asymptote

See also: Asymptote

English

Etymology

circa 1650, from Ancient Greek ἀσύμπτωτη (asúmptōtē), the feminine of Apollonius Pergaeus' (circa 200 BC) Ancient Greek adjective ἀσύμπτωτος (asúmptōtos, “not falling together”), from ἀ- (a-, “not”) +‎ συν- (sun-, “together”) +‎ πτωτός (ptōtós, “fallen”).

Pronunciation

• (General American) IPA^(key): /ˈæsɪmptoʊ̯t/, /ˈæsɪmtoʊ̯t/, /ˈeɪ̯sɪmtoʊ̯t/, /ˈæsɪmtɒt/

Noun

asymptote (plural asymptotes)

1. (mathematical analysis) A straight line which a curve approaches arbitrarily closely as it goes to infinity. The limit of the curve; its tangent "at infinity".
   • 1974, Stanisław Lem, translated by Michael Kandel, The Cyberiad:

     The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F₁) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out, fuming factorially, and fell upon the King and hurt him passing sore.

2. (by extension, figuratively) Anything which comes near to but never meets something else.
   • 1860, Frederic William Farrar, An Essay on the Origin of Language, page 117:

     Language, in relation to thought, must ever be regarded as an asymptote.

Derived terms

• asymptotia
• asymptotic
• asymptotical
• asymptotically
• asymptotics

 

Translations

a straight line which a curve approaches arbitrarily closely

• Basque: asintota
• Bengali: অসীমতট (ośimotoṭ)
• Catalan: asímptota (ca) f
• Czech: asymptota f
• Dutch: asymptoot (nl) m
• Finnish: asymptootti (fi)
• French: asymptote (fr) f
• German: Asymptote (de) f
• Greek: ασύμπτωτος (el) f (asýmptotos)
• Hebrew: אָסִימְפְּטוֹטָה (he) f (asimptotá)
• Hindi: अनंतस्पर्शी f (anantsparśī)
• Icelandic: aðfella f, ósnertill m
• Ido: asimptoto (io)
• Indonesian: asimtot (id)
• Italian: asintoto (it) m
• Japanese: 漸近線 (zenkinsen)
• Malay: asimptot
• Maori: rārangi pātata, tepe whakatata
• Polish: asymptota (pl) f
• Portuguese: assíntota f (Portugal), assímptota f (Brazil, Portugal), assintota f (Portugal), assimptota f (Brazil, Portugal)
• Romanian: asimptotă (ro) f
• Russian: асимпто́та (ru) f (asimptóta)
• Spanish: asíntota f
• Swedish: asymptot (sv) c
• Turkish: asimptot (tr)
• Welsh: asymptot m

Verb

asymptote (third-person singular simple present asymptotes, present participle asymptoting, simple past and past participle asymptoted)

1. (mathematical analysis) To approach, but never quite touch, a straight line, as something goes to infinity.
   • 2006: Neil deGrasse Tyson, The Perimeter of Ignorance

     As you become more scientific, yes, the religiosity drops off, but it asymptotes.

French

Etymology

Borrowed from Ancient Greek ἀσύμπτωτος (asúmptōtos).

Pronunciation

• IPA^(key): /a.sɛ̃p.tɔt/

• Audio:

  (file)

Noun

asymptote f (plural asymptotes)

1. (mathematical analysis) asymptote

Derived terms

• asymptotique

Further reading

• “asymptote”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.