# Dissecting a brick into bars

```@article{Feshchenko2008DissectingAB,
title={Dissecting a brick into bars},
author={Ivan S. Feshchenko and Danylo V. Radchenko and Lev Radzivilovsky and Maksym Tantsiura},
journal={Geometriae Dedicata},
year={2008},
volume={145},
pages={159-168}
}```
• Published 10 September 2008
• Mathematics
• Geometriae Dedicata
Consider the set of all lengths of sides of an N-dimensional parallelepiped. If this set has no more than k elements, the parallelepiped will be called a bar (the definition of a bar depends on k). We prove that a parallelepiped can be dissected into a finite number of bars if and only if the lengths of its sides span a linear space of dimension at most k over \$\${{\mathbb Q}}\$\$ . This extends and generalizes a well-known theorem of Max Dehn about the splitting of rectangles into squares…
3 Citations
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