Module: Modelle des Kosmos: Der gekruemmte Raum
Sequence: 0.0. START
Branching Point: Curved Spaces
Sequence: 0.1 Themenuebersicht
Branching Point: Curved Spaces (Overview of Topics)
Sequence: 1.0. 13400_Objektfolge_Only
Slide: Euclidean Surface
Slide: Elliptic Surface
Slide: Hyperbolic Surface
Slide: Curvature of the Universe
Slide: Einstein Manuscript Page
Slide: Geometry and Experience
Sequence: 1.1. Objekt 13400_1834_1: Euklidische Flaeche
Slide: Euclidean Surface
Sequence: 1.2. Objekt 13400_1834_2: Elliptische Flaeche
Slide: Elliptic Surface
Sequence: 1.3. Objekt 13400_1834_3: Hyperbolische Flaeche
Slide: Hyperbolic Surface
Sequence: 1.4. Objekt 13400_3220: Schwarzschild_Artikel_1900
Slide: Curvature of the Universe
Sequence: 1.5. Objekt 13400_1752: Einstein Manuskriptseite
Slide: Einstein Manuscript Page
Sequence: 1.6. Objekt 13400_1727: Geometrie und Erfahrung
Slide: Geometry and Experience
Sequence: 2.0. Animated explanation
Slide: The Appearence of Background Radiation Depends on the Curvature of Space
Sequence: 3.0. Biographie: Carl Friedrich Gauss
Slide: Carl Friedrich Gauss (1777–1855)
Sequence: 4.0. Biographie: Bernhard Riemann
Slide: Bernhard Riemann (1826–1866)
Sequence: 5.0. Biographie: Karl Schwarzschild
Slide: Karl Schwarzschild (1873–1916)
Slide: Curved Universes Before Einstein: Schwarzschild's Cosmological Speculations
Slide: Euclidean Surface
Slide: Elliptic Surface
Slide: Hyperbolic Surface
Slide: Curvature of the Universe
Sequence: 3.0. Biographie: Carl Friedrich Gauss
Slide: Carl Friedrich Gauss (1777–1855)
Sequence: 1.0. 13400_Objektfolge_Only
Slide: Euclidean Surface
Slide: Elliptic Surface
Slide: Hyperbolic Surface
Slide: Curvature of the Universe
Slide: Einstein Manuscript Page
Slide: Geometry and Experience
Sequence: 4.0. Biographie: Bernhard Riemann
Slide: Bernhard Riemann (1826–1866)
Sequence: 2.0. Animated explanation
Slide: The Appearence of Background Radiation Depends on the Curvature of Space
Sequence: 5.0. Biographie: Karl Schwarzschild
Slide: Karl Schwarzschild (1873–1916)
Slide: Curved Universes Before Einstein: Schwarzschild's Cosmological Speculations
Slide: Euclidean Surface
Slide: Elliptic Surface
Slide: Hyperbolic Surface
Slide: Curvature of the Universe
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Curved Spaces
For a long time, Euclidean geometry with its proofs was regarded as an unquestionable example of absolute knowledge. Doubts about its universal validity first emerge in the nineteenth century with Gauss’ theory of curved surfaces and the spectacular construction of non-Euclidean geometries.
In 1900, the astronomer Karl Schwarzschild publishes a study on the degree to which space can be curved without astronomers noticing its effects. When Einstein presents his General Theory of Relativity in 1915, Schwarzschild is virtually the only astronomer who recognizes the importance of the theory for astronomy and collaborates on elaborating and verifying it.
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