Finite Geometries: a tool for better understanding of Euclidean Geometry
Keywords:
Critics of the foundations, Hilbert's axioms, Finite geometries, ApplicationsAbstract
An effective tool to really understand Euclidean geometry is the study of alternative models and their applications. In fact, they allow you to understand the real extent of various axioms that, when viewed from the Euclidean geometry, seem obvious or even unnecessary. The work begins with a review of Hilbert's axiomatic, starting from more general point of view adopted by Albrecht Beutelspacher and Ute Rosenbaum in their book on the fundamentals of general projective geometry (1998), defined by a system of incidence axioms.
Le Geometrie Finite: uno strumento per una migliore comprensione della Geometria Euclidea
Uno strumento efficace per comprendere realmente la geometria euclidea è lo studio di modelli alternativi e delle loro applicazioni. Infatti essi permettono di capire la reale portata di vari assiomi che visti dall’interno della geometria euclidea sembrerebbero scontati o addirittura inutili. Il lavoro parte da una rivisitazione dell’assiomatica di Hilbert a partire dal punto di vista più generale adottato da Albrecht Beutelspacher e Ute Rosenbaum nel loro libro del 1998 sui fondamenti della geometria proiettiva generale, definita attraverso un sistema di assiomi di incidenza.
Parole Chiave: Critica dei fondamenti; Geometrie finite; Assiomi di Hilbert; Applicazioni.
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References
Beutelspacher A., Rosenbaum U., (1998), Projective Geometry, Cambridge University Press, Cambridge.
Cerasoli M., Eugeni F., Protasi M., (1988), Elementi di Matematica Discreta, Zanichelli, Bologna.
Hilbert D., (1899), Grundlagen der Geometrie, B. G. Teubner, Stuttgart, ed. italiana Fondamenti della Geometria, (1970), Feltrinelli, Milano.
Hirschfeld J.W.P., Thas J.A. (1991), General Galois Geometries, Clarendon Press, Oxford.
Hirschfeld J.W.P., (1998), Projective Geometries over Finite Fields, Clarendon Press, Oxford.
Innamorati S., Maturo A., (1991), On blocking sets of smallest cardinality in the projective plane of order seven, Combinatorics '88, Mediterranean Press, Cosenza, 1991, 79-96.
Innamorati S., Maturo A., (1999), The spectrum of minimal blocking sets, Discrete Mathematics, 208/209, 339-347.
Maturo A. (2003), Cooperative Games, Finite Geometries and Hyperstructures, Ratio Mathematica, 14, 2003, pp.57-70.
Maturo A, Ventre A.G.S. (2008), Models for Consensus in Multiperson Decision Making. In: NAFIPS 2008 Conference Proceedings. Regular Papers 50014. IEEE Press, New York
Maturo, A., Ventre, A.G.S. (2009). Aggregation and consensus in multi objective and multi person decision making. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems vol.17, no. 4, 491-499.
Richardson M., (1956), On finite projective games, Proc. American Mathematical Society, 7 (1956), 458-465.
Scafati M., Tallini G., (1995), Geometria di Galois e teoria dei codici, CISU, Roma
Shapley L. S., (1962), Simple Games - An outline of the theory, Rand Corporation P-series Report.
Tallini G., (1991), Strutture Geometriche, Liguori Editore, Napoli.
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