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Logosquares
Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.
Ball Bearings
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Age 16 to 18 Short
Challenge Level
This problem uses basic notions of trigonometry and areas of triangles which are fundamental to developments in A-level mathematics.
Being able to work with diagrams such as this is useful prepation for both coordinate geometry and mechanics.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.