Francesco De Comité

Associate Professor of Computer Science
Computer Science Department, Univeristy of Lille, France
Lille, France

Manipulation of digital images, and use of ray-tracing software can help you to concretize mathematical concepts. Either for giving you an idea of how a real object will look or to represent imaginary landscapes only computers can handle.

Things become yet more interesting, when you can transform your two-dimensional dream objects in real three dimensional sculptures. You can then handle your creations, and look at them from an infinity of view angles.

A Steiner Chain Trapped Inside Two Sets of Villarceau Circles
60 x 80 cm
Digital print on cardboard

Ring cyclides are images of tori under sphere inversion. If certain conditions are fullfilled, a torus can contain a set of tangents spheres. Since the tangency property is preserved by inversion, this set of tangent spheres find its place inside the cyclide.

Hypocycloidal Virtual String Art
60 x 80 cm
Digital Print on Cardboard

Hypocycloids are basically two-dimensionnal curves. We can add the third dimension by moving the pen up and down while drawing it. One can then imagine two points moving on this curve, and draw a line between these two points at regular intervals. Playing with the curve and the speed of the moving points makes one explore an infinite variety of shapes.