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The Koch Snowflake n Nn Ln Pn An 0 3 1 3 ( 3)/4 1 12 1/3 4 ( 3)/3 2 48 1/9 5 1/3 10 ( 3)/27 3 192 1/27 7 1/9 94 ( 3)/243 Number of Sides 3 x 4 = 12 12 x 4 = 48 48 x 4 = 192 Each successive term is a result of multiplying the previous one by 4. Therefore, this is a geometric sequence and the common ration is 4. The equation for this sequence is as follows: n = stage no. N = number of sides r = common ratio Nn = N0 x rn Length of Sides 1 ÷ 3 = 1/3 1/3 ÷ 3 = 1/9 1/9 ÷ 3 = 1/27 Each successive term is a result of dividing the previous term by 3. This shows that it is a geometric sequence and the common ratio is 3. Therefore the equation for this sequence is: L = length of side n = stage no. r = common ratio Ln = N0/rn e.g. L2 = 1/3² = 1/9 Perimeter 4 ÷ 3 = 1.333... 5 1/3 ÷ 4 = 1.333... 7 1/9 ÷ 5 1/3 = 1.333... Therefore...

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