SERPINSKI TRIANGLE
Source=http://www.visionol.net/~jy/serp.htm
Area of Serpinski Triangle |
||||||
|---|---|---|---|---|---|---|
Stage |
0 |
1 |
2 |
3 |
4 |
n |
Area Shaded |
1 |
3/4 |
9/16 |
27/64 |
81/128 |
? |
Did you find the pattern to be that we multiply by 3/4 at each stage? So, the last entry is (3/4)n. Since 3/4 < 1, we multiply and get a smaller area each time. As the stages converge to infinity, the total area of the triangle goes to zero. Amazing!
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