Area Under the Tractrix

The tractrix is a curve such that any tangent segment from the tangent point on the curve to its asymptote (the axis) has constant length . Using this definition, slices of a disk are placed in contact with each other and the axis. As you increase the number of slices, their envelope tends to the tractrix. When you use the "align" slider, these slices form a half-disk. Therefore, the area under the tractrix is equal to the area of a half-disk with radius , which is equal to .