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I've read somewhere that it was possible to cut any rectangle into a finite number of pieces and reassemble it into another rectangle with a side of length 1 but I can't see how this is done... Can anyone explain this to me or give me any helpful links?

Thanks in advance for the help!

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  • $\begingroup$ Search under Bolyai-Gerwien Theorem. (The second guy's name has variable spelling.) The stronger result is proved is that if $A$ and $B$ are polygonal regions with the same area, then $A$ can be cut up into polygonal pieces and reassembled to make $B$. The result you refer to is sometimes a lemma in this proof. The key thing is that a rectangle can be cut up and reassembled to make a square. $\endgroup$ – André Nicolas Aug 11 '14 at 16:05
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Hilbert third problem . We can cut and resamble any poligonal sufaces into another poligonal suface of the same area.But the demonstration have many steps.

First cut rectanle $a$x$b$ in a sqare like here trasform rectangle in sqare_1 or here transform rectangle in square_2 or if you like Youtube Quadrature: Rectangle to Square With Equal Area and more in square from rectangle

Take rectangle of $1$x$(ab)$ and do the same thing.

Now you have $2$ identical sqares but otherwise cut. Put one sqare above the other sqare and cut all "intersections". Now you have all components.

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