Making Circular and Oval Celtic Knots

Draw a set of concentric circles.

The width of the circles will affect the width of strands.

Don't worry about how many lines. Just make sure that you have enough!

Draw lines from the centre at fixed angles.

You only need to do a quarter of the circle.

Here there are 10 lines (at 9°), which will work for 5 strands, closely packed. I think this means that if you want N strands, then the angle of the lines to each other must be 90/(2N). You could probably have a multiple of this, but it wouldn't repeat in a quarter circle. Twice would repeat in a half circle, for example.

Draw lines to outline the first strand. These go diagonally from one edge to the other. At the edge, the strand goes along the edge a bit.

Every line goes from one corner of the grid (made by the red and blue lines) to another.

You set the inner edge at this point. Five strands requires six concentric circles. So for N strands, closely packed, you need N+1 concentric circles (but I'm not sure what the pattern would look like for some N - it may be too closely packed for N=3).

Colour the strand in so you can see what you are doing.

Draw in the next strand, and colour it in.

Don't bother to colour in where the strands cross. You haven't yet decided which goes over or under which.

Do the rest of the strands. There are five in all for this example.

Remove the grid (the red and blue lines).

Colour in all the missing bits.

Colour in the unders and overs.

Outline strands with background colour (or any other colour that you prefer).

Copy this pattern three times, and rotate it, to produce the circular design.

Stretch the shape (using a computer Paint program) to make the oval.

Here is a looser Celtic knot in a circle, with three strands. It is drawn the same way as the previous, creating a grid from concentric circles and angles radiating outwards, but the grid is different.

This shows the grid lines still in place. There are 7 concentric circles, and the lines are at 7.5° to each other. This is 90° / 12.

I think that for N strands, you need 2N + 1 concentric circles, and angles of 90°/(4N).