### 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?

### Center Path

Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of the point X and prove your assertion.

### The Old Goats

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't fight each other but can reach every corner of the field?

# Rolling Triangle

##### Stage: 3 Challenge Level:

Notice what happens to the motion when the sides of the triangle are perpendicular to the floor and plank.

Notice the differences to what happens on the floor and on the plank when the triangle rolls in opposite directions.

You might like to try cutting out a very accurate rolling triangle with which to experiment.