Asymptote
In 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 — i.e. approaching a value or curve arbitrarily closely.
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Origin
From the Greek asumptōtos (ἀσύμπτωτος), meaning "not falling together." Apollonius of Perga first used the word around 200 BC in his treatise on conic sections, though he applied it more broadly to any line that does not intersect a given curve. The modern mathematical sense — a line that a curve approaches but never reaches — emerged in the 1650s.
Updated February 22, 2026