Sunday, 13 October 2013

integral length

A rectangle is tiled with smaller rectangles, each of which has at least one side of integral length.
Prove that the tiled rectangle also must have at least one side of integral length.

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Define f:RR by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \ 0, ...