# Hyperbolic

The adjective **hyperbolic** is used to describe two separate phenomena named in two different nouns. One is used in a mathematical sense, the other in a literary sense.

A **hyperbola** is the name of a curve in mathematics. *OED* says "One of the conic sections; a plane curve consisting of two separate, equal and similar, infinite branches, formed by the intersection of a plane with both branches of a double cone (i.e. two similar cones on opposite sides of the same vertex). It may also be defined as a curve in which the focal distance of any point bears to its distance from the directrix a constant ratio greater than unity. It has two foci, one for each branch, and two asymptotes, which intersect in the centre of the curve, midway between the vertices of its two branches. (Often applied to one branch of the curve.)...Extended (after Newton) to algebraic curves of higher degrees denoted by equations analogous to that of the common hyperbola." To those of us who are not mathematicians, it may be easier to think of it - if we know that much - as the graph of y = x^{-1}, and similar equations.

**Hyperbolic** is also the adjective for the Figure of Speech called **hyperbole** (~ 'exaggeration') - see hyperbole for an explanation.