Investigation

## Possible questions

Take a look at the image below.

What do you make of it?

• Can I recreate the image using only straight-edge and compasses?

• Can I find line segments of lengths $2$, $3$, $4$, $\dots$?

• Are there any lengths that do not occur in the diagram?

• How many steps would I need to construct $\sqrt{5}$ in the diagram?

• Can I construct $\sqrt{13}$ in any other way (using straight-edge and compasses)?

• Which other lengths can I construct in other ways (using straight-edge and compasses)?

• How will the spiral change if I start with a $2\times 2$ right-angled triangle instead?

• How will the spiral change if I start with a right-angled triangle that isn’t isosceles?