Koch's Snowflake

  Mathematicians have had a class of objects which they refered to as 'Monsters.' While these shapes are easy to describe, they have characteristics which defy common sense.

One such 'Monster' is the Koch Snowflake. To construct this shape, start with a simple equilateral triangle. In sucessive operations divide each straight section into three equal parts. Then remove the middle section and replaces it with two links of length similar to the removed section. Do this for all straight section. Repeat this process any number of times.

Question: Starting with a simple triangle drawn on a piece of paper on your desktop, what is the perimeter of this object after 74 iterations?

Answer: The perimeter is the distance from the Earth to the Moon.

Koch 0

This is what we start with. Just a simple equilateral triangle. (Click on this image to get a better view)

Koch 1

After applying the process once, the center section of each side has been replaced with two angled sides.

Koch 3

After three iterations ...

Koch 5

After five iterations, etc, etc, etc.