Level Set

The level set of a differentiable function corresponding to a real value is the set of points

${(x_1,...,x_n) in R^n:f(x_1,...,x_n)=c}.$

For example, the level set of the function corresponding to the value is the sphere with center and radius .

If , the level set is a plane curve known as a level curve. If , the level set is a surface known as a level surface.

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Gray, A. "Level Surfaces in

." §12.7 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 291-293, 1997.