The Formulas

The formulas for the Costa surface are etched into the side of the sculpture, and involve complex numbers and special functions from the nineteenth century called Weierstrass elliptic and Weierstrass zeta functions. The Mathematica code below shows how one can define Costa in terms of these functions, where the domain is the unit square in the complex plane. That is, given with u and v between 0 and 1, one can define a point in 3-space by the Costa formula that follows. Because one can also go from a square to a torus, this provides the link between Costa and torus that is exploited to get the morphing movie in the Triply Punctured Torus section.