Richard Kallweit

Bethany, Ct

I use artistic means to develop mathematical ideas. These include use of materials, close observations, long periods of contemplation and a developed sense of play. I believe that the intuitive and playful aspects of art expression can lead to many unexpected discoveries.

Cantor Dust
Cantor Dust
wood , spray paint

This is a variation on a Cantor diagram in three dimensions. In this arrangement the negative and positives spaces alternate going from 13 cubes in a nine square pattern to 14 cubes in a nine square pattern to make the larger piece. .
This type of work began first with gluing together sugar cubes (an available cubic resource) in order to make simple/complex structures after looking at the first publication by Mandelbrot 1977. I later switched to wooden cubes and then began attaching them edge to edge and stacking them in various combinations. The use of negative space is paramount.The corners of the cubes have been truncated as a decorative device as well as changing the cubes into a different polyhedral shapes.

Stellar Icosahedron
Stellar Icosahedron
printed paper

I have long used a pentagonal lozenge of 72 and 108 degrees. If you score and fold this shape lengthwise you get this polyhedron. If you score and fold in reverse it is a triacontahedron with curved surfaces. Both use 30 shapes. I was just joining and using this one shape in various combinations and came up with these polyhedra.The pattern on the planes is one I developed long ago and reuse.