What is "asymptote"

Asymptote \As"ymp*tote\ (?; 215), n. [Gr. ? not falling together; 'a priv. + ? to fall together; ? with + ? to fall. Cf. Symptom.] (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.

"straight line continually approaching but never meeting a curve," 1650s, from Greek asymptotos "not falling together," from a- "not" + syn "with" + ptotos "fallen," verbal adjective from piptein "to fall" (see symptom). Related: Asymptotic.

n. 1 (context analysis English) A straight line which a curve approaches arbitrarily closely, as they go to infinity. The limit of the curve, its tangent "at infinity". 2 (context by extension figuratively English) Anything which comes near to but never meets something else. vb. (context analysis English) To approach, but never quite touch, a straight line, as something goes to infinity.

n. a straight line that is the limiting value of a curve; can be considered as tangent at infinity; "the asymptote of the curve"

In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors. In some contexts, such as algebraic geometry, an asymptote is defined as a line which is tangent to a curve at infinity.

The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos) which means "not falling together", from ἀ priv. + σύν "together" + πτωτ-ός "fallen". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve.

There are potentially three kinds of asymptotes: horizontal, vertical and oblique asymptotes. For curves given by the graph of a function , horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to Vertical asymptotes are vertical lines near which the function grows without bound.

More generally, one curve is a curvilinear asymptote of another (as opposed to a linear asymptote) if the distance between the two curves tends to zero as they tend to infinity, although the term asymptote by itself is usually reserved for linear asymptotes.

Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph. The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis.

• Asymptote, a line that a curve approaches as the independent variable tends to some value

Asymptote may also refer to:

• Asymptote Architecture, an architectural design firm
• Asymptote (journal), an online magazine featuring literature translations

In science and technology:

• Asymptote (vector graphics language)
• Asymptotic analysis, a method for describing limiting behaviour
• Asymptotic computational complexity, in theory of computation
• Asymptotic curve, a concept in differential geometry
• Asymptotic expansion
• Method of matched asymptotic expansions, a method in mathematics for computing the solution to a singularly perturbed problem such as a boundary layer in a fluid flow

Asymptote is a descriptive vector graphics language — developed by Andy Hammerlindl, John C. Bowman (University of Alberta), and Tom Prince — which provides a natural coordinate-based framework for technical drawing. Asymptote runs on all major platforms ( Unix, Mac OS, Microsoft Windows). It is free software, available under the terms of the GNU Lesser General Public License (LGPL).

Asymptote is a Singaporean quarterly online literary magazine dedicated to translations of world literature, including poetry, fiction, nonfiction, and drama, mostly to English, but also to other languages. Reviews, interviews, blogs, visual arts and audiovisual materials are also found on the website. The magazine was established in 2011 by Singaporean writer Lee Yew Leong, who is the editor-in-chief. Lee said in 2011, "We operate differently from other translation journals in that we don't just sit back and wait for translations to come to us. We actually identify the good work from writers [that haven't yet been introduced to the English speaking world] and actively seek out translators to help to translate the work for us."