Dissecting a brick into bars

  title={Dissecting a brick into bars},
  author={Ivan S. Feshchenko and Danylo V. Radchenko and Lev Radzivilovsky and Maksym Tantsiura},
  journal={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… 

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