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What is known about the area of the symmetric Pythagorean tree? (Closed unit square as base, area of enclosed triangles not included.) The problem in calculating the area is that squares start to overlap from the sixth iteration onwards.

Without much effort it can be computed that height is 4 and breadth is 6, so an upper bound for the area is 24. Wikipedia reports that lower and upper bounds can with some effort be tightened to 5 and 18, respectively. The accompanying Wikipedia talk page reports on numerical approximations (pixel counts) that end somewhere near 14. Other than that, no trace of a hint of an exact answer in the literature.

Seems like a simple high-school problem. On closer inspection I believe it is not, due to the problem of overlapping squares.

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Why do you care? –  Anton Petrunin May 4 '13 at 1:04
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I reiterate Anton's (trollish?!) question. I think this question should be closed unless it is edited. From the FAQ: "MathOverflow is not the right place to ask open problems. You should post questions you're actually seriously thinking about. If you're thinking about a well-known open problem, provide some background and ask about something specific related to the problem." –  Yoav Kallus May 8 '13 at 19:05
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Definitely the question should be edited to include a precise definition of the Pythagorean tree, at least. –  Greg Martin May 8 '13 at 21:02
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I don't know, guys. The linked Wikipedia article seems to give a clear enough indication of what the (symmetric) Pythagorean tree is; just click on it if you want to know. If the question were slightly edited to "what is known about the area?" (beyond what is contained in the Wikipedia article or articles linked therein), then it wouldn't disqualify itself on the grounds of being an open problem, and probably about as acceptable as many other MO questions, although I agree with Deane that the response to Anton was really uncalled for (and could warrant a flag). If you don't like it, skip it. –  Todd Trimble May 9 '13 at 0:35
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@Gerard: such a pro tem explanation is good enough for me. It would be ridiculous to hold every MO question to the same standard (explain to me why I should care), and in my view many other questions that appear on MO are of even less intrinsic interest. I expect the problem is indeed challenging. People should work on it only if they feel like it. –  Todd Trimble May 9 '13 at 16:57

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