satisfies the triangle inequality, but it is not symmetric. Thus, a new non-Euclidean geometry is introduced. Both circles and midpoints are defined and classified in this new geometry. Two types of circles and more than one point that can be called a midpoint are obtained. Examples, graphs, and geometric interpretations are presented for a better understanding.