Klein-Arnold tensegrities
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913548969443328 |
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| author | Karpenkov, Oleg Mohammadi, Fatemeh Müller, Christian Schulze, Bernd |
| author_facet | Karpenkov, Oleg Mohammadi, Fatemeh Müller, Christian Schulze, Bernd |
| contents | In this paper, we introduce new classes of infinite and combinatorially periodic tensegrities, derived from algebraic multidimensional continued fractions in the sense of F. Klein. We describe the stress coefficients on edges through integer invariants of these continued fractions, as initiated by V.I. Arnold, thereby creating a novel connection between geometric rigidity theory and the geometry of continued fractions. Remarkably, the new classes of tensegrities possess rational self-stress coefficients. To establish the self-stressability of the frameworks, we present a projective version of the classical Maxwell-Cremona lifting principle, a result of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12729 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Klein-Arnold tensegrities Karpenkov, Oleg Mohammadi, Fatemeh Müller, Christian Schulze, Bernd Combinatorics Metric Geometry In this paper, we introduce new classes of infinite and combinatorially periodic tensegrities, derived from algebraic multidimensional continued fractions in the sense of F. Klein. We describe the stress coefficients on edges through integer invariants of these continued fractions, as initiated by V.I. Arnold, thereby creating a novel connection between geometric rigidity theory and the geometry of continued fractions. Remarkably, the new classes of tensegrities possess rational self-stress coefficients. To establish the self-stressability of the frameworks, we present a projective version of the classical Maxwell-Cremona lifting principle, a result of independent interest. |
| title | Klein-Arnold tensegrities |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2410.12729 |