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Begin with a polygon P_0.$P_0$. Place two points on every edge of the polygon such that they divide each side equally into three parts. Create a new polygon P_1 $P_1$ by connecting all new points with lines. If we begin with a square and iterate this process, what is the limit as the number of iterations approaches infinity? It is clearly not a circle, but what the correct answer is, I do not know. |
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Limit of a sequence of polygons.Begin with a polygon P_0. Place two points on every edge of the polygon such that they divide each side equally into three parts. Create a new polygon P_1 by connecting all new points with lines. If we begin with a square and iterate this process, what is the limit as the number of iterations approaches infinity? It is clearly not a circle, but what the correct answer is, I do not know.
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