asymptote

American  

[as-im-toht] / ˈæs ɪmˌtoʊt /

noun

Mathematics.

1. a straight line approached by a given curve as one of the variables in the equation of the curve approaches infinity.

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asymptote British  

/ ˈæsɪmˌtəʊt /

noun

1. a straight line that is closely approached by a plane curve so that the perpendicular distance between them decreases to zero as the distance from the origin increases to infinity

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asymptote Scientific  

/ ăs′ĭm-tōt′ /

1. A line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve.

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Etymology

Origin of asymptote

1650–60; < Greek asýmptōtos, equivalent to a- a- ⁶ + sýmptōtos falling together ( sym- sym- + ptōtós falling, derivative of ptō-, variant stem of píptein to fall + -tos verbid suffix)

Explanation

In geometry, an asymptote of a curve is a straight line that gets closer and closer but never touches the curve. An asymptote is sometimes called a tangent. This is a term you're most likely to come across in math class. An asymptote is a straight line, but specifically one that approaches or nears a curve but never meets it. The noun asymptote has been a geometry term since the 1600's, and it comes from the Greek root asymptotos, or "not falling together," which combines a, "not," syn, "with," and ptotos, "fallen."

Example Sentences

The horizontal asymptote of an exponential function tells us the limit of the function’s values as the independent variable gets either extremely large or extremely small.

From Textbooks • Dec. 21, 2021

Find the horizontal asymptote and interpret it in context of the problem.

From Textbooks • Dec. 1, 2021

Do they all have the same vertical asymptote?

From Textbooks • Sep. 23, 2020

Figure 4.53 The graph of this rational function approaches a horizontal asymptote as x → ±∞.

From Textbooks • Mar. 30, 2016

To-day is but the asymptote of to-morrow, that curve perpetually drawing near, but never reaching the straight line flying into infinity.

From The Atlantic Monthly, Volume 18, No. 107, September, 1866 by Various