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The Koch Snowflake
Member rating: No Rating | Words: 2390 | Submitted: Fri Sep 28 2007
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THE KOCH SNOWFLAKE Q.1) Using an initial side length of 1, create a table that shows the values of Nn, Ln, Pn and An for n = 0, 1, 2 and 3. Use exact values in your results. Explain the relationship between successive terms in the table for each quantity Nn, Ln, Pn and An. ANS 1) STAGE SIDES ( Nn ) LENGTH ( Ln ) PERIMETER ( Pn ) AREA ( An ) STAGE 0 3 1 3 0.433013 STAGE 1 12 0.3333333333 4 0.577350 STAGE 2 48 0.1111111111 5.3333333333 0.641500 STAGE 3 192 0.037037037 7.1111111111 0.670011 At first, let us take a look at the change in the sides of the snowflake with increase in stages. It is soon realized that with increase in stage, the snowflake structure changes and so do the sides consequently. On further observation, it is seen that the snowflake sides increase in geometric progression. This is seen because: 12/3=48/12=192/48=4:1 4:1 is the constant ratio. The sides increase by four times with each increase in stage. Next, we have the length of sides...
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