On an Assumption of Geometric Foundation of Numbers

Autor/inn/en	Anatriello, Giuseppina; Tortoriello, Francesco Saverio; Vincenzi, Giovanni
Titel	On an Assumption of Geometric Foundation of Numbers
Quelle	In: International Journal of Mathematical Education in Science and Technology, 47 (2016) 3, S.395-407 (13 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2015.1078004
Schlagwörter	Mathematics; Mathematics Instruction; Geometry; Numbers; Geometric Concepts; Plane Geometry; Mathematical Concepts; Logical Thinking; Algebra; Teaching Methods + Suchen Sie Ihr Suchwort? Mathematik; Mathematics lessons; Mathematikunterricht; Geometrie; Zahlenraum; Elementare Geometrie; Planimetrie; Teaching method; Lehrmethode; Unterrichtsmethode
Abstract	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. (As Provided).
Anmerkungen	Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01