Aiman Soliman
Mathematical art is a unique form of artistic expression. Unlike other
forms of art, the rigor of mathematics provides a guide for the
imagination, although it could be restrictive sometimes compared to
free artistic expression. Yet, these strict mathematical rules allow
for judging, objectively, the success of an art project. I also find
that mathematical artists share a similar experience with scientists
in that solving a problem will usually lead to discovering another
and, therefore, the continuation of their work in a natural way.
This work presents an artistic depiction of the classic Calisson
geometry. The Calisson problem is about filling a hexagon space
using rhombuses in the three different orientations, which are
permissible by the rhombus shape. Regardless of the configuration
used to pack the hexagon space with rhombuses, we will always end
with an equal number of rhombuses from the three orientations.
Here, I present the three orientations as a fish, a lizard, and a
bird with matching edges to fill the space with no gaps. A parquet
deformation transforms the motifs to 3D cubes following the
intuitive proof without words of this problem suggested by David
and Tomei in 1989, which is ‘unfortunately’ subject to optical
illusions.