### Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

### Khun Phaen Escapes to Freedom

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

### Frieze Patterns in Cast Iron

A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.

# Pink and White

##### Stage: 3 Short Challenge Level:

A square piece of wood, of side 8cm, is painted pink and fixed to a table. An equal square, painted white, is placed on the table alongside the pink square, and has a point P marked one quarter of the way along the diagonal as shown. Whilst keeping the orientation on the table and always remaining in contact with the pink square, the white square now slides once around the pink square.

Through what distance does P move?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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