Koch Curves

  • Thread starter mharten1
  • Start date
  • #1
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Homework Statement



In a lecture that I was unable to attend, we discussed the koch snowflake. The lecturer went through the process of finding the area of the koch snowflake. For homework, we are asked to find the area of a koch square curve, as seen on this website: http://snowflakecurve.weebly.com/index.html


Homework Equations





The Attempt at a Solution


I was unable to attend the lecture and my friend tried to help me, but he didn't know how to solve it himself. I'm completely lost, and the lecturer isn't having office hours before the assignment is due. Any help on getting started would be greatly appreciated. I know that the perimeter is infinite and the area is finite, and that's about it.
 

Answers and Replies

  • #2
I would say, calculate the area iteration step by iteration step.
You start with a triangle.
Then in the next step, you add the area of 3 smaller triangles. Try to figure out the length of their baseline and deduce their area from it.
Then, in the second step, how many triangles do you add? What are their areas?
Once you get can compute how large the total area is for every interation step n, you can let n go to infinity and derive the absolute area.
 

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