asymptote

noun

as·​ymp·​tote ˈa-səm(p)-ˌtōt 

: a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line

asymptotic

ˌa-səm(p)-ˈtä-tik 

adjective

asymptotically

ˌa-səm(p)-ˈtä-ti-k(ə-)lē 

adverb

Illustration of asymptote

• asymptotes to the hyperbola

Examples of asymptote in a Sentence

Recent Examples on the Web

Even at a technical level, traditional pot still distillation is seemingly reaching the asymptote of its innovation curve. —Chris Perugini, Forbes, 16 Jan. 2025

Death, though, is not an asymptote. —Daniel Fienberg, The Hollywood Reporter, 10 Apr. 2023

In contrast, speed over middle and long distances, at least at the elite level, appears to be reaching an asymptote. —Seriously Science, Discover Magazine, 21 July 2017

Bear in mind, though, that hyperbolic functions diverge to infinity at the asymptote. —Seriously Science, Discover Magazine, 2 Feb. 2018

Across the world, most countries have reopened but there remains disquieting uncertainty on whether or not the pandemic has indeed approached its asymptote of endemicity. —David Walcott, Forbes, 17 May 2022

Word History

Etymology

probably from New Latin *asymptotus, from Greek asymptōtos not meeting, from a- + sympiptein to meet — more at symptom

First Known Use

1656, in the meaning defined above