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
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by
replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc..
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Cables can be made stronger by compacting them together in a hexagonal formation.
Here is a 'size 5' cable made up of 61 strands:
How many strands are needed for a size 10 cable?
How many for a size n cable?
Can you justify your answer?
Once you've had a go at the problem, click below to see the diagrams some 15 year old students produced when they worked on it.
Do these diagrams give you any ideas for how you could work out the number of strands needed?
The work that these students did using their diagrams is given on the Getting Started page, if you would like a bigger hint.
Which of the four approaches makes the most sense to you?
What do you like about your favourite approach?
Can you think of any other approaches?