In this paper we propose a synthetic way (ensuing from Euclid’s Elements) to geometrize the method of coordinates and thus to reformulate analytic geometry using a synthetic, axiomatic approach. In the theory that we will develop, the segment arithmetic (Streckenrechnung) introduced by David Hilbert in his Grundlagen der Geometrie plays a crucial role. Analytic geometry has fundamental scientific and mathematical significance since, e.g., it is essential for the application of mathematics to physical and natural sciences. Our synthetic approach is certainly useful for a theoretical understanding of hierarchical structures of axiomatic theories, it can stimulate problem solving in the spirit of undergraduate mathematics, and it can even help to enhance classroom learning, all this being very important in modern times.
A synthetic way to geometrize the method of coordinates
MARTINI, HORST;Vincenzi Giovanni
2018-01-01
Abstract
In this paper we propose a synthetic way (ensuing from Euclid’s Elements) to geometrize the method of coordinates and thus to reformulate analytic geometry using a synthetic, axiomatic approach. In the theory that we will develop, the segment arithmetic (Streckenrechnung) introduced by David Hilbert in his Grundlagen der Geometrie plays a crucial role. Analytic geometry has fundamental scientific and mathematical significance since, e.g., it is essential for the application of mathematics to physical and natural sciences. Our synthetic approach is certainly useful for a theoretical understanding of hierarchical structures of axiomatic theories, it can stimulate problem solving in the spirit of undergraduate mathematics, and it can even help to enhance classroom learning, all this being very important in modern times.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
