The name “point-free geometry" denotes a series of researches on foundation of geometry in which the main primitive notion is the one of "solid body", (or, better, "region"), while “points”, “lines”, “planes” are defined. This paper starts from the observation that, as far as we know, the existing researchers in point-free geometry paid attention only to the logical aspects of the proposed theory (consistency, categoricity, independence and so on). However, in our opinion, it should be interesting to search for a point-free axiomatization taking into account also their possible educational potentialities. This leads to search for primitive notions which are simple and intuitive and axioms whose validity can be experimented through appropriate laboratory activities.

POINT-FREE FOUNDATION OF GEOMETRY LOOKING AT LABORATORY ACTIVITIES

Giangiacomo Gerla;Annamaria Miranda
2020

Abstract

The name “point-free geometry" denotes a series of researches on foundation of geometry in which the main primitive notion is the one of "solid body", (or, better, "region"), while “points”, “lines”, “planes” are defined. This paper starts from the observation that, as far as we know, the existing researchers in point-free geometry paid attention only to the logical aspects of the proposed theory (consistency, categoricity, independence and so on). However, in our opinion, it should be interesting to search for a point-free axiomatization taking into account also their possible educational potentialities. This leads to search for primitive notions which are simple and intuitive and axioms whose validity can be experimented through appropriate laboratory activities.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4734904
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