### Coke Machine

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

### Get Cross

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

### Illusion

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

# Rotations Are Not Single Round Here

##### Age 14 to 16 Challenge Level:

The Frieze Symmetries are an important mathematical idea.
The question is about an infinite sequence of translations mapping onto itself by :

Reflection, V (vertical mirror line)
or Reflection, H (horizontal mirror line)
or Rotation, R
or by a combination of H with a half unit shift left or right (G, glide reflection) .

This is an excellent opportunity for children to categorize : R or not R, V or not V, etc.

There are in fact only 7 categories, and there's plenty to explore and discuss as the combination options are investigated.