In differential geometry, a minimal surface is an idealized soap film. Scherk's first surface, described in 1834, satisfies two unusual properties. First, it is doubly periodic, made of repeating units in two non-parallel directions. Second, each basic unit is a graph over a square, together with vertical lines at each corner. The full surface casts a checkerboard shadow. In this image, the portion of surface over a 5 by 5 is shown with a grid of curves obtained by holding one variable or the other constant.
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