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Last active December 2, 2015 01:33
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koch.md

How long is the coastline of England?

Say you were to measure it...

  • Wikipedia says 19,491 miles... but how did they measure it?
  • What size measuring stick did they use, what size should they use?
  • Is smaller better?
  • Intuition: as measuring stick goes down, perimeter goes up, but limits towards the right answer.

The Koch Snowflake

  • That intuition is wrong! Consider a country shaped like the following...
  • Start with an equilateral triangle.
  • Break each side into thirds and form a new triangle on the middle third.
  • Continue ad infinitum
  • Properties... infinite perimeter, finite area, and... the smaller the measuring stick, the greater the estimated perimeter, to infinity.

Conclusions

  • Is England like the snowflake? If so..
  • OH MY GOD... the coastline length is totally arbitrary! (or is it?)
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