Volume/Issue :

Article type :

Case study

Page No :

100-123

Abstract :

The purpose of this analysis is to show that strong connections might exist between the teaching of mathematics, science and art. This is due to the particular geometrical configurations behind several paintings and other artistic creations. Therefore, the knowledge of this connection might be of help for the students to guess that mathematics and science also have possible applications to art. This is particularly relevant for the high schools of art. Since too often, mathematics is taught in high schools without any relevant link to reality, this can be one of the reasons of students’ disaffection for this subject. In this analysis, a teaching experiment developed by the author in an Italian (Udine) high school of art is proposed. In particular, Escher’s periodic drawings, and the ornamental motifs that characterize many products in reality, offer an interesting opportunity to make high school students understand the relevance of mathematics and especially of geometry in art. The discovery of mathematical laws, that derive from crystallography, behind Escher’s drawings should persuade students that such an artistry is reachable only by means of mathematical knowledge. In what follows the main features of the outlined didactical proposal are presented and discussed.

Keywords :

Escher, periodic drawings, mathematics and art, mathematics teaching, cristallography

References :

Aiton, E. J., Duncan, A. M., & Field, J. V. (1997). The Harmony ok the world by Johannes Kepler. American Philosophical Society.
Castaldi, L., & Ghione, F. (2011). Matematica e Arte [Mathematics and art]. Springer-Italia.
Dedò, M. (1999). Forme, simmetria, topologia [Shapes, symmetry, topology]. Decibel-Zanichelli.
Di Maggio, M. (2006). Gruppi cristallografici nell’arte di M.C. Escher [Crystallographic groups in Escher’s art]. Graduation Thesis, University of “Roma Tre”.
Hilbert, D., & Cohn-Vossen, S. (1952, first edition 1932). Geometry and the imagination. Chelsea Publishing.
Morandi, P. J. (2003). The classification of wallpaper patterns: From group cohomology to Escher tessellations. New Mexico State University.
Rigault, G. (1976). Introduzione alla cristallografia [Introduction of crystallography]. Libreria editrice universitaria Levrotto & Bella.
Schattschneider, D. (1990). Visions of symmetry. Notebooks, periodic drawings, and related works of M. C. Escher. W. H. Freeman and Company.
Weyl, H. (1952). Symmetry. Princeton University Press.

Cite as :

Canciani, S. (2020). A didactic itinerary through mathematics, science and art on Escher’s periodic drawings. Gamtamokslinis ugdymas / Natural Science Education, 17(2), 100-123. https://doi.org/10.48127/gu-nse/20.17.100