Ciro Santilli $$ Sponsor Ciro $$ 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件邓家贵、低端人口、西藏骚乱

Geometry

| nosplit | ↑ parent "Mathematics" | words: 0 | descendant words: 9k | descendants: 154

nosplit | ⇓ toc | ↑ parent "Mathematics" | Wikipedia | words: 0 | descendant words: 9k | descendants: 154

Table of contents | 0, 9k, 154
- Fractal | 🔗 link | nosplit | ↑ parent "Geometry"
- Point (geometry) | 0, 53, 3 | 🔗 link | nosplit | ↑ parent "Geometry"
  - Line (geometry) | 🔗 link | nosplit | ↑ parent "Point"
  - Hyperplane | 53, 53, 1 | 🔗 link | nosplit | ↑ parent "Point"
    - Plane (geometry) | 🔗 link | nosplit | ↑ parent "Hyperplane"
- n-sphere ( $S^{n}$ ) | 0, 10, 7 | 🔗 link | nosplit | ↑ parent "Geometry"
  - Antipodal point | 🔗 link | nosplit | ↑ parent "n-sphere"
  - Diameter | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "n-sphere"
    - Radius | 🔗 link | nosplit | ↑ parent "Diameter"
  - Circle ( $S^{1}$ , 1-sphere) | 🔗 link | nosplit | ↑ parent "n-sphere"
  - Sphere ( $S^{2}$ , 2-sphere) | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "n-sphere"
    - Great circle | 🔗 link | nosplit | ↑ parent "Sphere"
  - 3-sphere ( $S^{3}$ ) | 10 | 🔗 link | nosplit | ↑ parent "n-sphere"
- Projective geometry | 0, 1k, 12 | 🔗 link | nosplit | ↑ parent "Geometry"
  - Projective space ( $P (V)$ ) | 86, 86, 1 | 🔗 link | nosplit | ↑ parent "Projective geometry"
    - Projective plane | 🔗 link | nosplit | ↑ parent "Projective space"
  - Real projective space ( $R P^{n}$ , $P (R^{n + 1})$ ) | 31, 965, 9 | 🔗 link | nosplit | ↑ parent "Projective geometry"
    - Real projective line ( $R P^{1}$ , $P (R^{2})$ ) | 27 | 🔗 link | nosplit | ↑ parent "Real projective space"
    - Real projective plane ( $R P^{2}$ , $P (R^{3})$ ) | 95, 907, 7 | 🔗 link | nosplit | ↑ parent "Real projective space"
- Polytope | 37, 487, 28 | 🔗 link | nosplit | ↑ parent "Geometry"
  - Convex polytope | 🔗 link | nosplit | ↑ parent "Polytope"
  - Regular polytope | 5, 390, 5 | 🔗 link | nosplit | ↑ parent "Polytope"
    - Classification of regular polytopes | 148, 385, 4 | 🔗 link | nosplit | ↑ parent "Regular polytope"
      - Simplex | 48 | 🔗 link | nosplit | ↑ parent "Classification of regular polytopes"
      - Hypercube | 112, 132, 1 | 🔗 link | nosplit | ↑ parent "Classification of regular polytopes"
        
        Hyperrectangle | 20 | 🔗 link | nosplit | ↑ parent "Hypercube"
      - Cross polytope | 57 | 🔗 link | nosplit | ↑ parent "Classification of regular polytopes"
  - Polygon | 0, 15, 12 | 🔗 link | nosplit | ↑ parent "Polytope"
    - Quadrilateral | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Polygon"
      - Rectangle | 🔗 link | nosplit | ↑ parent "Quadrilateral"
    - Parallelogram | 0, 15, 2 | 🔗 link | nosplit | ↑ parent "Polygon"
      - Parallelepiped | 15, 15, 1 | 🔗 link | nosplit | ↑ parent "Parallelogram"
        
        Volume of the parallelepiped | 🔗 link | nosplit | ↑ parent "Parallelepiped"
    - Regular polygon | 0, 0, 6 | 🔗 link | nosplit | ↑ parent "Polygon"
      - Regular convex polygon | 0, 0, 5 | 🔗 link | nosplit | ↑ parent "Regular polygon"
        
