Let (K_{0} subset mathbb{R}^{2}) be a line of length 1 . We get (K_{1}) by replacing the

Question:

Let $K_{0} \subset \mathbb{R}^{2}$ be a line of length 1 . We get $K_{1}$ by replacing the middle third of $K_{0}$ by the sides of an equilateral triangle. By iterating this procedure we get the curves $K_{0}, K_{1}, K_{2}, \ldots$ (see Fig. 1.5 ) which defines in the limit Koch's snowflake $K_{\infty}$. Find the length of $K_{n}$ and $K_{\infty}$.

Figure 1.5