## Harry Benke |

Giclee Print. 18" x 14.8", 2009.

The Vase is composed of a digitally modeled vase with "Lilies" which are Dini's Surfaces. A surface of constant negative curvature obtained by twisting a pseudosphere is known as Dini's Surface.
Imagine cutting the pseudosphere along one of the meridians and physically twisting it. Its parametric equations are:

x=acos(u)sin(v); y=asin(u)sin (v);
z=a{cos(v)+ln[tan(v/2)]}+bu, where 0≤u≤2π and 0< v< π. Take a=1 and b=0.2.

Harry Benke, Artist / Mathematician

Novato, California

"I'm primarily an artist. My shadow is mathematics. I'm helpless at preventing mathematics from intruding in my work and it's delightful to have the body of mathematics to work with. My art attempts to produce a nexus between mathematical beauty and the beauty of the natural world to produce a satisfying aesthetic experience."