Costa Surface

Named after Brazilian mathematician Celsoe Costa, who, inspired by the twirling of a street dancer's skirt, formulated the equations describing a minimal surface with holes: the Costa surface.

This sculpture exemplifies applied mathematics over the course of the past two centuries: start with physical observations about soap films in nature (Plateau), write down a differential equation model describing area minimizing surfaces (Euler-Lagrange), define a minimal surface geometrically in terms of curvature (Gauss), discover a minimal surface with non-trivial topology (Costa), draw computer images of the surface (Hoffman-Hoffman), recognize symmetry and prove the surface has no self intersections (Hoffman-Meeks), discover fast parametric equations for the surface (Gray), and finally return to nature with a sculpture, a solid form of a 'soap film' big enough to touch and climb on. The CRADA between NIST and my studio is a vehicle for applying new technological tools to create aesthetic objects.

(Ferguson, Helaman, Sam Ferguson, Alfred Gray, Claire Ferguson Costa IV Minimal Surface: Sculpture by Virtual Image Projection invited paper given at the ISIS-Symmetry Conference, Washington D.C., August 12-20, 1995.)

ref., paper in Global Geometry, Alfred Gray Memorial Issue

photos by sam ferguson