### A Knight's Journey

This article looks at knight's moves on a chess board and introduces you to the idea of vectors and vector addition.

### 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?

# Surprising Transformations

##### Stage: 4 Challenge Level:

This problem follows on from Translating Lines and Reflecting Lines.

I took the graph $y=4x+7$ and performed the four transformations shown on the cards below.

Unfortunately, I can't remember the order in which I carried out the four transformations, but I know that I ended up with the graph of $y=4x-2$.

Can you find an order in which I could have carried out the transformations?
There is more than one way of doing this - can you find them all?

Can you explain why different orders can lead to the same outcome?

What other lines could I have ended up with if I had performed the four transformations in a different order?