asymptote love

# asymptote

## Definitions

### 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.

• 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.

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

## Etymologies

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