enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Projective space - Wikipedia

    en.wikipedia.org/wiki/Projective_space

    A projective space of dimension 1 is a projective line, and a projective space of dimension 2 is a projective plane. Projective spaces are widely used in geometry , allowing for simpler statements and simpler proofs.

  3. Projective geometry - Wikipedia

    en.wikipedia.org/wiki/Projective_geometry

    In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (projective space) and a selective set of basic geometric concepts.

  4. Real projective space - Wikipedia

    en.wikipedia.org/wiki/Real_projective_space

    In mathematics, real projective space, denoted ⁠ ⁠ or ⁠ (), ⁠ is the topological space of lines passing through the origin 0 in the real space ⁠ +. ⁠ It is a compact , smooth manifold of dimension n , and is a special case ⁠ G r ( 1 , R n + 1 ) {\displaystyle \mathbf {Gr} (1,\mathbb {R} ^{n+1})} ⁠ of a Grassmannian space.

  5. Algebraic geometry of projective spaces - Wikipedia

    en.wikipedia.org/wiki/Algebraic_geometry_of...

    The group of symmetries of the projective space is the group of projectivized linear automorphisms + (). The choice of a morphism to a projective space j : X → P n {\displaystyle j:X\to \mathbf {P} ^{n}} modulo the action of this group is in fact equivalent to the choice of a globally generating n -dimensional linear system of divisors on a ...

  6. Proj construction - Wikipedia

    en.wikipedia.org/wiki/Proj_construction

    We also construct a sheaf on ⁡, called the “structure sheaf” as in the affine case, which makes it into a scheme.As in the case of the Spec construction there are many ways to proceed: the most direct one, which is also highly suggestive of the construction of regular functions on a projective variety in classical algebraic geometry, is the following.

  7. Real projective plane - Wikipedia

    en.wikipedia.org/wiki/Real_projective_plane

    Projective geometry is not necessarily concerned with curvature and the real projective plane may be twisted up and placed in the Euclidean plane or 3-space in many different ways. [1] Some of the more important examples are described below.

  8. Complex projective space - Wikipedia

    en.wikipedia.org/wiki/Complex_projective_space

    In mathematics, complex projective space is the projective space with respect to the field of complex numbers.By analogy, whereas the points of a real projective space label the lines through the origin of a real Euclidean space, the points of a complex projective space label the complex lines through the origin of a complex Euclidean space (see below for an intuitive account).

  9. Homogeneous coordinates - Wikipedia

    en.wikipedia.org/wiki/Homogeneous_coordinates

    This leads to the concept of duality in projective geometry, the principle that the roles of points and lines can be interchanged in a theorem in projective geometry and the result will also be a theorem. Analogously, the theory of points in projective 3-space is dual to the theory of planes in projective 3-space, and so on for higher dimensions.