2D shapes and their properties

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

Look at the mathematics that is all around us - this circular window is a wonderful example.

Weekly Problem 5 - 2006
How many times does the inside disc have to roll around the inside of the ring to return to its initial position?

Work out the radius of a roll of adhesive tape.

Weekly Problem 1 - 2006
The diagram shows two circles enclosed in a rectangle. What is the distance between the centres of the circles?

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?