Question

Part II - Snowflake Island 0r The fractal called snowflake island (or Koch's snowflake) is constructed as follows be You will make foam versions of each iteration you create. It will help iteration as a pattern for you to cut out of the foam. Step 1: Begin with cutting out an equilateral triangle. to make paper versions of each rever you see a straight line, draw an equilateral triangle on the middle third of the line segment and erase its base. Step 3: Repeat Step 2 infinitely many times. We will stop after 3 iterations- this should be enough repetitions to give you an idea of the final outcome. However, feel free to do more iterations - if you can! a) Complete the following table: Assume the original triangle has side length 1 unit, and the area is A square units. Step (n) Number ofArea of new triangles snowflake (An) Length of one side (Sn) Number of Perimeter (p) Area of one new triangle (an) sides 3 3 0 12 2 3 5 Using series notation, answer parts (b) and (c): h) What happens to pn, the perimeter, as n goes to infinity? c) What happens to An, the total area of the snowflake, as n goes to infinity?

Answer 1

3 와 27 3 1414 327

3 3 3

'h-子 added m T. tration m ビ: 1