These pictures were made quite simply by starting with a square,
finding the half-way point on each side and joining those points
up. This creates a smaller shape (which also happens to be a
square) inside the original. The half-way points of this new
shape are then joined up to make a third shape. This way of making
new shapes is continued until it gets too small to do
You can, of course, start with any straight-lined shape.
Here's one where I've coloured each new halving line to help to see
what has happened more clearly.
So, it's your turn to have a go.
It's probably good to start with a fairly large shape since it's
going to get smaller and smaller each time.
Here are some challenges for you to
Having made a design like one above,
cut out the triangles and the smallest inner shape and rearrange
the pieces to form a new shape/design.
Talk about and record the things you
notice as you have drawn more and more halving lines.
What is happening to the enclosed
area each time the sides are halved? (Try
investigating a regular shape first.)
This problem is based on an idea
suggested by Ian Short.