Koch Snowflake Area paradox: it's infinite I say.

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I don't agree the area of the Koch snowflake is finite as claimed. The calculation may give the result of finite number - from a fixed point - but as the system is iterating infinity, as is assumed, the area of each added triangle will be real, and these areas infinitely diminishing - asymptotically. 

 If we were to zoom into the 'last' iteration area size where the area goes finite, I am sure we would 'see' iteration continuing and with this diminishing added area.

 Infinite Series and convergence.
There seems to be a paradox here, a practical result conflicting with a calculated result. I think in reality it is both: these infinite series must go on (converging), presenting ever diminishing values, and thus the 'limit' must be irrational, not finite. But I am not going to challenge the finite calculation, I have not the authority or ability to do that. Interesting.

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