Electronic Proceedings
of the 12th Asian Technology Conference in Mathematics
Abstract
for 12957
Two explorations with Cabri
3D leading to two theorems
Authors: Jean-Jacques Dahan
Affiliations: IREM of Toulouse
Keywords: Intermediate, Advanced, Undergraduate Level, Graduate
Level, experiment, conjecture, discovery, quasi-tessellation, convex
hull
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 Center of Hong Kong. The proof will
be exposed. Eventually we will present quasi-tessellations to
illustrate the Schwarz paradox in relation with the lateral area of
a cylinder.