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'Snake Coils' printed from http://nrich.maths.org/
Why do this problem?
engages the pupils in both a spatial and numerical context. It gives them also the freedom to choose how they go about it - visualising in their head, using paper, string etc. that they have requested and/or making use of a spreadsheet. They can learn a lot from adopting one method and then realising that an alternative method would be
Presented as on the problem page.
Very open questions, like "tell me about this . . . . "
What have you found out so far?
Consider the sizes of the circles as they get smaller and smaller.