What is the perimeter of the Sierpinski Triangle?
Each time we iterate we increase the number of triangles by a factor of 3 each with a perimeter of 1/2 the previous triangles’ perimeter. In other words, each time we increase the total area by a factor of 3/2 After the Nth iteration, the perimeter is (3/2)N*P, where P is the original triangle’s perimeter. Since 3/2 is greater than 1, (3/2)N*P grows towards infinity as N gets larger and larger. Thus the perimeter of the “infinite” Sierpinski Triangle is infinite!
