A fractal is a geometric figure that has similar characteristics at all levels of magnification. One example of a fractal is Koch's (sounds like "Cokes") snowflake. To build this fractal, start with an equilateral triangle whose sides each have length 1. Then on the middle 1/3 of each side, create a triangular "bump" to make a new figure having 12 sides. On the middle 1/3 of each of these 12 sides, create a smaller bump, and so on. The upper part of the illustration shows the first four stages in the construction of a Koch's snowflake. The "real" snowflake is the result of carrying on this process forever!
The lower part of the illustration shows how, when a bump is added to any side, the length you have is multiplied by 4/3. If a bump is added to every side of a snowflake figure, then the entire perimeter is multiplied by .
4/3
Which of the following sequences represents the total perimeter length for each of the stages 1, 2, 3, 4, and so on (illustrated above) in building Koch's snowflake, starting with the equilateral triangle?
A. 3, 4,16/3 ,64/9 , ...
B. 3,12, 48, 192, ...
C. 4, 12, 36, 108, ...
D. 1, 4/3,16/9 ,64/27 , ...
E. 3,2/3 ,3/4 ,3/8 ,
The lower part of the illustration shows how, when a bump is added to any side, the length you have is multiplied by 4/3. If a bump is added to every side of a snowflake figure, then the entire perimeter is multiplied by .
4/3
Which of the following sequences represents the total perimeter length for each of the stages 1, 2, 3, 4, and so on (illustrated above) in building Koch's snowflake, starting with the equilateral triangle?
A. 3, 4,16/3 ,64/9 , ...
B. 3,12, 48, 192, ...
C. 4, 12, 36, 108, ...
D. 1, 4/3,16/9 ,64/27 , ...
E. 3,2/3 ,3/4 ,3/8 ,
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A
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So, which answer when dividing the largest by the next smallest equals 4/3 (1.333333333)?