Arnold's Projective Plane and 𝑟-Matrices
We will explain Arnold's 2-dimensional (shortly, 2D) projective geometry (Arnold, 2005) by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular 𝑟-matrices is the pencil of tangent lines of a quadratic curve on Arnold's projective plane.
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2010/956128 |
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| _version_ | 1850175482524336128 |
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| author | K. Uchino |
| author_facet | K. Uchino |
| author_sort | K. Uchino |
| collection | DOAJ |
| description | We will explain Arnold's 2-dimensional (shortly, 2D) projective geometry (Arnold, 2005) by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular 𝑟-matrices is the pencil of tangent lines of a quadratic curve on Arnold's projective plane. |
| format | Article |
| id | doaj-art-ce40f70a72394760af48309c862d09e7 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ce40f70a72394760af48309c862d09e72025-08-20T02:19:27ZengWileyAdvances in Mathematical Physics1687-91201687-91392010-01-01201010.1155/2010/956128956128Arnold's Projective Plane and 𝑟-MatricesK. Uchino0Tokyo University of Science, Wakamiya, 26 Shinjyuku, Tokyo, JapanWe will explain Arnold's 2-dimensional (shortly, 2D) projective geometry (Arnold, 2005) by means of lattice theory. It will be shown that the projection of the set of nontrivial triangular 𝑟-matrices is the pencil of tangent lines of a quadratic curve on Arnold's projective plane.http://dx.doi.org/10.1155/2010/956128 |
| spellingShingle | K. Uchino Arnold's Projective Plane and 𝑟-Matrices Advances in Mathematical Physics |
| title | Arnold's Projective Plane and 𝑟-Matrices |
| title_full | Arnold's Projective Plane and 𝑟-Matrices |
| title_fullStr | Arnold's Projective Plane and 𝑟-Matrices |
| title_full_unstemmed | Arnold's Projective Plane and 𝑟-Matrices |
| title_short | Arnold's Projective Plane and 𝑟-Matrices |
| title_sort | arnold s projective plane and 𝑟 matrices |
| url | http://dx.doi.org/10.1155/2010/956128 |
| work_keys_str_mv | AT kuchino arnoldsprojectiveplaneandrmatrices |