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Mathematics-Online lexicon:

Level Curves and Level Surfaces

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Let $ f = f(x,y) $ be a real function of two variables and let $ c \in \mathbb{R} $ be a constant. Then

$\displaystyle \{(x,y) \in \mathbb{R}^2 ; f(x,y) = c \} $

is called the level curve with value $ c .$

Let $ f = f(x,y,z) $ be a real function of three variables and let $ c \in \mathbb{R} $ be again a constant. Then

$\displaystyle \{(x,y,z) \in \mathbb{R}^3 ; f(x,y,z) = c \} $

is called the level surface of $ f$ with value $ c .$

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  automatically generated 5/21/2008