A Patchwork Piece

I have decided to make another patchwork quilt. The end result should look something like this:



It is a design known as "World without end" and is based on a series of squares like this:

The problem is to make the individual pattern pieces the right size (and shape!).

Although it is not exactly obvious this design is based on a regular octagon in a square. These diagrams show the transformations required:

This helps in making the individual pattern pieces. Can you work out how each of the above steps was achieved? Try it with a square piece of paper.

How could you make the pattern if you only have a ruler and a pair of scissors?

What about if you were allowed to use a pair of compasses as well?

Let us know how you achieved each step. You can send in pictures of your final piece, too.

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Here are the first four squares of the actual quilt: