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We present a multidimensional version of the Three Gap Theorem of Steinhaus, proving that the number of the so-called primitive arcs is bounded in any dimension.
C. Cobeli, et al. "Generalization of a theorem of Steinhaus." Colloquium Mathematicae 92.2 (2002): 257-266. <http://eudml.org/doc/285289>.
@article{C2002, abstract = {We present a multidimensional version of the Three Gap Theorem of Steinhaus, proving that the number of the so-called primitive arcs is bounded in any dimension.}, author = {C. Cobeli, G. Groza, M. Vâjâitu, A. Zaharescu}, journal = {Colloquium Mathematicae}, keywords = {three gap theorem; number of primitive spacings; fractional parts}, language = {eng}, number = {2}, pages = {257-266}, title = {Generalization of a theorem of Steinhaus}, url = {http://eudml.org/doc/285289}, volume = {92}, year = {2002}, }
TY - JOUR AU - C. Cobeli AU - G. Groza AU - M. Vâjâitu AU - A. Zaharescu TI - Generalization of a theorem of Steinhaus JO - Colloquium Mathematicae PY - 2002 VL - 92 IS - 2 SP - 257 EP - 266 AB - We present a multidimensional version of the Three Gap Theorem of Steinhaus, proving that the number of the so-called primitive arcs is bounded in any dimension. LA - eng KW - three gap theorem; number of primitive spacings; fractional parts UR - http://eudml.org/doc/285289 ER -