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From The Collaborative International Dictionary of English v.0.48:
Unicursal \U`ni*cur"sal\, a. [Uni- + L. currere, cursum, to run.] (Geom.) That can be passed over in a single course; -- said of a curve when the coordinates of the point on the curve can be expressed as rational algebraic functions of a single parameter [theta]. [1913 Webster] Note: As [theta] varies minus infinity to plus infinity, to each value of [theta] there corresponds one, and only one, point of the curve, while to each point on the curve there corresponds one, and only one, value of [theta]. Straight lines, conic sections, curves of the third order with a nodal point, curves of the fourth order with three double points, etc., are unicursal. [1913 Webster]