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ERIC Number: EJ1091962
Record Type: Journal
Publication Date: 2016
Pages: 13
Abstractor: As Provided
ISSN: ISSN-0020-739X
On an Assumption of Geometric Foundation of Numbers
Anatriello, Giuseppina; Tortoriello, Francesco Saverio; Vincenzi, Giovanni
International Journal of Mathematical Education in Science and Technology, v47 n3 p395-407 2016
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 "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in "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.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A