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

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Building Gnomons

Stage: 4 Challenge Level: Challenge Level:1

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.

How to build gnomons

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?