The book I am so pleased to present represents a true innovation in the field of the mathematical didactics and, specifically, in the field of geometry. Based on the long neglected discoveries made by Grassmann, Hamilton and Clifford in the nineteenth century, it presents the geometry -the elementary geometry of the plane, the space, the spacetime- using the best algebraic tools designed specifically for this task, thus making the subject democratically available outside the narrow circle of individuals with the high visual imagination capabilities and the true mathematical insight which were required in the abandoned classical Euclidean tradition. The material exposed in the book offers a wide repertory of geometrical contents on which to base powerful, reasonable and up-to-date reintroductions of geometry to present-day high school students. This longed-for reintroductions may (or better should) take advantage of a combined use of symbolic computer programs and the cross disciplinary relationships with the physical sciences.

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