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The x-axis and y-axis are asymptotes of the hyperbola xy = 3.


 (ăs′ĭm-tōt′, -ĭmp-)
A line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve.

[Ultimately from Greek asumptōtos, not intersecting : a-, not; see a-1 + sumptōtos, intersecting (from sumpiptein, sumptō-, to converge : sun-, syn- + piptein, to fall; see pet- in Indo-European roots).]

as′ymp·tot′ic (-tŏt′ĭk), as′ymp·tot′i·cal adj.
as′ymp·tot′i·cal·ly adv.


(Mathematics) a straight line that is closely approached by a plane curve so that the perpendicular distance between them decreases to zero as the distance from the origin increases to infinity
[C17: from Greek asumptōtos not falling together, from a-1 + syn- + ptōtos inclined to fall, from piptein to fall]


(ˈæs ɪmˌtoʊt)

Math. a straight line approached by a given curve as one of the variables in the equation of the curve approaches infinity.
[1650–60; < Greek asýmptōtos literally, not meeting =a- a-6 + sýmptōtos, v. adj. of sympíptein to converge; see symptom]
click for a larger image
left: The x- and y-axes are both asymptotes of the curve (a hyperbola).
right: The x-axis is the asymptote of the wave.


A line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.asymptote - a straight line that is the limiting value of a curve; can be considered as tangent at infinity; "the asymptote of the curve"
straight line - a line traced by a point traveling in a constant direction; a line of zero curvature; "the shortest distance between two points is a straight line"
References in periodicals archive ?
If the system has stable equilibrium point, the control goal is to design the controller to make the system (2.2) global asymptotical stabilization approach the equilibrium point.
Besides, the asymptotical stability of the methods is also discussed in the present paper.
Unlike the case of Friedmann-Robertson-Walker scale factor, one cannot hide the function S in the definitions of the spatial coordinates, which are already set by the assumption to have the asymptotical Minkowski (or de Sitter) metric.
(31) are described in [39] in terms of Bessel, Kummer, and Tricomi special functions, but here we are not interested in the asymptotical behavior of the solution at zero or infinity.
In Section 4, we profile these solution operator families in terms of vector-valued Laplace transform, while in Section 5 we consider asymptotical behaviour of analytic integrated solution operator families for (1).
There have been many results about the sliding control algorithms for PMLM in the literature, such as [13,19], and the most of control laws are based on the design of continuous-time SMC laws with asymptotical convergence.
The asymptotical solution, however, does not depend on this starting point (that is, the attractor is globally asymptotically stable).
In this section, we study the stability of nonlinear fractional differential systems with Caputo derivative by utilizing a Lyapunov-like function, taking into account the relation between asymptotical stability and generalized Mittag-Leffler criteria.
[28] derive some sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional-order a satisfying 0 < [alpha] < 2.
In this section, we dynamically analyze system (7) to study the existence, uniqueness and orbital asymptotical stability of the OOPS.
However, others have been also studied lately, each one with the respective mathematical description (Ishizaka & Labib 2011), among which are: Power, Root Square, Geometric, Inverse linear, Asymptotical, Balanced and Logarithmic.
By investigating the properties of this Markov chain, the asymptotical average throughput is derived.

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