### Coke Machine

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

### At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

### Cosines Rule

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

# Orbiting Billiard Balls

##### Age 14 to 16Challenge Level

This is a hard but hopefully interesting scenario.

Drawing out the table(s) and experimenting with different paths (angles) will generate a 'feel' for the problem and begin to suggest some features and underlying relationships.

Ideally the context is rich in possibilities for extension and fresh questions. For example are orbital paths possible where a rebound does not always take the ball on to the adjacent side but instead across to the opposite side, and if such paths exist, what is the connection between simple orbits and those where the cycle involves more than 4 rebounds?