Borsuk's Conjecture
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High Quality Content by WIKIPEDIA articles! The Borsuk problem in geometry, for historical reasons incorrectly called a Borsuk conjecture, is a question in discrete geometry.In 1932 Karol Borsuk has shown that an ordinary 3-dimensional ball in Euclidean space can be easily dissected into 4 solids, each of which has a smaller diameter than the ball, and generally d-dimensional ball can be covered with d + 1 compact sets of diameters smaller than the ball. At the same time he proved that d subsets are not enough in general. The proof is based on the Borsuk Ulam theorem.
