Volume of a simplex as a multivalued algebraic function of the areas of its two-faces
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arXiv
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| Format: | Preprint |
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2013
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| _version_ | 1866913580373245952 |
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| author | Gaifullin, Alexander A. |
| author_facet | Gaifullin, Alexander A. |
| contents | For n greater than or equal to 4, the square of the volume of an n-simplex satisfies a polynomial relation with coefficients depending on the squares of the areas of 2-faces of this simplex. First, we compute the minimal degree of such polynomial relation. Second, we prove that the volume an n-simplex satisfies a monic polynomial relation with coefficients depending on the areas of 2-faces of this simplex if and only if n is even and at least 6, and we study the leading coefficients of polynomial relations satisfied by the volume for other n. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1310_3417 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Volume of a simplex as a multivalued algebraic function of the areas of its two-faces Gaifullin, Alexander A. Metric Geometry Combinatorics Primary: 51M25, Secondary: 13A18 For n greater than or equal to 4, the square of the volume of an n-simplex satisfies a polynomial relation with coefficients depending on the squares of the areas of 2-faces of this simplex. First, we compute the minimal degree of such polynomial relation. Second, we prove that the volume an n-simplex satisfies a monic polynomial relation with coefficients depending on the areas of 2-faces of this simplex if and only if n is even and at least 6, and we study the leading coefficients of polynomial relations satisfied by the volume for other n. |
| title | Volume of a simplex as a multivalued algebraic function of the areas of its two-faces |
| topic | Metric Geometry Combinatorics Primary: 51M25, Secondary: 13A18 |
| url | https://arxiv.org/abs/1310.3417 |