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Koch Snowflake Proof by Induction.

by 96hicksy
Tags: induction, koch, proof, snowflake
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96hicksy
#1
Jul13-14, 08:06 AM
P: 11
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 :).
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Simon Bridge
#2
Jul13-14, 10:04 AM
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Simon Bridge's Avatar
P: 12,739
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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