        Triangle | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
        
        Square | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
        
        Pentagon | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
        
        Hexagon | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
        
        Octagon | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
  - Polyhedron | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Polytope"
    - Tetrahedron | 🔗 link | nosplit | ↑ parent "Polyhedron"
    - Octahedron | 🔗 link | nosplit | ↑ parent "Polyhedron"
  - Regular polyhedron | 0, 45, 1 | 🔗 link | nosplit | ↑ parent "Polytope"
    - Platonic solid | 45 | 🔗 link | nosplit | ↑ parent "Regular polyhedron"
  - 4-polytope | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Polytope"
    - Regular 4-polytope | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "4-polytope"
      - Tesseract | 🔗 link | nosplit | ↑ parent "Regular 4-polytope"
- Differential geometry | 12, 7k, 98 | 🔗 link | nosplit | ↑ parent "Geometry"
  - Lie group | 278, 7k, 97 | 🔗 link | nosplit | ↑ parent "Differential geometry"
    - Applications of Lie groups to differential equations (How to use Lie Groups to solve differential equations) | 104 | 🔗 link | nosplit | ↑ parent "Lie group"
    - Lie algebra | 424, 1k, 15 | 🔗 link | nosplit | ↑ parent "Lie group"
    - Continuous symmetry | 18, 348, 2 | 🔗 link | nosplit | ↑ parent "Lie group"
      - Local symmetry | 162, 330, 1 | 🔗 link | nosplit | ↑ parent "Continuous symmetry"
        
        Local symmetries of the Lagrangian imply conserved currents | 168 | 🔗 link | nosplit | ↑ parent "Local symmetry"
    - Important Lie group | 0, 5k, 65 | 🔗 link | nosplit | ↑ parent "Lie group"
      - Matrix Lie group | 9, 471, 4 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Every closed subgroup of $G L (n, C)$ is a Lie group | 8 | 🔗 link | nosplit | ↑ parent "Matrix Lie group"
        
        Lie algebra of a matrix Lie group | 219, 454, 2 | 🔗 link | nosplit | ↑ parent "Matrix Lie group"
        
        Lie bracket of a matrix Lie group | 119 | 🔗 link | nosplit | ↑ parent "Lie algebra of a matrix Lie group"
        
        One parameter subgroup | 116 | 🔗 link | nosplit | ↑ parent "Lie algebra of a matrix Lie group"
      - Classical group | 0, 222, 3 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Symplectic group ( $S p (n, F)$ ) | 222, 222, 2 | 🔗 link | nosplit | ↑ parent "Classical group"
        
        Symplectic matrix | 🔗 link | nosplit | ↑ parent "Symplectic group"
        
        Unitary symplectic group ( $S p (n)$ ) | 🔗 link | nosplit | ↑ parent "Symplectic group"
      - General linear group ( $G L (n)$ , $G L (n, F)$ ) | 91, 170, 1 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Finite general linear group ( $G L (n, F_{m})$ , $G L (n, m)$ ) | 79 | 🔗 link | nosplit | ↑ parent "General linear group"
      - Lie algebra of $G L (n)$ | 109 | 🔗 link | nosplit | ↑ parent "Important Lie group"
      - Special linear group ( $S L (n)$ ) | 18, 638, 4 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Special linear group of dimension 2 ( $S L (2)$ ) | 🔗 link | nosplit | ↑ parent "Special linear group"
        
        Lie algebra of $S L (n)$ | 0, 569, 1 | 🔗 link | nosplit | ↑ parent "Special linear group"
        
        Lie algebra of $S L (2)$ | 569 | 🔗 link | nosplit | ↑ parent "Lie algebra of $S L (n)$ "
        
        Finite special general linear group ( $S L (n, m)$ ) | 51 | 🔗 link | nosplit | ↑ parent "Special linear group"
      - Isometry group | 69, 206, 1 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Lie algebra of a isometry group | 137 | 🔗 link | nosplit | ↑ parent "Isometry group"
      - Orthogonal group ( $O (n)$ ) | 0, 1k, 22 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Definition of the orthogonal group | 8, 391, 4 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        The orthogonal group is the group of all matrices that preserve the dot product | 72, 244, 1 | 🔗 link | nosplit | ↑ parent "Definition of the orthogonal group"
        
        What happens to the definition of the orthogonal group if we choose other types of symmetric bilinear forms | 172 | 🔗 link | nosplit | ↑ parent "The orthogonal group is the group of all matrices that preserve the dot product"
        
        The orthogonal group is the group of all invertible matrices where the inverse is equal to the transpose | 102 | 🔗 link | nosplit | ↑ parent "Definition of the orthogonal group"
        
        The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns | 37 | 🔗 link | nosplit | ↑ parent "Definition of the orthogonal group"
        
        Topology of the orthogonal group | 0, 343, 2 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        The orthogonal group is compact | 🔗 link | nosplit | ↑ parent "Topology of the orthogonal group"
        
        Connected components of the orthogonal group (The orthogonal group has two connected components) | 343 | 🔗 link | nosplit | ↑ parent "Topology of the orthogonal group"
        
        Lie algebra of $O (n)$ | 9 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        Special orthogonal group ( $S O (n)$ , Rotation group) | 46, 275, 3 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        Lie algebra of $S O (3)$ | 180, 211, 1 | 🔗 link | nosplit | ↑ parent "Special orthogonal group"
        
        Lie bracket of the rotation group | 31 | 🔗 link | nosplit | ↑ parent "Lie algebra of $S O (3)$ "
        
        3D rotation group ( $S O (3)$ ) | 18 | 🔗 link | nosplit | ↑ parent "Special orthogonal group"
        
