from The American Heritage® Dictionary of the English Language, 5th Edition.

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

from The Century Dictionary.

  • In mathematics, approaching indefinitely close, as a line to a curve, but never meeting. See II.
  • noun 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.
  • noun 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 the GNU version of the Collaborative International Dictionary of English.

  • noun (Math.) 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 Wiktionary, Creative Commons Attribution/Share-Alike License.

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

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

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


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

[Ultimately from Greek asumptōtos, not intersecting : a-, not; see a– + sumptōtos, intersecting (from sumpiptein, sumptō-, to converge : sun-, syn- + piptein, to fall; see pet- in Indo-European roots).]

from Wiktionary, Creative Commons Attribution/Share-Alike License

From Apollonius Pergaeus's Ancient Greek term ἀσύμπτωτος (asúmptôtos, "not falling together"), from ἀ "not" + σύν "together" + πτωτός "fallen."


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

    May 20, 2011