Non-Euclidean geometry
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A non-Euclidean geometry is characterized by a non-vanishing Riemann curvature tensor it is the study of shapes and constructions that do not map directly to any n-dimensional Euclidean system. Examples of non-Euclidean geometries include the hyperbolic and elliptic geometry, which are contrasted with a Euclidean geometry. The essential difference between Euclidean and non-Euclidean geometry is the nature of parallel lines. Euclid's fifth postulate, the parallel postulate, is equivalent to Playfair's postulate, which states that, within a two-dimensional plane, for any given line and a point A, which is not on , there is exactly one line through A that does not intersect . In hyperbolic geometry, by contrast, there are infinitely many lines through A not intersecting , while in elliptic geometry, any line through A intersects (see the entries on hyperbolic geometry, elliptic geometry, and absolute geometry for more information).
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786130261757
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- Sprache Englisch
- Genre Mathematik
- Größe H220mm x B150mm x T5mm
- Jahr 2009
- EAN 9786130261757
- Format Fachbuch
- ISBN 978-613-0-26175-7
- Titel Non-Euclidean geometry
- Untertitel Euclidean geometry, Three-dimensional space, Higher dimension, Curved space, Non-Euclidean geometry, Albert Einstein, General relativity, History of geometry, Axiom
- Gewicht 149g
- Herausgeber Alphascript Publishing
- Anzahl Seiten 88
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