# Teaching tiles

**António Leal Duarte**, Mathematics Department, University of Coimbra

The mathematical glazed tiles (azulejos) of the Jesuit College in the city of Coimbra, in Portugal, are remarkable and unique artifacts. They seem to be the only known example of glazed tiles for classroom use displaying geometrical diagrams of true mathematical (Euclidian) demonstrations. Scientific motifs as decorative elements in buildings were widely used in Europe and, in particular, in spaces built by the Society of Jesus. Panels of azulejos using ornamental mathematical motifs are well known in Portugal and elsewhere. But the mathematical azulejos of Coimbra are unique in that they are genuine didactical aids to the teaching of mathematics and not merely decorative artifacts.

The majority of the Coimbra mathematical azulejos display strictly geometrical (Euclidian) matters, while a few concern other scientific matters. The Euclidian diagrams are drawn from one of André Tacquet’s famous and very popular editions of Euclid’s Elements, which were extensively used in Jesuit schools. The first edition, with the title Elementa geometriae planae ac solidae quibus accedunt selecta ex Archimede theoremata was published in 1654; many other editions and translations were published in the next decades.

A Portuguese translation of Tacquet’s Elements appeared in 1735, thus roughly at the same time as when the tiles were created, and it is tempting to relate the two events and assume that they were drawn from this edition. However, a closer examination reveals that this is not the case. It is clear today that the diagrams in the azulejos were copied from one (or more) of Tacquet’s Latin editions.

This talk is part of the program of the CICM 2014, Conferences on Intelligent Computer Mathematics and of the ADG 2014, 10th International Workshop on Automated Deduction in Geometry