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Definition, some properties. Feel free to expand!
A '''level curve''' is the [[curve]] formed by the intersection of an '''''n'''''-dimensional function with an '''''n-1'''''-dimensional plane. For example, a two-dimensional level curve is formed by the intersection of a 3-dimensional function with a plane. Level curves are often used in [[mathematics]] to show on a two-dimensional graph how three-dimensional functions are changing.
The value of a function is identical at every point along any of its level curves. For example, the level curve of the [[paraboloid]] <math>Z(x,y)=x^2+y^2</math> at Z=4 is the circle <math>x^2+y^2=4</math>. Therefore, the [[gradient]] of a function (which represents the rate of fastest change) is always [[perpendicular]] to its level curves.
[[Category:Mathematics]]
[[Category:Geometry]]
The value of a function is identical at every point along any of its level curves. For example, the level curve of the [[paraboloid]] <math>Z(x,y)=x^2+y^2</math> at Z=4 is the circle <math>x^2+y^2=4</math>. Therefore, the [[gradient]] of a function (which represents the rate of fastest change) is always [[perpendicular]] to its level curves.
[[Category:Mathematics]]
[[Category:Geometry]]