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It intuitively seems to be true that no finite set of non-overlapping rectangles can fill the unit disk. Is this proposition really true? If so, how can one prove it?

Behzad
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    If the rectangles are required to be inside the disk, "non-overlapping" seems to be unnecessary (and if the rectangles are not required to be inside the disk, the statement is plainly false anyway). – Gerry Myerson Feb 24 '14 at 08:58

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Hint: Find an infinite set of points, such that any 3 cannot be covered by a rectangle contained within the unit disc.

Calvin Lin
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