Vergleichende Betrachtungen über neuere geometrische Forschungen" (Erlangen Program)¶
Klein, F. (1893). Vergleichende Betrachtungen über neuere geometrische Forschungen" (Erlangen Program). Bulletin of the American Mathematical Society, 1888-1893.
Cited by¶
4 citations across 4 artifacts.
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Primes¶
- Associativity
- Invariance
- … spaces and structures: Euler's 1752 formula V − E + F = 2 established the first topological invariant (the Euler characteristic); Poincaré's 1895 Analysis Situs launched algebraic topology by defining homology and homotopy invariants that distinguish spaces up to continuous deformation; Klein's 1872 Erlangen program
This sourceReformulated geometry as the study of properties invariant under a specified transformation group (Erlangen program). Historical reception: Hawkins, Emergence of the Theory of Lie Groups (Springer, 2000), ch. 3..
- … spaces and structures: Euler's 1752 formula V − E + F = 2 established the first topological invariant (the Euler characteristic); Poincaré's 1895 Analysis Situs launched algebraic topology by defining homology and homotopy invariants that distinguish spaces up to continuous deformation; Klein's 1872 Erlangen program
- Noether's Theorem
- Noether's 1918 work synthesized three mathematical traditions: (1) Lagrange's generalized coordinates and cyclic-variable invariance (1788), showing how symmetries encode into equations of motion; (2) Klein's Erlangen program (1872)
This sourceReformulated geometry as the study of properties invariant under a specified transformation group (Erlangen program). Historical reception: Hawkins, Emergence of the Theory of Lie Groups (Springer, 2000), ch. 3..
- Noether's 1918 work synthesized three mathematical traditions: (1) Lagrange's generalized coordinates and cyclic-variable invariance (1788), showing how symmetries encode into equations of motion; (2) Klein's Erlangen program (1872)
- Symmetry
- … closes as a group, it inherits the full algebraic apparatus of group theory (subgroups, cosets, orbits, quotients, representations), and this apparatus is what generates the characteristic dividends of symmetry reasoning — conservation laws via Noether's theorem, geometric classification via Klein's Erlangen program
This sourceReformulated geometry as the study of properties invariant under a specified transformation group (Erlangen program). Historical reception: Hawkins, Emergence of the Theory of Lie Groups (Springer, 2000), ch. 3..
- … closes as a group, it inherits the full algebraic apparatus of group theory (subgroups, cosets, orbits, quotients, representations), and this apparatus is what generates the characteristic dividends of symmetry reasoning — conservation laws via Noether's theorem, geometric classification via Klein's Erlangen program
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