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Faisal from Arnold House School offered a strategy for working on this problem:What we did was take a dart board and rolled it around 4 metre rulers.
We had several more good solutions for the first part of this problem from pupils at Highcliffe Primary School. Whitney and Joe said:The new shape (i.e. the locus of the centre of the circle) will be a square with rounded corners.
Sam and John explained that the length of the locus ...
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?
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?
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.