Back خط المستوى Arabic Üfüqi səth Azerbaijani Conjunt de nivell Catalan Niveaumenge German Conjunto de nivel Spanish مجموعه تراز Persian Ligne de niveau French Insieme di livello Italian 等位集合 Japanese 레벨집합 Korean
Points at constant slices of x2 = f (x1).
Lines at constant slices of x3 = f (x1, x2).
Planes at constant slices of x4 = f (x1, x2, x3).
(n − 1)-dimensional level sets for functions of the form f (x1, x2, …, xn) = a1x1 + a2x2 + ⋯ + anxn where a1, a2, …, an are constants, in (n + 1)-dimensional Euclidean space, for n = 1, 2, 3.
Points at constant slices of x2 = f (x1).
Contour curves at constant slices of x3 = f (x1, x2).
Curved surfaces at constant slices of x4 = f (x1, x2, x3).
(n − 1)-dimensional level sets of non-linear functions f (x1, x2, …, xn) in (n + 1)-dimensional Euclidean space, for n = 1, 2, 3.
In mathematics, a level set of a real-valued function f of n real variables is a set where the function takes on a given constant value c, that is:
When the number of independent variables is two, a level set is called a level curve, also known as contour line or isoline; so a level curve is the set of all real-valued solutions of an equation in two variables x1 and x2. When n = 3, a level set is called a level surface (or isosurface); so a level surface is the set of all real-valued roots of an equation in three variables x1, x2 and x3. For higher values of n, the level set is a level hypersurface, the set of all real-valued roots of an equation in n > 3 variables.
A level set is a special case of a fiber.