# David Bachman

## Artists

## Statement

As a mathematician, I see the intrinsic beauty in mathematics. Art is a way for me to share this beauty with others. My work begins with a shape that I find aesthetically pleasing. I then boil it down to its mathematical essence with equations and code. In that form I can play with it, modify it, and search for new ways to present it. Fabrication is done in a variety of media using 3D printing and finished by hand.

## Artworks

This piece is a reinterpretation of the classic Yin-Yang motif as a mathematical surface. The surface that separates the two spheres is defined by a parameterization of my own invention, given (in cylindrical coordinates) by (t, theta, z)=(t*cos(f), theta, t*sin(f)), where f=arcsin(t)*sin(3*theta).

The basic profile curve, seen on the edge of the shell, was "hand" drawn on a computer screen. Then a script was written which used this curve to parametrically generate the outer surface of the shell and add the spines. Further modification was then done to create a 3D printable model from this surface. Finally, coloring was added from a photograph of a real shell.

The familiar Mobius band is a line segment which is given 1/2 of a twist as it is swept around a circle. This form is created from sweeping a "Y" shape around a circle and adding 1/3 of a twist. The resulting object has just one continuous edge to it. If capped off with a disk (in four dimensions, of course!), the result would be what topologists call the "spine" of the lens space L(3,1), a possible alternate universe from our own.