# asymptote

## Definitions

• WordNet 3.6
• n asymptote a straight line that is the limiting value of a curve; can be considered as tangent at infinity "the asymptote of the curve"
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Webster's Revised Unabridged Dictionary
• n Asymptote (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.
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Century Dictionary and Cyclopedia
• asymptote In mathematics, approaching indefinitely close, as a line to a curve, but never meeting. See II.
• n asymptote 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. The asymptote is often defined as the tangent to the curve at an infinite distance, and this definition answers for Euclidean space; but, in view of non-Euclidean hypotheses, it is preferable to define it as a common chord of the curve and the absolute (which see), and thus as not necessarily a tangent.
• n asymptote 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. The smaller of the surfaces bounded by these lines occupies about one fourth of the circumference of the aperture and is marked with loop-lines of growth curving forward.
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Chambers's Twentieth Century Dictionary
• n Asymptote a′sim-tōt (math.) a line that continually approaches nearer to some curve without ever meeting it
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## Etymology

Webster's Revised Unabridged Dictionary
Gr. not falling together; 'a priv. + to fall together; with + to fall. Cf. Symptom
Chambers's Twentieth Century Dictionary
Gr. asymptōtos, not coinciding—a, not, syn, with, ptōtos, apt to fall, pipt-ein, to fall.

## Usage

### In literature:

Those two lines are asymptotes, and will never meet.
"Father Goriot" by Honore de Balzac
Any persons whom it could please could have no better notion of what the words referred to signify than of the meaning of apsides and asymptotes.
"The Professor at the Breakfast Table" by Oliver Wendell Holmes (Sr.)
ASYMPTOTE, a line always approaching some curve but never meeting it.
"The Nuttall Encyclopaedia" by Edited by Rev. James Wood
You must import into your establishment that remarkable phenomenon whose existence is demonstrated in the asymptotes of geometry.
"The Physiology of Marriage, Complete" by Honore de Balzac
Even so there are asymptote figures in geometry where an infinite length makes only a finite progress in breadth.
"Theodicy" by G. W. Leibniz
The curve is symmetrical about the axis of y and has the axis of x for its asymptote.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 7" by Various
The best known example of an asymptotic expansion is Stirling's formula for n!
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3" by Various
Two asymptotes and any two tangents to an hyperbola may be considered as a quadrilateral circumscribed about the hyperbola.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
Any line cuts off equal distances between the curve and the asymptotes.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 2" by Various
That is, up stream A0A1 is asymptotic to C0C1.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 1" by Various
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### In news:

Asymptote at the Venice Biennale.
The Venice Biennale kicks off next week and I caught up with Hani Rashid, co-founder of experimental architectural collective Asymptote , right before he left New York for Europe.
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### In science:

Certainly, a dependence on t and N of the main asymptotic term of SN (t) for large N has been proposed [see Eq. (1)], but nothing is known about the value of its amplitude or prefactor and on the relevance (if any) of the other (corrective) asymptotic terms.
I. Territory covered by N random walkers on deterministic fractals. The Sierpinski gasket
However the spacetime need not be locally AdS asymptotically – locally asymptotically ﬂat cases may also be included .
Generalized entropy and Noether charge
Our proof is based on a novel asymptotic property of the skew-orthogonal polynomials: an integral over the corresponding wavefunctions oscillates about half its asymptotic value in the region of the bulk of the zeros.
Spectral Universality of Real Chiral Random Matrix Ensembles
I would conjecture that asymptotically at small x ≡ 2πRE , the density matrix (19), with all the entropy-maximization procedures given above for a density matrix of this form, gives B (x) that does asymptotically approach the unknown global maximum function BN (x) for a single massless scalar ﬁeld.
Defining Entropy Bounds
The energy E is more problematic, at least if the universe is not asymptotically ﬂat, though if one can restrict to quantum states in which the universe is asymptotically ﬂat, then E also might have a good deﬁnition in quantum gravity.
Defining Entropy Bounds
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