geometric duality

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• Duality (mathematics) — In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one to one fashion, often (but not always) by means of an involution operation: if the dual… …   Wikipedia

• Duality (projective geometry) — A striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this metamathematical concept. There are two approaches to the subject of …   Wikipedia

• Geometric algebra — In mathematical physics, a geometric algebra is a multilinear algebra described technically as a Clifford algebra over a real vector space equipped with a non degenerate quadratic form. Informally, a geometric algebra is a Clifford algebra that… …   Wikipedia

• Geometric genus — In algebraic geometry, the geometric genus is a basic birational invariant p g of algebraic varieties, defined for non singular complex projective varieties (and more generally for complex manifolds) as the Hodge number h n ,0 (equal to h 0, n by …   Wikipedia

• Poincaré duality — In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if M is an n dimensional compact oriented manifold, then the k th… …   Wikipedia

• Comparison of vector algebra and geometric algebra — Vector algebra and geometric algebra are alternative approaches to providing additional algebraic structures on vector spaces, with geometric interpretations, particularly vector fields in multivariable calculus and applications in mathematical… …   Wikipedia

• Lefschetz duality — In mathematics, Lefschetz duality is a version of Poincaré duality in geometric topology, applying to a manifold with boundary. Such a formulation was introduced by Solomon Lefschetz in the 1920s, at the same time introducing relative homology,… …   Wikipedia

• principle of duality — a principle in projective geometry: from a geometric theorem another theorem may be derived by substituting in the original theorem the word point for the word line in the case of a point or line in the plane or the word point for the word plane… …   Useful english dictionary

• Dual polygon — In geometry, polygons are associated into pairs called duals, where the vertices of one correspond to the edges of the other. Contents 1 Properties 2 Kinds of duality 2.1 Rectification …   Wikipedia

• Matrix representation of conic sections — In mathematics, the matrix representation of conic sections is one way of studying a conic section, its axis, vertices, foci, tangents, and the relative position of a given point. We can also study conic sections whose axes aren t parallel to our …   Wikipedia

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