Experimental approaches to theoretical thinking: artefacts and prof

Abstract. It is well known that any sort of instruments, from straightedge and compass to a variety of computational tools created in the course of history, are deeply intertwined with the genesis and development of many abstract concepts and ideas in mathematics. As will be discussed in this chapter, their use introduces an “experimental” dimension in mathematics, and a tense dynamics between the empirical nature of the activities with them, which encompasses perceptual and operational components, and the deductive nature of the discipline, which entails a rigorous and sophisticated formalization