The Indivisibles: a travel in time and space from Archimedes to Cavalieri

This paper presents a teaching experiment that brings together the history of mathematics and mathematics laboratory of three-dimensional Euclidean geometry, with the use of artefacts and physical experiences. It has been realized with a class group of 24 high school students (12th grade), who were encouraged to become time traveller historians and mathematicians, investigating analogies and differences between Archimedes’ and Cavalieri’s methods to estimate volumes. The project had a double goal: from a research point of view, it pointed at evaluating the effectiveness of an historical inspired activity to update students’ common culture about mathematics, while from a didactical point of view, the aim of this experience was exploiting the feeling of personal discovery that epitomizes hands-on activities as a pivot to promote a critical attitude towards Euclidean geometry as well as to endorse a historical approach to calculus.