1.6. Exercises 25 − π 4 0 π 4 − π 4 0 π 4 -4 0 4 Figure 1.13. Scherk’s first minimal surface 1.6.10. Scherk’s minimal surface. Take the minimal surface equa- tion, equation (1.47), and look for a solution of the form f(x, y) = g(x) + h(y) . (1.70) Show that the resulting differential equation is separable. Solve for g(x) and h(y) to obtain Scherk’s (first) minimal surface, f(x, y) = c ln cos (x/c) cos (y/c) . (1.71) This surface was the first minimal surface discovered after the catenoid and the helicoid. A piece of this surface, for c = 1, −π/2 x π/2, and −π/2 y π/2, is shown in Figure 1.13.
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