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Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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Pericut

Two semicircle sit on the diameter of a semicircle centre O of twice their radius. Lines through O divide the perimeter into two parts. What can you say about the lengths of these two parts?

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Giant Holly Leaf

Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).

Holly

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Possible extension
Try the problem Giant Holly Leaf. It does not require any more mathematical knowledge than this problem but it introduces the concept of curvature.

See also the article Curvature of Surfaces.