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Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane |
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| Authors: | V Arnold |
| Institution: | Ceremade, Université Paris Dauphine, Paris, France, V. A. Steklov Institute of Mathematics, Moscow, Russia |
| Abstract: | An isomorphism between the Lobachevsky and de Sitter’s world geometries with the symplectic geometry and the Lie algebra of binary quadratic forms is used to derive the altitudes concurrence for the Lobachevsky and de Sitter triangles. |
| Keywords: | Projective geometry de Sitter world Symplectic algebra Klein model |
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