The *hypocycloid* is the path traced by a point on the circumference of a small circle rolling around inside a larger circle, the larger circle having radius *n* times that of the smaller circle, usually *n* is taken to be an integer. For *n* = 2, the path is along a diameter, this degenerate case is the Tusi Couple. For *n* = 3, the curve is called a *deltoid*, from its resemblance to the Greek letter delta.

Try *n* = 5, then, keeping that curve, go to a different color and plot *n* = 5.1 (be patient!). Interpret the result. Now add in *another* color *n* = 3. How does *that* relate?

In the limit of large *n*, taken as infinite outer circle radius, the curve approaches the *cycloid*, the path of a point on the edge of a wheel rolling along a straight line.

*Code by Casey Bowler*