Tractrix is the curve

Curve

In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...

 along which a small object moves, under the influence of friction, when pulled on a horizontal plane

Horizontal plane

In geometry, physics, astronomy, geography, and related sciences, a plane is said to be horizontal at a given point if it is perpendicular to the gradient of the gravity field at that point— in other words, if apparent gravity makes a plumb bob hang perpendicular to the plane at that point.In...

 by a piece of thread and a puller that moves at a right angle to the initial line between the object and the puller at an infinitesimal

Infinitesimal

Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.In common speech, an...

 speed

Speed

In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...

. It is therefore a curve of pursuit

Curve of pursuit

A curve of pursuit is a curve constructed by analogy to having a point or points which represents pursuers and pursuees, and the curve of pursuit is the curve traced by the pursuers....

. It was first introduced by Claude Perrault

Claude Perrault

Claude Perrault is best known as the architect of the eastern range of the Louvre Palace in Paris , but he also achieved success as a physician and anatomist, and as an author, who wrote treatises on physics and natural history.Perrault was born and died in Paris...

 in 1670, and later studied by Sir Isaac Newton (1676) and Christian Huygens (1692).

Suppose the object is placed at (a,0) [or (4,0) in the example shown at right], and the puller in the origin

Origin (mathematics)

In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space. In a Cartesian coordinate system, the origin is the point where the axes of the system intersect...

, so a is the length of the pulling thread [4 in the example at right].