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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?

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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?

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Turning Triangles

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

Rolling Triangle

Age 11 to 14 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.