Didactic Situations of Parallelism: Perception and Visualization.

Abstract

The way teachers and students perceive the parallelism of two lines can be extended to other curved lines. This perception has a local character and, to a certain extent, is justified in Euclid's conception of parallel lines. The image of parallel segments remains invariant although the student acquires the definition of parallelism in other contexts that are not purely geometric.

The visualization of the parallelism of two lines has a global conception, where at least one line is required to be visualized. The visualization of parallel segments is distorted between students and teachers when these segments do not have common perpendicular lines.

This article deals with the visualization processes of the parallelism of lines, circles and other differentiable curves in almost every point of their domain.

Keywords: Parallelism, Parallel Segments, Parallel Lines, Concentric Circumferences, Parallel Curves, Equidistant Locus.