Let P0 be an equilateral triangle of area 10. Each side of P0 is trisected into three segments of equal length, and the corners of P0 are snipped off, creating a new polygon (in fact, a hexagon) P1. What is the area of P1? Now repeat the process to P1 – i.e. trisect each side and snip off the corners – to obtain a new polygon P2. What is the area of P2? Now repeat this process infinitely to create an object P∞. What can you say about the shape P∞? What is the area of P∞

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