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Quantitative estimates related to the classical Borsuk problem of splittingset in Euclidean space into subsets of smaller diameter are considered. For agiven $k$ there is a minimal diameter of subsets at which there exists acovering with $k$ subsets of any planar set of unit diameter. In order to findan upper estimate of the minimal diameter we propose an algorithm for findingsub-optimal partitions. In the cases $10 \leqslant k \leqslant 17$ some upperand lower estimates of the minimal diameter are improved. Another result isthat any set $M \subset \mathbb{R}^3$ of a unit diameter can be partitionedinto four subsets of a diameter not greater than $0.966$.

Coverings of planar and three-dimensional sets with subsets of smaller diameter