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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.
Sine Problem
In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
Age 16 to 18 Challenge Level:
Draw a right-angled triangle with angles $90^\circ$,
$(45+x)^\circ$ and $(45-x)^\circ$.
What does Pythagoras' Theorem tell you about these
angles?
Use this information to find $ \sin^2 1^\circ + \sin^2 2^\circ
+ \, \cdots \,+ \sin^2 359 ^\circ + \sin^2 360^\circ$.
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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.