Problem 11
One cold February afternoon you are walking outside when it begins to snow. As you watch the beautiful white snow fall, you notice something peculiar about the snowflakes. The snowflakes are highly symmetric.Each one can be drawn in the following way:
1)Start by drawing an equilateral triangle with sides of length S.
2)On each outside edge of the triangle, draw a new equilateral triangle whose base is the middle third of the edge.
3) For each new triangle you have drawn, go back to step two.
Three example iterations
First iteration:
Second iteration:
Third interation:
This process is repeated indefinitely. What is the area of the snowflake? **Hint it is the sum of an infinite sequence.
