### Gnomon Dimensions

These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.

### What Is the Question?

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

# Building Gnomons

##### Stage: 4 Challenge Level:

This screenshot shows you how to use the Cellular resource to build gnomons from scratch. Alternatively, you can choose the "build gnomons" starter drawing and manipulate them in the same way.

Here are the perimeters of $G_6$.

Here are the perimeters of $G_6$ rewritten in terms of their Fibonacci numbers ($F_1 = 1, F_2 = 1, F_3 = 2, F_4 =3$ and so on).

Can you draw a diagram showing what happens more generally?