Invisible Handshake: Costa Minimal Surface

The images shown here were taken by Claire Ferguson on site in Breckenridge, Colorado in January 19-24, 1999 at the International Snow Sculpture Championships. This piece was entitled "Invisible Handshake" because it is the negative space of two hands just before the two hands clasp. Two such wye forms about to couple succinctly describes the topology of the Costa surface itself and suggests the differential geometry of negative Gaussian curvature. I carved this work with the assistance of Stan Wagon, Dan Schwalbe, Tomas Nemeth, and posthumously Alfred Gray. We began with a 12'x10'x10' 20 ton block of dense artificial snow; we were given four days to complete it, no power tools were allowed. Cf., Barry Cipra, "Minimal Till It Melts", SIAM News, March 1999, two photos, page 20; "Melting Minimalist", SCIENCE, volume 283, 5 February 1999, one photo, page 787; also, forthcoming articles in MiER and the Mathematical Intelligencer.

I choose this negative Gaussian curvature geometric form specifically because of the material properties of snow. Snow with its fair compressive strength and poor tensile strength is a caricature of stone. But negative Gaussian curvature, even in snow, presents a fabric of saddle points everywhere. Each point of the surface is the keystone of a pair of principle arches. There were 14 other snow sculptures completed at the Breckenridge affair; a week later they all completely imploded in the heat wave. Our negative Gaussian curvature snow carving stood, retained its structure, sublimed, thinned, gracile.

photos by claire ferguson