Copyright © University of Cambridge. All rights reserved.

## 'Arclets' printed from http://nrich.maths.org/

Each of the following shapes is made from arcs of a circle of radius $r$. What is the perimeter of a shape with $3$, $4$, $5$ and $n$ "nodes"?

What happens when $n$ is very large?

Explain the relationship between your answers and the perimeter of the original circle.