Hyperbolically

Hyperbolically is an adverb derived from the adjective hyperbolic. It describes the manner in which something is performed or described, and it can pertain to both mathematical concepts related to hyperbolas and to rhetorical usage involving exaggeration.

In rhetoric, to speak hyperbolically means to use hyperbole—the deliberate use of exaggeration for emphasis or humorous effect. Hyperbolic statements are typically not intended to be taken literally, and they rely on audience understanding of the exaggeration for its effect.

In mathematics and related disciplines, hyperbolically describes aspects tied to hyperbolas or hyperbolic functions. Hyperbolic functions such as sinh, cosh, and tanh arise from the geometry of a unit hyperbola, and their properties can be described as hyperbolic. The term may also be applied to geometric contexts, such as hyperbolic geometry, where notions of distance and curvature differ from those in Euclidean geometry, leading to growth and relationship patterns that are described as hyperbolic.

Etymology and usage notes: hyperbolics traces to Greek hyperbolē, meaning excess or overstep, with the prefix hyper- meaning over or beyond. The adverb hyperbolically clarifies that a description or behavior operates in a manner associated with hyperbole in language, or with hyperbolic structures in mathematics, without implying literal truth.