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| Brief Explaination: | Area Calculations: |
| Start with any triangle,
and include its interior.
Create an inner triangle by connecting the mid-points of the original triangle's sides, and remove the inner triangle's interior. Do the same to each of the 3 remaining triangles, removing their inner triangles' interiors. Do the same to each of the 9 remaining triangles, removing their inner triangles' interiors. Continue this process. Notice that with each step, the area is reduced to 3/4 of the previous step's area. So, as n increases without bound, the area decreases and approaches zero. Sierpinski's gasket is the limit toward which the geometrical structure gets closer and closer. It is devoid of all area, but has an infinite number of sides of an infinite number of triangles. |
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