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In geometry, space partitioning is the process of dividing an entire space (usually a Euclidean space) into two or more disjoint subsets (see also partition of a set). In other words, space partitioning divides a space into non-overlapping regions. Any point in the space can then be identified to lie in exactly one of the regions.
A variation of the polynomial method, often called polynomial partitioning, was introduced by Guth and Katz in their solution to the Erdős distinct distances problem. [4] Polynomial partitioning involves using polynomials to divide the underlying space into regions and arguing about the geometric structure of the partition.
In number theory and computer science, the partition problem, or number partitioning, [1] is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S 1 and S 2 such that the sum of the numbers in S 1 equals the sum of the numbers in S 2.
Arrangement (space partition), a partition of the plane given by overlaid curves or of a higher dimensional space by overlaid surfaces, without requiring the curves or surfaces to be flat; Mathematical Bridge, a bridge in Cambridge, England whose beams form an arrangement of tangent lines to its arch
When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...
The Kelvin problem on minimum-surface-area partitions of space into equal-volume cells, and the optimality of the Weaire–Phelan structure as a solution to the Kelvin problem [74] Lebesgue's universal covering problem on the minimum-area convex shape in the plane that can cover any shape of diameter one [75]