### 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.

### Continued Fractions I

An article introducing continued fractions with some simple puzzles for the reader.

### LOGO Challenge - Circles as Bugs

Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.

# Building Gnomons

##### Age 14 to 16 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?