## Robert Bosch

* "Knot?" *

Digital print, 34" x 34", 2006

"Knot?" is a continuous line drawing constructed
from the solution to a 5000-city instance of the
Traveling Salesman Problem. From afar, the piece
appears to be a picture of a celtic knot (a black
cord on a white background). From up close, the
piece is seen to be a simple closed curve (in
white, on a black background) and therefore not
a knot at all!

* "What's Inside?" *

Digital print on canvas, 44" by 34", 2006

"What's Inside?" is a continuous line drawing constructed
from the solution to a 25000-city instance of the Traveling
Salesman Problem. It is a simple closed curve drawn in
black ink on a white background. From afar, it resembles
one of Warhol's Soup Cans paintings. (Note: This piece
is paired with the third piece.)

* "This is!" *

Digital print on canvas, 44" by 34", 2006

The piece "What's Inside?" is a simple closed curve. The
Jordan Curve Theorem states that any simpled closed curve
in the plane divides the plane into two regions: the part
that lies inside the curve, and the part that lies outside.
The piece "This is!" displays the interior of the "What's
Inside?" curve, drawn in tomato-soup red. (Note: This
piece is paired with the second piece.)

Robert Bosch

Professor of Mathematics,
Robert and Eleanor Biggs Professor of Natural Science, Department of Mathematics, Oberlin College

Founder of http://www.dominoartwork.com

Statement about my art:

"I specialize in "Opt Art", the use of mathematical
optimization techniques to create pictures, portraits,
and sculpture. I have used integer programming to
create portraits out of complete sets of dominoes. I
have used linear programming to create pointillistic
portraits. And I was the first to use instances of the
Traveling Salesman Problem to create continuous line
drawings. (Craig S. Kaplan, a collaborator who helped
me improve my method considerably, submitted a stunning
"TSP Art" portrait of Khachiyan last year.)
What all my pieces have in common---aside from how
they were constructed---is that they look very different
up close than they do from afar.
I create my artwork out of a love of optimization---the
theory, the algorithms, its numerous applications. I
believe that optimization can be applied to virtually any
imaginable field, and I believe that my artwork does a
good job of helping me make that point!"