Definitions

from The American Heritage® Dictionary of the English Language, 4th Edition

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

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. A straight line which a curve approaches arbitrarily closely, as they go to infinity. The limit of the curve, its tangent "at infinity".
  • n. Anything which comes near to but never meets something else.
  • v. To approach, but never quite touch, a straight line, as something goes to infinity.

from the GNU version of the Collaborative International Dictionary of English

  • n. A line which approaches nearer to some curve than assignable distance, but, though infinitely extended, would never meet it. Asymptotes may be straight lines or curves. A rectilinear asymptote may be conceived as a tangent to the curve at an infinite distance.

from The Century Dictionary and Cyclopedia

  • In mathematics, approaching indefinitely close, as a line to a curve, but never meeting. See II.
  • n. A straight line whose distance from a curve is less than any assignable quantity, but which does not meet the curve at any finite distance from the origin.
  • n. In zoology, either of two straight lines drawn from the apex to the aperture of the conical part of the phragmocone in the belemnites or fossil dibranchiate cephalopods.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

  • n. a straight line that is the limiting value of a curve; can be considered as tangent at infinity

Etymologies

Ultimately from Greek asumptōtos, not intersecting : a-, not; see a-1 + sumptōtos, intersecting (from sumpiptein, sumptō-, to converge : sun-, syn- + piptein, to fall.
(American Heritage® Dictionary of the English Language, Fourth Edition)
From Apollonius Pergaeus's Ancient Greek term ἀσύμπτωτος (asúmptôtos, "not falling together"), from ἀ "not" + σύν "together" + πτωτός "fallen." (Wiktionary)

Examples

Comments

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  • JM draws a line at asymptote after finding that it just goes on and on and on.

    May 20, 2011