For what it's worth, I got $1-\sqrt{3}-\frac{\pi}{3}$, but I can't follow all my scribbling to check it. Too much thinking for a Saturday afternoon.
Saturday, April 23, 2011
Saturday Puzzle
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Puzzles
Just thought I'd create the graphic for jd2718's question. The source of the puzzle is unknown to me but I'm sure that I've seen it before. The problem is simple ... given a square of side 1 and four circles each of radius 1 centered at the four corners of the square, what is the area of the "rounded square" in the middle?
For what it's worth, I got $1-\sqrt{3}-\frac{\pi}{3}$, but I can't follow all my scribbling to check it. Too much thinking for a Saturday afternoon.
For what it's worth, I got $1-\sqrt{3}-\frac{\pi}{3}$, but I can't follow all my scribbling to check it. Too much thinking for a Saturday afternoon.
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We probably agree (because a friend shared his solution with me. I was stuck). One of us may have a sign error.
ReplyDeleteThanks for the drawing.
I was positive I saw it here a few weeks ago, but clearly I am going nuts.