Suppose we have three rectangles, named 1, 2, and 3. 1 and 2 are identically sized, are axis-aligned, and overlap with 3, but not each other. 1's center is closer to 3's center than is 2's center. Is it safe to say, then, that the rectangle created by the overlap of 1 and 3 is bigger than the rectangle created by the overlap of 2 and 3? My intuition says "yes".
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$\begingroup$ Are the rectangles axis-aligned? $\endgroup$– Element118Dec 12, 2015 at 3:04
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$\begingroup$ @Element118 Yes. $\endgroup$– moonman239Dec 12, 2015 at 3:38
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$\begingroup$ Any thoughts on the answer I posted. $\endgroup$– Gerry MyersonDec 13, 2015 at 8:11
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1 Answer
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Suppose rectangle 3 is a square of side 2, centered at the origin, rectangle 1 is centered at $(0,1.1)$ and has height just over $1.1$, rectangle 2 is centered at $(.9,-.9)$. I think you'll find your hypotheses are satisfied, but not your conclusion.
answered Dec 12, 2015 at 4:22