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One Reflection Implies Another

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.