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April 16th, 2011, 06:15 PM   #1
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Area of square with convex parts - area of circle

I need to find the area of the blue in this image where n = whatever. I'm having a really hard time. n is the number of times where an edge of one of the squares is touching the edge of the circle. The diameter of the circle is 1, and

I think that the right first move is to break it up so we are only seeing one quadrant of the square/circle. We can then think of the area missing from blue in this certain quadrant as a bunch of small squares where the amount of small squares is (n^2+n)/2 (triangular numbers). The next step is the most difficult, and that is finding the area of each of these small squares.

Can anyone help me solve this or get me thinking in the right direction? Thanks!
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April 17th, 2011, 04:25 PM   #2
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How is the blue area constructed when n = 2? Even if n is required to be a triangular number, it's not clear how the blue shape is constructed.
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