Using Dynamic Geometry Software to Simulate Physical Motion

In this paper we analyse to what extent the computational model of the geometry implemented in a dynamic geometry environment provides models for physical motion, focusing on the continuity issues related to motion. In particular, we go over the utility of dynamic geometry environments to simulate the motion of mechanical linkages, as this activity allows us to compare, by means of dynamic drawings, the computable representation of geometric properties with the real motion of a mechanism. Analysing a simple example, we provide theoretical foundations for particular behaviours observed in the motion of a picture on the screen, which require a subtle interpretation to be understood in a purely physical context. In this way, we reflect on some requirements imposed by the computable representation of knowledge. We consider this work to be a necessary step to determine didactic consequences related to students' perceptions of the moving displays; in particular those concerning the uses of the dragging mode as a tool not only for automatic drawing of many instances of a construction,but also to produce continuous motion. This revised version was published online in July 2006 with corrections to the Cover Date.