General trend: Indications for the role of the History of Mathematics in its didactics, as part of an alternative curriculum for teaching Geometry in a transformational framework in High School, with educational and interdisciplinary scopes.

Emphasis on:

– a brief survey for the introduction of the needed theoretical background of the transformations of Plane Euclidean Geometry, reducing the formalities with the aid of simple figures; here, the History of Transformations plays an essential role in choosing the basic notions and pointing out their functionality;

– some exercises for the training of pupils to « think globally », which is the main educational purpose;

– the role of transformations in the structure and aesthetics of tribal decorations and of painting.