To get you started on your paper, we ask the following
question that relates the ideas of series and fractals using the snowflake
curve. Cut an equilateral triangle of side a out of paper, as shown in Figure
G.a. Next, three equilateral triangles, each of side a/3, are cut out and
placed in the middle of each side of the first triangle, as shown in Figure
G.b. Then 12 equilateral triangles, each of side a/9, are placed halfway along
each of the sides of this figure, as shown in Figure G.c. Figure G.d shows
the result of adding 48 equilateral triangles, each of side a/27, to the previous
figure. As part of the work on this paper, find the perimeter and the area
of the snowflake curve formed if you continue this process indefinitely.
Figure G.9 Construction of a snowflake curve