\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016e.00602}
\itemau{Anatriello, Giuseppina; Tortoriello, Francesco Saverio; Vincenzi, Giovanni}
\itemti{On an assumption of geometric foundation of numbers.}
\itemso{Int. J. Math. Educ. Sci. Technol. 47, No. 3, 395-407 (2016).}
\itemab
Summary: In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the {\it Elements} of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in {\it Ausdehnungslehre} in 1844. Assuming as axioms, the cognitive contents of the theorems of Pappus and Desargues, through their configurations, in an Euclidean plane a natural field structure can be identified that reveals the purely geometric nature of complex numbers. Reasoning based on figures is becoming a growing interdisciplinary field in logic, philosophy and cognitive sciences, and is also of considerable interest in the field of education, moreover, recently, it has been emphasized that the mutual assistance that geometry and complex numbers give is poorly pointed out in teaching and that a unitary vision of geometrical aspects and calculation can be clarifying.
\itemrv{~}
\itemcc{F50 G40}
\itemut{Euclidean geometries; geometric constructions; plane geometry; complex numbers; Pythagorean theorem}
\itemli{doi:10.1080/0020739X.2015.1078004}
\end