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Koch Snowflake Proof by Induction.

  1. Jul 13, 2014 #1
    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:
    An+1=An+[itex]\frac{3√3}{16}[/itex]([itex]\frac{4}{9}[/itex])n
    and
    An=[itex]\frac{2√3}{5}[/itex]-[itex]\frac{3√3}{20}[/itex]([itex]\frac{4}{9}[/itex])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 :).
     
  2. jcsd
  3. Jul 13, 2014 #2

    Simon Bridge

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    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.
     
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