Koch Snowflake Proof by Induction.

[96hicksy]

Hi, I was wondering if there is a way to prove the area of the Koch Snowflake via induction?
At the moment I have the equations:
A_n+1=A_n+\frac{3√3}{16}(\frac{4}{9})ⁿ
and
A_n=\frac{2√3}{5}-\frac{3√3}{20}(\frac{4}{9})ⁿ
These two don't seem to work together very well when trying to prove by induction. Can anyone offer any advice? This is not homework by the way :).

 

[Simon Bridge]

So you need to find some consistent relation for the area of a koch snowflake?
Using you knowledge of geometry (it's all triangles after all) and the Koch snowflake itself, you should be able to come up with your own.