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DECOMPOSITION OF BALLS IN
$\mathbb{R}^{d}$
Published online by Cambridge University Press: 22 January 2016
Abstract
We investigate the problem of the decomposition of balls into a finite number of congruent pieces in dimension $d=2k$. In addition, we prove that the
$d$-dimensional unit ball
$B_{d}$ can be divided into a finite number of congruent pieces if
$d=4$ or
$d\geqslant 6$. We show that the minimal number of required pieces is less than
$20d$, if
$d\geqslant 10$.
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- Research Article
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- Copyright © University College London 2016
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