__Electronic Proceedings
of the 12 ^{th} Asian Technology Conference in Mathematics__

**Abstract for 12724 **

Two explorations with Cabri 3D leading to two theorems

Authors: Jean-Jacques Dahan

Affiliations: IREM of Toulouse

Keywords:

Topics: Applications using
Dynamic/Interactive Geometry or/and CAS

Exploring the volume of the convex envelope of a net of a cube with Cabri 3D, as the net opens and closes will lead to a conjecture about the maximum of this volume. We will prove this conjecture. We will also solve experimentally the problem of the tessellation of a cylinder with equilateral triangles after the observation of a picture taken in the convention enter of Hong Kong. The proof will be exposed. Eventually we will present quasi-tesselations to illustrate the Schwarz paradox in relation with the lateral area of a cylinder