Asymptote Definition

ăsĭm-tōt, -ĭmp-
noun
A straight line always approaching but never meeting a curve; tangent to a curve at infinity.
Webster's New World

(analysis) A straight line which a curve approaches arbitrarily closely, as they go to infinity. The limit of the curve, its tangent "at infinity".

Wiktionary
(by extension, figuratively) Anything which comes near to but never meets something else.
Wiktionary
A line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve.
American Heritage
verb

(analysis) To approach, but never quite touch, a straight line, as something goes to infinity.

Wiktionary

Other Word Forms of Asymptote

Noun

Singular:
asymptote
Plural:
asymptotes

Origin of Asymptote

  • Ultimately from Greek asumptōtos not intersecting a- not a–1 sumptōtos intersecting (from sumpiptein sumptō- to converge) (sun- syn-) (piptein to fall pet- in Indo-European roots)

    From American Heritage Dictionary of the English Language, 5th Edition

  • From Apollonius Pergaeus's Ancient Greek term ἀσύμπτωτος (asúmptōtos, “not falling together”), from (a, “not”) + σύν (sun, “together”) + πτωτός (ptōtos, “fallen”).

    From Wiktionary

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