Snowflake Curve Series Problem: Figure 14-3c shows Kochs snowflake curve, which you may

Chapter 14, Problem 10

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Snowflake Curve Series Problem: Figure 14-3c shows Kochs snowflake curve, which you may have encountered in Section 11-5. Figure 14-3c In the first iteration, segments 1 unit long are marked on the sides of an equilateral triangle of side 3, and three equilateral triangles (shaded) are drawn. In the second iteration, equilateral triangles of side unit are constructed on each side of the first iteration. The iterations are carried on this way infinitely. The snowflake curve is the boundary of the resulting figure. a. Find the total perimeter of the first iteration. Find the total perimeter of the second iteration. What kind of sequence do the lengths of the iterations form? How do you conclude that the perimeter of the completed snowflake curve is infinite? b. What is the total area of the shaded triangles in the first iteration? What area is added to this with the shaded triangles in the second iteration? What kind of series do the areas of the iterations form? Does this series converge? If so, to what number? If not, show why not.