Hypocycloid Families

The applet below gives a nice demonstration of the power of mathematics in general, and analytic geometry and complex variables in particular. The available explanation may be too difficult for a school student, but do play with the applet by all means.

The applet shows and allows you rotate families of hypocycloids with an increasing number of cusps. Cycloids are so located inside each other that they appear gliding on each other's curves. They are rotated by dragging the "turns" on a small circle in the lower left corner.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

What if applet does not run?

71536859