Module Menu

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

Hyperbolic Surface

Illustration of curved spaces by means of two-dimensional models

A hyperbolically curved surface can be conceived of as a two-dimensional model of three-dimensional hyperbolic spaces. In hyperbolic spaces the sum of the angles in a triangle is less than 180 degrees. The circumference of a growing circle increases more quickly than its radius.

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