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In geometry, a hyperplane of an n-dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V.The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can ...
In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of 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 space.
This is a partial list of works that use metafictional ideas. Metafiction is intentional allusion or reference to a work's fictional nature. It is commonly used for humorous or parodic effect, and has appeared in a wide range of mediums, including writing, film, theatre, and video gaming.
Conversely, if is a closed set with nonempty interior such that every point on the boundary has a supporting hyperplane, then is a convex set, and is the intersection of all its supporting closed half-spaces. [2] The hyperplane in the theorem may not be unique, as noticed in the second picture on the right.
Then N is called the simultaneous hyperplane with respect to v. The relativity of simultaneity is a statement that N depends on v. Indeed, N is the orthogonal complement of v with respect to η. When two world lines u and w are related by =, then they share the same simultaneous hyperplane. This hyperplane exists mathematically, but physical ...
[5]: 238–239 [9]: 75 [10] In The Mystery of Element 117 (1949) by Milton Smith, a window is opened into a new "hyperplane of hyperspace" containing those who have already died on Earth, [8]: 181 and similarly, in Bob Shaw's The Palace of Eternity (1969), hyperspace is a form of afterlife, where human minds and memories reside after death.
In mathematics, a hyperplane section of a subset X of projective space P n is the intersection of X with some hyperplane H. In other words, we look at the subset X H of those elements x of X that satisfy the single linear condition L = 0 defining H as a linear subspace .
Oriented-matroid theory allows a combinatorial approach to the max-flow min-cut theorem.A network with the value of flow equal to the capacity of an s-t cut. An oriented matroid is a mathematical structure that abstracts the properties of directed graphs, vector arrangements over ordered fields, and hyperplane arrangements over ordered fields. [1]