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Dissecting brick into bars | | Ivan Feshchenko
; Danylo Radchenko
; Lev Radzivilovsky
; Maksym Tantsiura
; | | Date: |
10 Sep 2008 | | Abstract: | An $N$-dimensional parallelepiped will be called a bar if and only if there
are no more than $k$ different numbers among the lengths of its sides (the
definition of bar depends on $k$). We prove that a parallelepiped can be
dissected into finite number of bars iff the lengths of sides of the
parallelepiped span a linear space of dimension no more than $k$ over $QQ$.
This extends and generalizes a well-known theorem of Max Dehn about partition
of rectangles into squares. Several other results about dissections of
parallelepipeds are obtained. | | Source: | arXiv, 0809.1883 | | Services: | Forum | Review | PDF | Favorites | |
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