(This resource is still in draft form.)

This applet shows a square with slide length \(2\) rolling over an upside-down catenary with equation \(y=-\cosh x\). When the square is horizontal, the centre of its base touches the vertex of the catenary.

Move the slider to roll the square.

Screenshot of the applet.
  • What is the locus of the centre of the square?

  • How far can the square roll with the same side still touching the catenary?

  • What do you already know about catenaries?

  • When the square has turned a certain amount, what are some different ways in which you could describe its location?