Contribution for the ICTMT9 - University of Metz - July 2009
In this contribution we address the complementary topics of auto-reference of objects in dynamic geometry and of magnetized objects (as implemented in CarMetal).
Auto-reference will be described as a process creating memory of the manipulation of the user within the figure (Part I).
Among the various uses of auto-reference, we will discuss several applications (Part II).
Magnetized objects have didactic applications such as the extension of the notion of point on objects either from a topological point of view, or from a point of view of increased mathematical reality. These notions will be illustrated with examples at secondary school level and also at university level where magnetization provides a striking approach of finite geometries (Part III).
Part III.5 is an example of algebraic magnetism in PG(3,2) : we see that the determinism is naturaly broken by this type of magnetization.
Finally, in Part IV, we will mix the two technologies, i.e. autoreference and algebraic magnetization, to open up a new realm for dynamic geometry.