1. A geometric object in mathematics that is one dimension lower than the space it occupies; the generalization of a surface to higher-dimensional spaces.
Usage: technical; mathematics

Examples

• In three-dimensional space, a hypersurface is a two-dimensional surface.
• A sphere is an example of a hypersurface in four-dimensional space.
• The equation x² + y² + z² = 1 defines a hypersurface in three dimensions.
• Mathematicians study the properties of hypersurfaces to understand higher-dimensional geometry.
• In algebraic geometry, hypersurfaces are defined by polynomial equations.