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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.
Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics.As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental psychology, neuroscience and cognitive linguistics.
Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
[6] [7] The partition lattice of a 4-element set has 15 elements and is depicted in the Hasse diagram on the left. The meet and join of partitions α and ρ are defined as follows. The meet is the partition whose blocks are the intersections of a block of α and a block of ρ, except for
The values (), …, of the partition function (1, 2, 3, 5, 7, 11, 15, and 22) can be determined by counting the Young diagrams for the partitions of the numbers from 1 to 8. In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n.
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another). It is usually required that the dissection use only a ...
Binary space partitioning arose from computer graphics needing to rapidly draw three-dimensional scenes composed of polygons. A simple way to draw such scenes is the painter's algorithm , which produces polygons in order of distance from the viewer, back to front, painting over the background and previous polygons with each closer object.
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.