# John M. Sullivan

Professor of Mathematics

Technische Universität Berlin

Berlin, Germany

My art is an outgrowth of my work as a mathematician. My research studies curves and surfaces whose shape is determined by optimization principles or minimization of energy. A classical example is a soap bubble which is round because it minimizes its area while enclosing a fixed volume.

Like most research mathematicians, I find beauty in the elegant structure of mathematical proofs, and I feel that this elegance is discovered, not invented, by humans. I am fortunate that my own work also leads to visually appealing shapes, which can present a kind of beauty more accessible to the public.

Like most research mathematicians, I find beauty in the elegant structure of mathematical proofs, and I feel that this elegance is discovered, not invented, by humans. I am fortunate that my own work also leads to visually appealing shapes, which can present a kind of beauty more accessible to the public.

Minimal Flower 3

3" x 4" x 4"

Sculpture (3D FDM print)

2001

"Minimal Flower 3" shows a nonorientable minimal surface spanning (like a soap film) a certain knotted boundary curve. The surface, like the knotted boundary itself, has 322 symmetry, meaning three-fold and two-fold rotational symmetry but no mirrors. The mathematical surface is thickened into a three-dimensional sculpture by simulating the process of blowing a bit of air in between two parallel sheets of soap film. To create a more pleasing result, the surfaces are actually modeled in 3D hyperbolic space. This sculpture is an homage to Brent Collins, whose "Atomic Flower II" has the same topology.

Minimal Flower 4

3" x 5" x 5"

Sculpture (3D FDM print)

2010

"Minimal Flower 4" shows a nonorientable minimal surface spanning (like a soap film) a certain knotted boundary curve. The surface, like the knotted boundary itself, has 422 symmetry, meaning four-fold and two-fold rotational symmetry axes but no mirrors. The mathematical surface is thickened into a three-dimensional sculpture by simulating the process of blowing a bit of air in between two parallel sheets of soap film. To create a more pleasing result, the surfaces are actually modeled in 3D hyperbolic space.