Evolute of a Tractrix
- Author:
- Tim Brzezinski
- Topic:
- Straight Lines
Shown below is a tractrix (pursuit curve) and a BIG GRAY POINT that lies on it. The reflection of this point about the x-axis is also shown (as a much smaller gray point).
The pink lines are normal to the tractrix. (Recall that a normal line to a curve at a point is the line that is perpendicular to the line tangent to the curve at that point.)
Drag the BIG GRAY POINT along this tractrix and observe this envelope of normal lines (i.e. the traces of the pink lines). As you do, be sure to keep your finger pressed down on your mouse button as you get closer and closer to the x-axis. (Otherwise, the GRAY POINT will disappear and you'll have to refresh the page or adjust the slider a bit.)
What do you see?
How do your results compare with that from this worksheet? https://tube.geogebra.org/m/FasSGc84