Learning new mathematics from old

This chapter presents a way from which to begin an investigation to develop an engaging project for the learning of mathematics based on its relationship with art. The project on which the chapter is based, was conceived and concluded whilst author worked with secondary mathematics teachers in training in the 2015-16 academic year. The initial research on the art and mathematics contained within the chosen images was conducted by the author, and students were introduced to the project with the aim of putting mathematics in historical and cultural context, to encourage them to seek new meaning in mathematics that they already knew. In the two paintings chosen as the starting point – the Rafael’s The School of Athens and the de’Barbari’s Luca Pacioli, there are two diagrams presented which are similar and both refer to the Euclid’s Elements book XIII. Their interpretations were investigated in the project to establish the relationship between the images and offer new insights related to Euclid’s Elements. The project’s results relate to both historical analysis of these images, and to the use of such a research for giving opportunities to the teachers in training to engage with the study of mathematics through art, in order to examine their views of mathematics and their own relationship towards it. The results point to both the historical analysis of these images, and the use of such research to create opportunities to engage with the study of mathematics