Dynamic Geometry from 2D to 3D: Specific Issues

Examples out of Cabri 3D

Jean-Marie Laborde
Cabrilog - Université Joseph Fourier Grenoble
38041 Grenoble Cedex 9, France

Abstract. Dynamic geometry has proven to be successful to allow for students (as well as for anybody!) to get a more in depth perception and understanding of geometric phenomena and finally of mathematical realty. Even if 2D oriented geometry environments like Cabri, Cinderella, Geometry Expert or GSP can be used to create 3D situations, it is clear that those are not truly 3D environments. In this presentation I will address some of the issues encountered in designing a 3D environment in the spirit of dynamic geometry, both from a cognitive point of view as from a computer science point of view. At first glance some problems seem not to be really difficult, based on static understanding of geometry, but actually they are not, they are even drastically more difficult to face in 3D than 2D: the question of implicit orientation, the question of intrinsic parameterization can be mentioned. Examples, out of newly appeared SW environment Cabri 3D, will be used.