On a Geometric Foundation of Mathematics (Su una Fondazione Geometrica della Matematica)
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Anatriello G., Tortoriello F.S., Vincenzi G., On an assumption of geometric foundation of numbers. Int. J. Math. Edu. in Sci. and Tech. 2016; 47(3): 395-407.
Barwise, J, Etchemendy, J, Visual information and valid reasoning, In W. Zimmerman S. Cunningham (Eds.), Visualizingin teaching and learning mathematics (pp. 9-24).Washington,
DC: Mathematical Association of America, (1991).
Betti R., L’analisi logica dell’intuizione spaziale, tra apriorismo ed esperienza. In D. Hilbert, Fondamenti della geometria. Con i Supplementi di Paul Bernays. 2009 FrancoAngeli Milano
Boyer C.B., Descartes and the geometrization of algebra, Amer. Math. Monthly (1959)
Brown J.R., Philosophy of mathematics: A contemporary introduction to the world of proofs and pictures. New York: Routledge; 2008.
Corry L., The empiricist roots of Hilbert’s axiomatic approach. In V. F. Hendricks, et al. (Eds.) Proof theory. Dordrecht: Springer Netherlands; 2000. p.35-54.
Edwards L, Radford L, Arzarello F. (Eds.),Gestures and multimodality in the teaching and learning of mathematics. Special issue of Educational Studies in Mathematics. 2009; 70(2): 91-215.
Freudenthal, H. Zur Geschichte der Grundlagen der Geometrie. Nieuw Archief voor Wiskunde, 4(5), 105-142. http://math.unipa.it/~brig/sds/MATERIALI/MATEMATICA/ sitofondamenti/
Freudenthal%20nuovocarattereago2005.htm
Frege G., Scritti postumi (a cura di Eva Picardi), (trad Nachgelassene Schriften und Wissenschaftlicher Briefwechsel vol 1. Hamburg: Felix Meiner Verlag; 1969) Bibliopolis, Napoli, 1986.
Giaquinto M. Visual thinking in mathematics. Oxford: Oxford University Press; 2007.
Giovannini E.N. Bridging the gap between analytic and synthetic geometry: Hilbert's axiomatic approach. Synthese. 2016; (193): 31-70.
Hamami Y, Mumma J. Prolegomena to a cognitive investigation of Euclidean diagrammatic reasoning. J Log Lang Inf. 2013; 22(4): 421-448.
Hilbert D. Grundlagen der mathematik. Vol. 2. Berlin: Springer; 1943.
Kvasz L. Patterns of change: linguistic innovations in the development of classical mathematics. Basel: Birkhäuser, 2008.
Miller N. Euclid and his twentieth century rivals:diagrams in the logic of Euclidean geometry. Stanford: CSLI Publications; 2007.
Petri B., Schappacher, N. On arithmetization. In: The Shaping of Arithmetic after CF Gauss’s Disquisitiones Arithmeticae. Springer Berlin Heidelberg, 2007. p. 343-374.
Rivera F.D. Toward a visually-oriented school mathematics curriculum: Research, theory, practice, and issues. Vol. 49. Springer Science Business Media, 2011
Rowe, D. The calm before the storm: Hilbert's early views on foundations. In V.F. Hendricks, et al. (Eds.). Proof theory. Dordrecht: Springer Netherlands; 2000. p.55-93.
Stillwell J. Ideal elements in Hilbert's Geometry. Perspectives on Science 2014; 22(1): 35-55.
Stillwell J. The four pillars of geometry. New York: Springer; 2005.
Vailati G. Sulla teoria delle proporzioni [On the theory of proportions]. In: Enriques E, editor. Questioni riguardanti le matematiche elementari - raccolte e coordinate da Federigo Enriques. Vol. I: Critica dei principii. Bologna: Zanichelli; 1912 p. 143-191.
DOI: http://dx.doi.org/10.23756/sp.v5i1.346
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