Hexagons and 6 point stars

Here's how to get started:

1.Draw a circle on the paper. Put the compass point anywhere on the circumference of the circle and allow the pencil to make a mark on the circumference. Move the point of the compass to the pencil mark and make another mark on the circumference.

2.Continue doing this until there are six marks. These six marks are equally spaced (Why?)

3.Join the six points to make a regular hexagon.

4.Now join up every second point. You have an equilateral triangle - how do you know it is equilateral?

5.Join up the other three points and you have a second equilateral triangle. Together these triangles make up a 6 point star.

1.2.

3.4.

5.

 

Continue to join points using the inner hexagon...What happens?

 

Can you make a linked pattern of 6 point stars?