# Hyperplanes

### Some articles on hyperplanes, hyperplane:

Duality (projective Geometry) - Higher Dimensional Duality
... space of dimension n, the points (dimension 0) are made to correspond with hyperplanes (codimension 1), the lines joining two points (dimension 1) are made to correspond with the intersection of two hyperplanes (co ... of Kn + 1 represent the (n − 1)- geometric dimensional hyperplanes of projective n-space over K ... in Kn + 1 also determines an (n - 1) - geometric dimensional subspace (hyperplane) Hu, by Hu = {(x0,x1...xn) u0x0 + … + unxn = 0 } ...
Matroid - Definition - Hyperplanes
... In a matroid of rank, a flat of rank is called a hyperplane ... flats that is, the only superset of a hyperplane that is also a flat is the set of all the elements of the matroid ... Hyperplanes are also called coatoms or copoints ...
Arrangement Of Hyperplanes
... In geometry and combinatorics, an arrangement of hyperplanes is a finite set A of hyperplanes in a linear, affine, or projective space S ... Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole ... that are obtained by intersecting some of the hyperplanes among these subspaces are S itself, all the individual hyperplanes, all intersections of pairs of ...
George Blakley - Secret-sharing Scheme
... the secret as a point in n-dimensional space, and gives out shares that correspond to hyperplanes that intersect the secret point ... Any n such hyperplanes will specify the point, while fewer than n hyperplanes will leave at least one degree of freedom, and thus leave the point unspecified ...
Tarski's Plank Problem - Statement
... Given a convex body C in Rn and a hyperplane H, the width of C parallel to H, w(C,H), is the distance between the two supporting hyperplanes of C that are parallel ... the infimum over all possible hyperplanes) is called the minimal width of C, w(C) ... The (closed) set of points P between two distinct, parallel hyperplanes in Rn is called a plank, and the distance between the two hyperplanes is called the width of the plank ...