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. |image2=Level sets linear function 3d.svg |caption2=Lines at constant slices of . |image3=Level sets linear function 4d.svg |caption3=Planes at constant slices of . |footer=-dimensional level sets for functions of the form where ''a''1, ''a''2, ..., ''a''''n'' are constants, in -dimensional Euclidean space, for ''n'' = 1, 2, 3.}} . |image2=Level sets non-linear function 3d.svg |caption2=Contour curves at constant slices of . |image3=Level sets non-linear function 4d.svg |caption3=Curved surfaces at constant slices of . |footer=-dimensional level sets of non-linear functions ''f''(''x''1, ''x''2, ..., ''x''''n'') in -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 of the form : that is, a set where the function takes on a given constant value ''c''. When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline. So a level curve is the set of all real-valued solutions of an equation in two variables ''x''1 and ''x''2. When ''n'' = 3, a level set is called a level surface (see also isosurface), and for higher values of ''n'' the level set is a level hypersurface. So a ''level surface'' is the set of all real-valued roots of an equation in three variables ''x''1, ''x''2 and ''x''3, and a level hypersurface is the set of all real-valued roots of an equation in ''n'' (''n'' > 3) variables. A level set is a special case of a fiber. ==Alternative names== Level sets show up in many applications, often under different names. For example, an implicit curve is a level curve, which is considered independently of its neighbor curves, emphasizing that such a curve is defined by an implicit equation. Analogously, a level surface is sometimes called an implicit surface or an isosurface. The name isocontour is also used, which means a contour of equal height. In various application areas, isocontours have received specific names, which indicate often the nature of the values of the considered function, such as isobar, isotherm, isogon, isochrone, isoquant and indifference curve. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Level set」の詳細全文を読む スポンサード リンク
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