You may also like

problem icon

Coke Machine

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

problem icon

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?

problem icon

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.