"Embrace," by Robert Bosch (Oberlin College, Oberlin, OH)

2010 Mathematical Art Exhibition, First Prize.

Stainless steel and brass, Diameter = 6 inches, thickness = 0.25 inches, 2009. 2010 Mathematical Art Exhibition, First Prize. I began by converting a drawing of a two-component link into a symmetric collection of points. By treating the points as the cities of a Traveling Salesman Problem and adding constraints that forced the salesman's tour to be symmetric, I constructed a symmetric simple-closed curve that divides the plane into two pieces: inside and outside. With a water jet cutter, I cut along this Jordan curve through quarter-inch thick, six-inch diameter disks of steel and brass. By swapping inside pieces I obtained two copies of the sculpture. Here, steel is inside and brass is outside. All artists are optimizers. All artists try to perform a task--creating a piece of artwork--at the highest level possible. The main difference between me and other artists is that I use optimization explicitly. Here's how I work: After I get an idea for a piece, I translate the idea into a mathematical optimization problem. I then solve the problem, render the solution, and see if I'm pleased with the result. If I am, I stop. If not, I revise the mathematical optimization problem, solve it, render its solution, and examine it. Often, I need to go through many iterations to end up with a piece that pleases me. I do this out of a love of mathematical optimization--the theory, the algorithms, the numerous applications. --- Robert Bosch (Oberlin College, Oberlin, OH) www.dominoartwork.com