Frieze Patterns in Cast Iron

A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.

The Frieze Tree

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

Friezes

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?

Mirror, Mirror...

Stage: 3 Challenge Level:

You might like to copy the diagram above onto squared paper to help you with this problem.

Reflect the flag in the left-hand line, and then reflect the image you obtain in the right-hand line. Can you describe the single transformation that takes the first flag to the last flag?

Repeat this with flags in different positions and orientations, and with different pairs of parallel lines.

Does it matter in which line you reflect first?
Does it matter whether the flag is to one side of the lines or between the lines?

Try to find a way to describe the single transformation for a general pair of parallel lines.