# Level curve

### From Conservapedia

In mathematics, a **level curve** is the curve formed by taking all the values of some functions such that the function is some constant value *c*. A set of level curves for different constants *c* is referred to as a contour plot.

These are also referred to as **isocurves** of the function. For functions of three variables, the terms **level surface** or **isosurface** are used.

The value of a function is identical at every point along any of its level curves. For example, the level curve of the paraboloid *Z*(*x*,*y*) = *x*^{2} + *y*^{2} at Z=4 is the circle *x*^{2} + *y*^{2} = 4. Therefore, the gradient of a function (which represents the rate of fastest change) is always perpendicular to its level curves because it is a vector that takes the direction of maximum increase in f.