SOME APPLICATIONS OF BINARY AND TERNARY SYSTEMS OF NUMERATION
Abstract
By means of binary and ternary number systems, the authors solve two problems: the search of finite collections of weights with any given total weight m € N (kg), in particular with minimal number of weights, such that one can weigh a load of any weight n € N П [1,m] (kg), using one-sided or two-sided placement of weights; a coordinate description of Sierpinski gasket and carpet, Menger sponge. On the ground of solution of the second problem, it is proved that restriction of the Euclidean metric to any of these three sets and inner metric, induced by this restriction, are bi-Lipschitz equivalent. It is given a direct proof of known fact that Hausdorff dimensions of all these sets coincide with their fractal dim
About the Authors
Valery Nikolaevich Berestovskii
Omsk branch of Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Irina Alexandrovna Zubareva
Omsk branch of Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
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Review
For citations:
Berestovskii V.N., Zubareva I.A. SOME APPLICATIONS OF BINARY AND TERNARY SYSTEMS OF NUMERATION. The Bulletin of Kemerovo State University. 2011;(3-1):106-118. (In Russ.)
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