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Geometry

| 🗖 nosplit | ↑ parent "Mathematics" | words: 0 | descendant words: 2k | descendants: 34

🗖 nosplit | ⇓ toc | ↑ parent "Mathematics" | Wikipedia | words: 0 | descendant words: 2k | descendants: 34

Table of contents | 0, 2k, 34
- 1. Sphere | 0, 11, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Geometry"
  - 1.1. 3-sphere ( $S^{3}$ ) | 11 | 🔗 link | 🗖 nosplit | ↑ parent "Sphere"
- 2. Four-dimensional space (4D) | 10, 38, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Geometry"
  - 2.1. Visualizing 4D | 28 | 🔗 link | 🗖 nosplit | ↑ parent "Four-dimensional space"
- 3. Polytope | 0, 273, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Geometry"
  - 3.1. Regular polytope | 5, 273, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Polytope"
    - 3.1.1. Platonic solid | 40 | 🔗 link | 🗖 nosplit | ↑ parent "Regular polytope"
    - 3.1.2. Classification of regular polytopes | 228 | 🔗 link | 🗖 nosplit | ↑ parent "Regular polytope"
- 4. Differential geometry | 12, 2k, 25 | 🔗 link | 🗖 nosplit | ↑ parent "Geometry"
  - 4.1. Lie group | 233, 2k, 24 | 🔗 link | 🗖 nosplit | ↑ parent "Differential geometry"
    - 4.1.1. Applications of Lie groups to differential equations | 29, 133, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
      - 4.1.1.1. How to use Lie Groups to solve differential equations | 104 | 🔗 link | 🗖 nosplit | ↑ parent "Applications of Lie groups to differential equations"
    - 4.1.2. Lie algebra | 25, 102, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
      - 4.1.2.1. Exponential map (Lie theory) | 70 | 🔗 link | 🗖 nosplit | ↑ parent "Lie algebra"
      - 4.1.2.2. Generator of a Lie algebra | 7 | 🔗 link | 🗖 nosplit | ↑ parent "Lie algebra"
    - 4.1.3. Continuous symmetry | 18, 318, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
      - 4.1.3.1. Local symmetry | 162, 300, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Continuous symmetry"
        
        4.1.3.1.1. Local symmetries of the Lagrangian imply conserved currents | 138 | 🔗 link | 🗖 nosplit | ↑ parent "Local symmetry"
    - 4.1.4. Important Lie groups | 0, 978, 14 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
      - 4.1.4.1. General linear group ( $G L (n)$ ) | 44 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
      - 4.1.4.2. Special linear group ( $S L (n)$ ) | 18 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
      - 4.1.4.3. Orthogonal group ( $O (n)$ ) | 159, 181, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
        
        4.1.4.3.1. Special orthogonal group ( $S O (n)$ ) | 22 | 🔗 link | 🗖 nosplit | ↑ parent "Orthogonal group"
      - 4.1.4.4. Unitary group ( $U (n)$ ) | 82, 155, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
        
        4.1.4.4.1. Unitary group of dimension 2 ( $U (2)$ ) | 5 | 🔗 link | 🗖 nosplit | ↑ parent "Unitary group"
        
        4.1.4.4.2. Unit circle | 19 | 🔗 link | 🗖 nosplit | ↑ parent "Unitary group"
        
        4.1.4.4.3. Special unitary group ( $S U (n)$ ) | 49 | 🔗 link | 🗖 nosplit | ↑ parent "Unitary group"
      - 4.1.4.5. Poincare group | 192, 580, 5 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
        
        4.1.4.5.1. Galilean transformation | 0, 285, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Poincare group"
        
        4.1.4.5.1.1. Galilean invariance | 285 | 🔗 link | 🗖 nosplit | ↑ parent "Galilean transformation"
        
        4.1.4.5.2. Lorentz group ( $S O (1, 3)$ ) | 61, 103, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Poincare group"
        
        4.1.4.5.2.1. Lorentz boost | 24 | 🔗 link | 🗖 nosplit | ↑ parent "Lorentz group"
        
        4.1.4.5.2.2. Indefinite orthogonal group ( $S O (m, n)$ ) | 18 | 🔗 link | 🗖 nosplit | ↑ parent "Lorentz group"
    - 4.1.5. Representation theory | 65 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"

Ancestors

Mathematics | 17, 13k, 336
Ciro Santilli's Homepage | 262, 182k, 3k