Create your Own Pattern!
1. Draw a circle with a compass. Keep the compass point at the same length. Put the compass point anywhere on the circle and swing the pencil so that a mark is made on the circle. Move the point of the compass to the pencil mark and make another pencil mark on the circumference. Continue doing this round the circle until there are six marks. From these six marks, the series of hexagons can be made – see the illustrations to the side.
2. Join up the points in sequence round the circle to make the six-sided polygon into a hexagon. Is the shape regular or irregular? How many parallel sides are there? How many angles? Can you measure the internal angles using a protractor? What do you notice?
3. Next join up every second point – you will now have a triangle. What is the special name of this shape? How do you know? How can you prove it?
4. Then you must join up the other three points of the hexagon to make a second equilateral triangle. Together these two triangles make up a star. One triangle points up to heaven, the other points down to earth. Three pairs of parallel lines make up the star. In the middle of the star is another hexagon.
5. Joining up every second point of the inner hexagon makes another equilateral triangle in the inner hexagon. Joining up the other points makes a second equilateral triangle and another six-pointed star with a hexagon in the middle.
6. This pattern can go on and on. In this sequence of patterns, the stars and hexagons change position.