Hyperbolie

Hyperbolie is a term used in French to refer to two distinct concepts, depending on the context: a rhetorical figure and a geometric conic. In everyday language and literature, hyperbolie denotes hyperbole, an intentional exaggeration used for emphasis, humor, or critique. It aims to magnify traits, events, or statements beyond literal truth, often to evoke strong feelings or to highlight absurdity. Hyperbolie is common in prose, speech, satire, and advertising, and it relies on the reader or listener recognizing that the claim is not meant to be taken literally.

In mathematics and geometry, hyperbolie names the hyperbola, a conic section. A hyperbola is the set of points in a plane such that the absolute difference of the distances to two fixed points, called foci, is constant. It consists of two separate branches and has characteristic features such as a center, real asymptotes, and a transverse axis. The standard Cartesian equation for a horizontal hyperbola is x^2/a^2 - y^2/b^2 = 1, with asymptotes y = ±(b/a)x. The foci are located at (±c,0) where c^2 = a^2 + b^2, and the eccentricity e = c/a satisfies e > 1.

Etymology and usage differ by field. In rhetoric, the term emphasizes exaggeration for effect; in geometry, it describes a precise, hyperbolic curve with specific algebraic properties. The shared root reflects the sense of going beyond ordinary bounds, whether in style or in shape. See also hyperbola and hyperbole.