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Sep 3, 2012 at 23:24 comment added Dick Palais You will probably get a more "natural" answer if you choose a "torus", i.e., identify opposite edges of a square, to eliminate edge effects.
Sep 3, 2012 at 22:29 answer added Karl Fabian timeline score: 2
Sep 3, 2012 at 19:55 history edited jwellens CC BY-SA 3.0
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Sep 3, 2012 at 16:37 history edited jwellens CC BY-SA 3.0
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Sep 3, 2012 at 16:13 comment added Igor Rivin @Noam's comment is obviously the answer, with the one caveat that a non-asymptotic result will be a little tricky.
Sep 3, 2012 at 15:58 comment added Noam D. Elkies Compute the probability $p$ that a given point of $S$ is not hit by any of the circles (which is constant away from the edge), and multiply $1-p$ by the area of $S$.
Sep 3, 2012 at 15:22 history asked jwellens CC BY-SA 3.0