TRACTRIX : Evolute

As usual we fing the evolute of this curve by drawing the normal at each point of the tractrix locus. The envelope of these normals generates the evolute of the tractrix.


Click on the linked diagram at right, and then click on the ‘Animate’ button. The red driver point Q moves along the horizontal x-axis, and correspondingly, the points P trace out the tractrix. The normals form an envelope. What is this evolute curve? Do you recognize it?

The evolute is the catenary.

Bibliography


http://mathworld.wolfram.com/TractrixEvolute.html