This experiment first appeared in Book of Curves by E.H. Lockwood. It will show that circ...

This experiment first appeared in Book of Curves by E.H. Lockwood. It will show that circles, as well as lines, can be used to generate classical curves. This is another example of the power of Sketchpad, which was unavailable at the time the remarkable Book of Curves was published.

[1] Draw a (base) circle AB, and select any point C not on that circle, but drag it to a position somewhere on circle AB. (Doing this will allow you to relocate point C to obtain other envelopes.) Locate point D on circle AB so that dragging it will not pull it off the circle.

[2] Using Circle By Center and Point under CONSTRUCT, construct a circle centered at D and passing through C.

[3] Trace the circle you just constructed, and animate with D on the base circle. Did you obtain a familiar curve? What curve is it?

NOTE: Save this construction for the next problem.