If you wanted to draw the design below, called a MYSTIC ROSE, how would you go about it? How could you be sure you had drawn all the lines? How would you know how many lines there were?

To draw a mystic rose you will need accuracy and patience:

1. Draw a circle, any size.
2. Divide it into equal parts around the circumference. (Use a protractor to measure the degrees.) Mark the divisions with dots. It is helpful to number all dots from 1 onwards.
3. Join each dot to every other dot with straight lines. For example, join dot 1 to dot 2, then dot 1 to dot 3 and so on...

This Mystic Rose has been made using an even number of points. What do you think would happen to the centre of the Rose if it was made using an odd number of points?

Jumping

The pattern below is made using a different rule called jumping. Like the mystic rose, the circle below is divided into equal parts - here there are 15 points which have been numbered from 1 to 15. Instead of linking each point to all the others, starting at 1, miss out (or 'jump') 3 points and join it to 4. In this way join continue to join 4 to 7, 7 to 10 and so on...until you are back at the first point.

If the circle had 12 points, how many times would there be a rule of jumping 4?... or 5?... or...?
What jumping rules can you use to draw a square or a pentragon in a circle with 20 points?