A level curve is a curve that connects all points of equal elevation on a surface. In mathematics, it is also known as an isocontour or contour line. Other synonyms for level curve include contour, isopleth, isoline, and equipotential line. These terms are commonly used in various fields such as geography, cartography, and physics to represent the shape and characteristics of a surface. In geography, level curves are used to depict elevation on topographical maps. In physics, they are used to show regions of constant potential energy or magnetic field strength. Regardless of the field, level curves provide valuable information on the shape and features of a surface.