pole of hyperplane

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• 3-sphere — Stereographic projection of the hypersphere s parallels (red), meridians (blue) and hypermeridians (green). Because this projection is conformal, the curves intersect each other orthogonally (in the yellow points) as in 4D. All curves are circles …   Wikipedia

• Complex projective space — The Riemann sphere, the one dimensional complex projective space, i.e. the complex projective line. In mathematics, complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a …   Wikipedia

• Möbius transformation — Not to be confused with Möbius transform or Möbius function. In geometry, a Möbius transformation of the plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − …   Wikipedia

• Stereographic projection — In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point mdash; the projection point. Where it is defined, the mapping is …   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

• Bipyramid — For Dipyramid, see mountain and Dipyramid (Alaska). Set of bipyramids (Example hexagonal form) Faces 2n triangles Edges 3n Vertices n + 2 …   Wikipedia

• Inversive geometry — Not to be confused with Inversive ring geometry. In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion. These… …   Wikipedia

• Polar set — See also polar set (potential theory). In functional analysis and related areas of mathematics the polar set of a given subset of a vector space is a certain set in the dual space.Given a dual pair (X,Y) the polar set or polar of a subset A of X… …   Wikipedia

• Plane (geometry) — Two intersecting planes in three dimensional space In mathematics, a plane is a flat, two dimensional surface. A plane is the two dimensional analogue of a point (zero dimensions), a line (one dimension) and a space (three dimensions). Planes can …   Wikipedia

• Projective space — In mathematics a projective space is a set of elements constructed from a vector space such that a distinct element of the projective space consists of all non zero vectors which are equal up to a multiplication by a non zero scalar. A formal… …   Wikipedia

• Hyperbolic space — In mathematics, hyperbolic n space, denoted H n , is the maximally symmetric, simply connected, n dimensional Riemannian manifold with constant sectional curvature −1. Hyperbolic space is the principal example of a space exhibiting hyperbolic… …   Wikipedia