Level Set

The level set of a differentiable function f:R^n->R corresponding to a real value c 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 f(x,y,z)=x^2+y^2+z^2 corresponding to the value c is the sphere x^2+y^2+z^2=c with center (0,0,0) and radius sqrt(c).

If n=2, the level set is a plane curve known as a level curve. If n=3, the level set is a surface known as a level surface.

See also

Contour Plot, Cross Section, Equipotential Curve, Level Curve, Level Surface

Explore with Wolfram|Alpha


Gray, A. "Level Surfaces in R^3." §12.7 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 291-293, 1997.

Referenced on Wolfram|Alpha

Level Set

Cite this as:

Weisstein, Eric W. "Level Set." From MathWorld--A Wolfram Web Resource.

Subject classifications