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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.
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.
Packing of irregular objects is a problem not lending itself well to closed form solutions; however, the applicability to practical environmental science is quite important. For example, irregularly shaped soil particles pack differently as the sizes and shapes vary, leading to important outcomes for plant species to adapt root formations and ...
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.
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
Line arrangements. In discrete geometry, an arrangement is the decomposition of the d-dimensional linear, affine, or projective space into connected cells of different dimensions, induced by a finite collection of geometric objects, which are usually of dimension one less than the dimension of the space, and often of the same type as each other, such as hyperplanes or spheres.