Hypersurfaces

Part of speech: noun

Definitions

1. A type of geometric entity that generalizes the notion of a surface to higher dimensions within the realm of mathematics
2. A multidimensional analogue of surfaces, often studied in differential geometry and topology, that can exist in various dimensions
3. An abstract concept describing subspaces that can be defined within higher-dimensional spaces, significant in various mathematical fields

Etymology: "Hypersurface" is a compound built from two parts. "Hyper-" comes from the Greek "hyper," meaning "over," "above," or "beyond," and it was used in mathematics to mean "more than three" dimensions. "Surface" comes from Latin "superficies," literally "that which lies on top of" (from "super," "above," plus "facies," "face" or "form"). Put together, a hypersurface is a surface-like object in a space of higher dimension than the ordinary three. The plural "hypersurfaces" is simply the form of "hypersurface" with an "-s" added for multiple objects. The singular itself is a technical coinage from the 19th-century study of geometry, when mathematicians began generalizing the notions of curves and surfaces to spaces with any number of dimensions. The exact date of its first appearance in print is uncertain, but the term belongs to that period of mathematical terminology rather than to older vocabulary.