• In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces...
    30 KB (3,558 words) - 01:24, 25 February 2024
  • In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that...
    39 KB (5,090 words) - 08:05, 12 March 2024
  • Thumbnail for Projective space
    a projective line, and a projective space of dimension 2 is a projective plane. Projective spaces are widely used in geometry, as allowing simpler statements...
    37 KB (5,624 words) - 15:29, 9 February 2024
  • of noncommutative algebra Fundamental theorem of projective geometry Fundamental theorem of random fields Fundamental theorem of Riemannian geometry Fundamental...
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  • Thumbnail for Projective plane
    projective spaces; such embeddability is a consequence of a property known as Desargues' theorem, not shared by all projective planes. A projective plane...
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  • Parabolic geometry Plane geometry Projective geometry Quantum geometry Riemannian geometry Ruppeiner geometry Spherical geometry Symplectic geometry Synthetic...
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  • In projective geometry, duality or plane duality is a formalization of the striking symmetry of the roles played by points and lines in the definitions...
    46 KB (5,587 words) - 19:24, 1 December 2023
  • theorems in Diophantine geometry that are of fundamental importance include: Mordell–Weil theorem Roth's theorem Siegel's theorem Faltings's theorem Serge...
    8 KB (935 words) - 20:18, 2 February 2024
  • projective plane Complex projective space Plane at infinity, hyperplane at infinity Projective frame Projective transformation Fundamental theorem of...
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  • in favor of a purely synthetic development of projective geometry. For example, the treatment of the projective plane starting from axioms of incidence...
    14 KB (1,738 words) - 11:40, 28 December 2023
  • Thumbnail for Wigner's theorem
    Wigner's theorem is in close connection with the fundamental theorem of projective geometry If G is a symmetry group (in this latter sense of being embedded...
    30 KB (4,547 words) - 10:27, 8 February 2024
  • Thumbnail for Projective linear group
    theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action of the general linear...
    44 KB (5,586 words) - 02:50, 2 March 2024
  • Thumbnail for Projective variety
    In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space Pn{\displaystyle \mathbb {P} ^{n}}...
    45 KB (7,219 words) - 18:38, 11 December 2022
  • principle of duality in projective geometry, among other fields. This meta-phenomenon can roughly be described as follows: in any theorem, exchange point...
    100 KB (9,862 words) - 21:48, 22 March 2024
  • Collineation (category Projective geometry)
    In projective geometry, a collineation is a one-to-one and onto map (a bijection) from one projective space to another, or from a projective space to...
    14 KB (1,739 words) - 15:24, 30 October 2023
  • making it an (smooth projective) algebraic curve. Under the name Riemann's existence theorem a deeper result on ramified coverings of a compact Riemann surface...
    19 KB (2,422 words) - 13:44, 20 March 2024
  • not in general affine or projective. By Serre's GAGA theorem, every projective complex analytic variety is actually a projective complex algebraic variety...
    26 KB (3,601 words) - 14:31, 7 September 2023
  • Thumbnail for Affine geometry
    parallel to L that passes through P.) is fundamental in affine geometry. Comparisons of figures in affine geometry are made with affine transformations,...
    20 KB (2,616 words) - 20:54, 28 March 2024
  • Anabelian geometry is a theory in number theory which describes the way in which the algebraic fundamental group G of a certain arithmetic variety X,...
    11 KB (1,235 words) - 03:52, 9 March 2024
  • Thumbnail for Finite geometry
    finite projective space of dimension three or greater is isomorphic to a projective space over a finite field (that is, the projectivization of a vector...
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  • Thumbnail for Euclidean geometry
    possible exception of the parallel postulate) that theorems proved from them were deemed absolutely true, and thus no other sorts of geometry were possible...
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  • and more specifically in projective geometry, a projective frame or projective basis is a tuple of points in a projective space that can be used for...
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  • Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form...
    23 KB (3,439 words) - 02:16, 15 March 2024
  • Thumbnail for Differential geometry of surfaces
    Gauss-Codazzi equations. A major theorem, often called the fundamental theorem of the differential geometry of surfaces, asserts that whenever two objects satisfy...
    128 KB (16,857 words) - 05:14, 22 December 2023
  • Hua's identity (category Theorems in algebra)
    homomorphism or an antihomomorphism. This theorem is connected to the fundamental theorem of projective geometry. One has ( a − a b a ) ( a − 1 + ( b − 1...
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  • differential geometry Line element Curvature Radius of curvature Osculating circle Curve Fenchel's theorem Theorema egregium Gauss–Bonnet theorem First fundamental...
    8 KB (679 words) - 11:05, 12 February 2024
  • the complex projective plane, usually denoted P2(C) or CP2, is the two-dimensional complex projective space. It is a complex manifold of complex dimension...
    3 KB (500 words) - 14:08, 10 March 2024
  • of derivatives and integrals in alternative calculi List of equations List of fundamental theorems List of hypotheses List of inequalities Lists of integrals...
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  • Thumbnail for Algebraic geometry
    projective space plays a fundamental role in algebraic geometry. Nowadays, the projective space Pn of dimension n is usually defined as the set of the...
    60 KB (7,374 words) - 08:44, 4 December 2023
  • Thumbnail for Pythagorean theorem
    mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states...
    94 KB (12,162 words) - 10:24, 12 March 2024