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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?
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 Around
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
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.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.