What is the hypersurfaces theory?

Answer 1

A hypersurface is "an n-dimensional manifold embedded in an n+1 dimensional space" (from http://www.mathpages.com/home/kmath520/kmath520.htm). A manifold is space that close up, appears Euclidean (normal high school geometry) but but be more complicated as a whole. For example, the earth is spherical, more or less, but the closer you get, the more it looks like a two-dimensional surface. Thus, a hyperspace is a surface that exists in a place one dimension higher than what it is. A line on a graph is an example, it is one-dimensional but exists in a two-dimensional world.