WOLFRAM|DEMONSTRATIONS PROJECT

Area Under the Tractrix

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slices
align
tractrix
The tractrix is a curve such that any tangent segment from the tangent point on the curve to its asymptote (the
x
axis) has constant length
a
. Using this definition, slices of a disk are placed in contact with each other and the
x
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
a
, which is equal to
π
2
a
/2
.