*asymptote*

n. [ Gr. &unr_; not falling together; 'a priv. + &unr_; to fall together; &unr_; with + &unr_; 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. [ 1913 Webster ]