Interlacing mathematics and art in the classroom: teaching symmetry and antisymmetry using Truchet tiles

Abstract

The construction of art works based on a module --- \textit{modular art} --- is present throughout all human history. Naturally, modularity is a fertile field for the occurrence of symmetries. In this paper we consider the use of a particular module consisting of a square divided by one of its diagonals into two triangles of different colors, known as a \textit{Truchet tile}. From this module we considered rosettes and friezes of different dimensions and studied their properties regarding possible symmetries and antisymmetries. We have also counted the different configurations that can be obtained for different dimensions of rosettes and friezes. Symmetry and antissymmetry can be useful when creating art works and interlacing mathematics with the arts in the classroom can be a successful way to promote the interest for both subjects. We present some works carried out by primary and secondary school students and teachers.