14.  Discussion

The purpose of this first article in a two-part series was to offer answers to a fundamental question that arises in both theory and practice: which geometric models should be used to represent and study Euclidean sets of ${ℝ}_2^n$  ? To answer this question, this article has provided a concise overview, branch by branch of geometry, of the main ideas and concepts necessary for a rigorous treatment of the modeling and geometric description of Euclidean sets, with numerous examples and illustrations in two and three dimensions.