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?
2026-03-27 21:43:32.1774647812
Filling the Unit Disk With Non-overlapping Rectangles
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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.