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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..

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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?

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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

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.