### Just Rolling Round

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 of P?

### Coke Machine

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..

### Rotating Triangle

What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?

# Steel Cables

##### Stage: 4 Challenge Level:

Do you know a quick way of adding up all the numbers from 1 to n?
If not, take a look at the problem Picturing Triangle Numbers.

Below are student diagrams from the problem page, but they now also show the working that the students used to explain their diagrams. Can you explain their reasoning?

Group 1

Group 2

Group 3

Group 4

If you are finding it difficult to make sense of the different groups' work, try to work out what they might have drawn for a size 6 cable.