Geometry: the Rational Aspect

The paper is a survey of the Italian researches on the teaching of "rational" geometry. Before collecting and describing 75 contributions to the theme, a general view is offered of the principal research lines, with particular emphasis on the "Italian case" for Geometry. Here, as a long lasting tradition, famous mathematicians (e.g., Peano, Enriques) devoted their attention to didactic questions as well as to theoretical ones. As a consequence, a whole research domain has been developed in the years, called "rational geometry". Since in the last, say, two decades, the international educational research has followed different paths, in the paper questions are also raised about the uncertain borders between educational and geometrical research domains