Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.
Published January 2001,February 2011.
Some local pupils lost a geometric opportunity recently as they
surveyed the cars in the car park. Did you know that car tyres, and
the wheels that they on, are a rich source of geometry?
The patterns that you find on car tyres are invariably based on
one of the SEVEN (only) frieze patterns. Frieze patterns are those
patterns that do not spread all over the plane (like a
tessellation) but are confined to a strip. They are generated by a
limited number of transformations - a translation, half turn, glide
The seven frieze patterns are replicated below.
Can you describe what is different about each of these
Starting with a basic shape of your own can you generate
patterns based on the seven friezes above?
How about looking at some of the tyre treads and see if you can
match them to these patterns.
You may also like to design your tyre treads on a more complex
motive than the b's, d's, p's and q's used above.