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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?

Coins on a Plate

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

Smaller and Smaller

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?

On the Edge

Age 11 to 14
Challenge Level
Take one colour at a time and see how many edges are being used up on the edge of the big square.

Once the edges have been used they can be 'hidden' in the middle


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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