        Unitary group ( $U (n)$ ) | 80, 205, 8 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        Unitary group of degree 1 ( $U (1)$ ) | 🔗 link | nosplit | ↑ parent "Unitary group"
        
        Unitary group of degree 2 ( $U (2)$ ) | 5 | 🔗 link | nosplit | ↑ parent "Unitary group"
        
        Unit circle | 19 | 🔗 link | nosplit | ↑ parent "Unitary group"
        
        Special unitary group ( $S U (n)$ ) | 49, 101, 4 | 🔗 link | nosplit | ↑ parent "Unitary group"
        
        Special unitary of degree 2 ( $S U (2)$ ) | 34, 52, 3 | 🔗 link | nosplit | ↑ parent "Special unitary group"
        
        Representations of $S U (2)$ | 0, 18, 2 | 🔗 link | nosplit | ↑ parent "Special unitary of degree 2"
        
        Lie algebra of $S U (2)$ | 10 | 🔗 link | nosplit | ↑ parent "Representations of $S U (2)$ "
        
        2D representation of $S U (2)$ | 8 | 🔗 link | nosplit | ↑ parent "Representations of $S U (2)$ "
      - Projective linear group | 19, 48, 5 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Finite projective linear group ( $P G L (q, p)$ ) | 🔗 link | nosplit | ↑ parent "Projective linear group"
        
        Projective special linear group | 0, 29, 3 | 🔗 link | nosplit | ↑ parent "Projective linear group"
        
        Finite projective special linear group ( $P S L (p, q)$ ) | 0, 29, 2 | 🔗 link | nosplit | ↑ parent "Projective special linear group"
        
        $P S L (2, p)$ | 0, 29, 1 | 🔗 link | nosplit | ↑ parent "Finite projective special linear group"
        
        PSL(2,7) | 29 | 🔗 link | nosplit | ↑ parent " $P S L (2, p)$ "
      - Poincaré group | 192, 2k, 16 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Galilean transformation | 0, 610, 5 | 🔗 link | nosplit | ↑ parent "Poincaré group"
        
        Translation (geometry) | 13, 238, 2 | 🔗 link | nosplit | ↑ parent "Galilean transformation"
        
        Translation group | 19, 225, 1 | 🔗 link | nosplit | ↑ parent "Translation"
        
        The derivative is the generator of the translation group | 206 | 🔗 link | nosplit | ↑ parent "Translation group"
        
        Galilean invariance | 285, 372, 1 | 🔗 link | nosplit | ↑ parent "Galilean transformation"
        
        Covariance | 87 | 🔗 link | nosplit | ↑ parent "Galilean invariance"
        
        Lorentz group ( $S O (1, 3)$ ) | 189, 794, 9 | 🔗 link | nosplit | ↑ parent "Poincaré group"
        
        Representation theory of the Lorentz group | 80, 137, 3 | 🔗 link | nosplit | ↑ parent "Lorentz group"
        
        Representation of the Lorentz group | 26, 57, 2 | 🔗 link | nosplit | ↑ parent "Representation theory of the Lorentz group"
        
        Lie algebra of the Lorentz group | 🔗 link | nosplit | ↑ parent "Representation of the Lorentz group"
        
        Spinor | 31 | 🔗 link | nosplit | ↑ parent "Representation of the Lorentz group"
        
        Lorentz boost | 47 | 🔗 link | nosplit | ↑ parent "Lorentz group"
        
        Indefinite orthogonal group ( $O (m, n)$ ) | 38, 421, 3 | 🔗 link | nosplit | ↑ parent "Lorentz group"
        
        Definition of the indefinite orthogonal group | 204, 383, 1 | 🔗 link | nosplit | ↑ parent "Indefinite orthogonal group"
        
        All indefinite orthogonal groups of matrices of equal metric signature are isomorphic | 179 | 🔗 link | nosplit | ↑ parent "Definition of the indefinite orthogonal group"
        
        Indefinite special orthogonal group ( $S O (m, n)$ ) | 🔗 link | nosplit | ↑ parent "Indefinite orthogonal group"
    - Representation theory | 304, 304, 3 | 🔗 link | nosplit | ↑ parent "Lie group"
      - Irreducible representation | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Representation theory"
        
        Casimir element | 🔗 link | nosplit | ↑ parent "Irreducible representation"
      - Schur's lemma | 🔗 link | nosplit | ↑ parent "Representation theory"
    - Simple Lie group | 0, 46, 1 | 🔗 link | nosplit | ↑ parent "Lie group"
      - Classification of simple Lie groups | 46 | 🔗 link | nosplit | ↑ parent "Simple Lie group"
    - Lie group bibliography | 32, 244, 4 | 🔗 link | nosplit | ↑ parent "Lie group"

Ancestors

Mathematics | 17, 34k, 763
Ciro Santilli's Homepage | 262, 237k, 4k

Incoming links

Positive definite matrix | 39