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."

## Examples

• In that case, if you plot the number of record highs or lows on a graph, you'd get a line that falls gradually as time progresses toward an asymptote, which is mathematically expressed as 1/n, where n is the number of years in your data set.

• Man is the asymptote of what he predicates God to be.

Getting Godless Bill Yarrow 2011

• "What part of an inverse tangent function approaching an asymptote don't you understand?"

• Little did they know that they were just a literary device for explaining the asymptote opposite to Ralph and Piggy, the social cage where expected behavior overwhelms the individual totally.

• Then I walk around downtown Cleveland, using the View option to study a random timeline as far up the 300 year Masterson asymptote as I can get (usually at least a quarter millennium).

• For his opening move — in which "Oh" would have been a feasible if less canonic alternative (fully licensed by the dictionary) — is a line that negotiates in process between the vocal base line of expressive oralilty, on the near hand, and, at expression's farthest reach, the vocative asymptote of natural communion with inanimate energy.

• Marked by the thickened release of "good" from "growing," what we find inscribed from within narrative time is both a phrase for cumulative social improvement and an asymptote of its visionary teleology as well, Tennyson secularized: the immediate "growing betterment" (participial adjective plus noun) as well as, hard on its heels, the "growing [ultimately] good"

• Like a curve forever approaching its asymptote but never touching it, I could potentially add to the list forever.

Assholes Finish First Tucker Max 2010

• Buchannan, at least, I think he can't displace; the man was practically an asymptote.

"Edge Of Darkness" (2010) Steven Barnes 2010

• Then I walk around downtown Cleveland, using the View option to study a random timeline as far up the 300 year Masterson asymptote as I can get (usually at least a quarter millennium).