Science & Art: Robert Longhurst

A minimal surface is one whose area becomes greater whenever it is distorted. At any given point, a minimal surface either is flat or has a saddle shape, and the mean curvature of such a surface is zero. When fabricated, minimal surfaces are quite strong; thus, these objects have many potential applications in design.

The form pictured to the right was expressed in 1864 by Alfred Enneper, a mathematician at the University of Göttingen. This highly symmetric surface that bears Enneper's name is defined by a simple equation, and its shape is complex and lovely. It is essentially a disk warped into a saddle shape until it self-intersects; here, its edge has been arrested just prior to self-intersection.

If you were to take a piece of wire and twist it around the edge of the sculpture, then dip the resulting loop in soapy water, the resulting form would echo the topology of the carved wood.

Minimal surfaces appear in a broad spectrum of physical problems with varying degrees of practicality. Either explicitly or implicitly, many sculptures make use of their forms and properties. Such works can be perceived as purely aesthetic abstract shapes, or as figurative representations of mathematical objects, depending on the mathematical literacy of the audience.

There is a rich history to using mathematical forms in works of art, and Robert Longhurst is one of many sculptors engaging this tradition. I am interested in how he uses organic material to achieve organic shapes, mediated by formulae and analyses often perceived as abstruse or dry. His work reveals a creative and elegant approach to critical thinking, giving lie to common misconceptions about the field of mathematics.