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### Number and algebra

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# Reflecting Squarely

## You may also like

### Frieze Patterns in Cast Iron

### The Frieze Tree

### Friezes

Links to the University of Cambridge website
Links to the NRICH website Home page

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Age 11 to 14

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An excellent solution from Andrei of School 205 Bucharest. I like this very much because of the effective and systematic approach he took to investigating the problem.

Here is Andrei's solution:

I worked systematically. I took the big (yellow) piece and I placed the rectangle in all the possible locations around it (both vertically and horizontally). Then I looked if the figure admitted a symmetry line (vertical, horizontal, or at a 45$^{\circ}$ angle) if I added a small square (blue). Here is all my work and the solutions I found, with the corresponding symmetry line:

Sara spotted that Andrei had missed a solution. Here
is Sara's complete set - her last solution is the one missing in
the list above.

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

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

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?