Wiktionary
n. (context mathematics English) A ''n''-dimensional surface in a space (often a Euclidean space) of dimension ''n''+1
Wikipedia
''' Ackley's function of three variables, with time the 3rd variable.
In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of dimensions is a hypersurface. Equivalently, the codimension of a hypersurface is one. For example, the n-sphere in R is called a hypersphere. Hypersurfaces occur frequently in multivariable calculus as level sets.
In R, every closed hypersurface is orientable. Every connected compact hypersurface is a level set, and separates R in two connected components, which is related to the Jordan–Brouwer separation theorem.
In algebraic geometry, a hypersurface in projective space of dimension n is an algebraic set (algebraic variety) that is purely of dimension . It is then defined by a single equation , a homogeneous polynomial in the homogeneous coordinates.
Thus, it generalizes those algebraic curves (dimension one), and those algebraic surfaces (dimension two), when they are defined by homogeneous polynomials.
A hypersurface may have singularities, and hence is not necessarily a submanifold in the strict sense. "Primal" is an old term for an irreducible hypersurface.
Usage examples of "hypersurface".
Some of the endless pink surfaces were spheres that seamlessly blended together -- surely these were views of the hyperspherical powerball finger of Om whose hypersurface enclosed the rest of his body.
As the wall went past, Ralph occupied himself by displaying four-dimensional hypersurfaces to himself .
He often did this, to no apparent purpose, but it sometimes happened that a particularly interesting hypersurface could serve to model a significant relationship.
I see hypersurfaces twisting in mathematical gales, hear the voices of the night, feel the three degree hum of the universe's birth as you feel the breeze that plays across your skin.
Intangible light and dark over impossible hypersurfaces, the Oaxacan entity was talking with its attenuated, emergent sibling.
Swirling above the planetary pole, coherent light and dark and with impossible volumes smeared across its intangible hypersurfaces, was the Child of Water that had once been Oaxaca.
The force diminished with distance as if it was being spread out over, respectively, an ever larger two-dimensional surface, producing an inverse-square law, or a four-dimensional hypersurface, yielding a visibly steeper inverse-fourth-power effect.