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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.
Overarch 2
Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?
Stonehenge
Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.
Age 16 to 18
Challenge Level
A standard English snooker table is 6' x 12'. We know that the shortest path between any two points on the table is given by the straight line between them. How do we figure out the shortest distance between two points if the ball must bounce off one wall? What if it must bounce off 2 walls? 3 walls?
If you want to try one yourself, let the bottom left hand corner of the pool table be the origin. Consider the case when the cue ball is at (5,5) and the target ball is at (10,2). Which wall gives the shortest path to the target?
NRICH is part of the family of activities in the Millennium Mathematics Project.