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Food for thought

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Problem

Please be aware that this resource is still in a somewhat draft form.

This applet shows a square with side 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.

• What is the locus of the centre of the square?

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

• An a final challenge, can you recreate this applet using GeoGebra?