An investigation of the plane in absolute geometry (Q1380277)
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scientific article; zbMATH DE number 1122772
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An investigation of the plane in absolute geometry |
scientific article; zbMATH DE number 1122772 |
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An investigation of the plane in absolute geometry (English)
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4 March 1999
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The author defines: An absolute geometry is a geometry that satisfies the axioms of the Euclidean geometry without possibly the axiom of parallels. He considers the two-dimensional case and proves that every absolute plane is a two-dimensional Riemann manifold of a constant nonpositive Gaussian curvature \(K\). If \(K=0\) then the plane is Euclidean, and if \(K<0\) then it is the Lobachevskij plane.
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absolute plane
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