Stage: 5 Challenge Level: 
Consider figures 1 and 2 showing a 'necklace' and a 'floret' of squares. All the squares are regularly spaced around the circles and have side length 1 unit. Calculate, in each case, the inner and outer radii of the rings (or annuli, the singular is annulus) that surround the squares. If you 'merged' the two figures would one annulus lie completely inside the other?
Index notation/Indices. Symmetry. Graph sketching. Pythagorean triples. Tangent. Circles. Mathematical reasoning & proof. Long problems. Pythagoras' theorem. Quadratic equations.
Published October 1999.
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