Definitions for asymptote
ˈæs ɪmˌtoʊtasymp·tote

Princeton's WordNetRate this definition:0.0 / 0 votes

1. asymptotenoun

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

   "the asymptote of the curve"

WiktionaryRate this definition:2.0 / 1 vote

1. asymptotenoun

   A straight line which a curve approaches arbitrarily closely, as they go to infinity. The limit of the curve, its tangent "at infinity".

2. asymptotenoun

   Anything which comes near to but never meets something else.

3. Etymology: From Apollonius Pergaeus's term ἀσύμπτωτος, from ἀ "not" + σύν "together" + πτωτός "fallen."

Samuel Johnson's DictionaryRate this definition:0.0 / 0 votes

1. Asymptotenoun

   Asymptotes are right lines, which approach nearer and nearer to some curve; but which, though they and their curve were infinitely continued, would never meet; and may be conceived as tangents to their curves at an infinite distance. Ephraim Chambers

   Etymology: from α, priv. σὺν, with, and πτόω, to fall; which never meet; incoincident.

   Asymptote lines, though they may approach still nearer together, till they are nearer than the least assignable distance, yet, being still produced infinitely, will never meet. Nehemiah Grew, Cosm.

WikipediaRate this definition:0.0 / 0 votes

1. Asymptote

   In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point 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 three kinds of asymptotes: horizontal, vertical and oblique. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. Vertical asymptotes are vertical lines near which the function grows without bound. An oblique asymptote has a slope that is non-zero but finite, such that the graph of the function approaches it as x tends to +∞ or −∞. 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.

ChatGPTRate this definition:0.0 / 0 votes

1. asymptote

   An asymptote is a line or curve that continually approaches a given curve but never actually meets or intersects it, no matter how far out it is extended. This concept is primarily used in calculus, geometry, and algebra within the context of limit theory. It expresses the idea that one quantity is approaching another quantity but will never actually reach it, which can be useful in many mathematical and theoretical models. There are three types: horizontal, vertical, and oblique.

Webster DictionaryRate this definition:1.0 / 1 vote

1. Asymptotenoun

   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

2. Etymology: [Gr. not falling together; 'a priv. + to fall together; with + to fall. Cf. Symptom.]

WikidataRate this definition:5.0 / 1 vote

1. Asymptote

   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 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 y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. Vertical asymptotes are vertical lines near which the function grows without bound. More generally, one curve is a curvilinear asymptote of another if the distance between the two curves tends to zero as they tend to infinity, although usually the term asymptote by itself is reserved for linear asymptotes.

Chambers 20th Century DictionaryRate this definition:0.0 / 0 votes

1. Asymptote

   a′sim-tōt, n. (math.) a line that continually approaches nearer to some curve without ever meeting it.—adjs. Asymptot′ic, -al.—adv. Asymptot′ically. [Gr. asymptōtos, not coinciding—a, not, syn, with, ptōtos, apt to fall, pipt-ein, to fall.]

The Nuttall EncyclopediaRate this definition:0.0 / 0 votes

1. Asymptote

   a line always approaching some curve but never meeting it.

Matched Categories

1. • Straight Line

How to pronounce asymptote?

1. Alex

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How to say asymptote in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of asymptote in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of asymptote in Pythagorean Numerology is: 8

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References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=asymptote
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Asymptote
3. ^ Samuel Johnson's Dictionary
   https://johnsonsdictionaryonline.com/views/search.php?term=asymptote
4. ^ Wikipedia
   https://en.wikipedia.org/wiki/Asymptote
5. ^ ChatGPT
   https://chat.openai.com
6. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/asymptote
7. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=asymptote
8. ^ Chambers 20th Century Dictionary
   https://www.gutenberg.org/files/37683/37683-h/37683-h.htm#:~:text=asymptote
9. ^ The Nuttall Encyclopedia
   https://www.gutenberg.org/cache/epub/12342/pg12342-images.html#Asymptote