The fractal called the snowflake island (or Koch island) is constructed as follows: Let I 0 be

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The fractal called the snowflake island (or Koch island) is constructed as follows: Let I0 be an equilateral triangle with sides of length 1. The figure I1 is obtained by replacing the middle third of each side of I0 with a new outward equilateral triangle with sides of length 1/3 (see figure). The process is repeated where In + 1 is obtained by replacing the middle third of each side of In with a new outward equilateral triangle with sides of length 1/3n + 1. The limiting figure as n→∞ is called the snowflake island.

a. Let Ln be the perimeter of In. Show that 'n, п0

b. Let An be the area of In. Find lim An. 'n' п>00 It exists!

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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