TractrixMamikon

Tractrix and Mamikon's device

The curve defined by the property to have constant tangent segments to a fixed line. In the figure below |AB| = a. Its equation is given:

The area included between the curve and the x-axis is equal to pi*a²/2. This follows immediately from Mamikon's device, consisting in translating the tangent AB to a parallel segment CD, C being fixed. Mamikon's theorem asserts that the area swept by the tangent AB is equal to the area swept by CD. The "driver" is used in the corresponding EucliDraw document to animate point A.

Tractrix and Mamikon's device

See Also