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It is the space of ordinary human experience and the starting point of our geometric intuition. Studied for two-and-a-half millenia, it has been the object of celebrated controversies, the most famous concerning the minimum number of properties necessary to define it completely. | An Introduction to GEOMETRICAL PHYSICS R. Aldrovandi J.G. Pereira Institute de Fisica Teorica State University of Sao Paulo - UNESP Sao Paulo Brazil To our parents Nice Dina Jose and Tito 1 .