## asymptote

as·ymp·toteMath. a straight line always approaching but never meeting a curve; tangent to a curve at infinity

Origin of asymptote

Modern Latin*asymptota*; from Classical Greek

*asympt?tos*; from

*a-*, not +

*sympt?tos*, self-intersecting ; from

*syn-*, together +

*piptein*, to fall: see feather

## asymptote

noun

A line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve.

Origin of asymptote

Ultimately from Greek*asumpt&omacron;tos*,

*not intersecting*:

*a-*,

*not*; see

**a–**

^{1}+

*sumpt&omacron;tos*,

*intersecting*(from

*sumpiptein*

*, sumpt&omacron;-*,

*to converge*:

*sun-*,

*syn-*+

*piptein*,

*to fall*; see

*pet-*in Indo-European roots).

*Related Forms:*

**as′ymp·tot′ic**,**as′ymp·tot′i·cal**adjective

**as′ymp·tot′i·cal·ly**adverb

**asymptote**

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

## asymptote

Noun

(*plural* asymptotes)

Verb

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

- (analysis) To approach, but never quite touch, a straight line, as something goes to infinity.

Origin

From Apollonius Pergaeus's Ancient Greek term *ἀσύμπτωτος* (asúmptōtos, “not falling together”), from *ἀ* (a, “not”) + *σύν* (sun, “together”) + *πτωτός* (ptōtos, “fallen”).