A PRACTICAL APPROACH TO THE AFFINE TRANSFORMATIONS OF THE EUCLIDEAN PLANE

Abstract

The aim of this paper is to give an elementary treatment of a classical item which plays central role in the applied geometry. The actual need for a more or less new presentation of such a well-known subject is explained by the fact that the use of computers easily allows us to work with any given affine transformation in a suitably (canonically) chosen coordinate-system. The choice of that new orthonormal coordinate-system is based on the diagonalization process of the Gram matrix belonging to the linear part of the transformation, and on the change of the origin for an eventual fixpoint of the given affine transformation. Nevertheless, the entire classification of the considered transformations could be given here by elementary algebraic tools. To simplify our discussion we omit too technical denotations and details, and restrict ourselves to plane geometry. For other aspects we refer e.g. to [4] in this volume.