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.

---

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

---

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.

---

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

No. A horizontal asymptote would suggest a limit on the range, and the range of any logarithmic function in general form is all real numbers.

From Textbooks • Dec. 21, 2021

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

From Textbooks • Dec. 1, 2021

When the graph approaches the y-axis so very closely but will never cross it, we call the line x = 0, the y-axis, a vertical asymptote.

From Textbooks • May 6, 2020

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

From Textbooks • Mar. 30, 2016

As still to its asymptote speedeth the curve, So approximates Man—Thee, who reachable not, Hast formed him to yearningly Follow thy whole Sole and single omniscience!”

From Browning and His Century by Clarke, Helen Archibald