Pick’s Theorem in Two-Dimensional Subspace of R3
In the Euclidean space R3, denote the set of all points with integer coordinate by Z3. For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick’s Theorem, kIP+1/2BP-1, where BP is the number of lattice points on the boundary of P in Z3, IP is the number of...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/535469 |
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| author | Lin Si |
| author_facet | Lin Si |
| author_sort | Lin Si |
| collection | DOAJ |
| description | In the Euclidean space R3, denote the set of all points with integer coordinate by Z3. For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick’s Theorem, kIP+1/2BP-1, where BP is the number of lattice points on the boundary of P in Z3, IP is the number of lattice points in the interior of P in Z3, and k is a constant only related to the two-dimensional subspace including P. |
| format | Article |
| id | doaj-art-3ad99e6c20cf46848993124a3a288f75 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-3ad99e6c20cf46848993124a3a288f752025-02-03T05:44:47ZengWileyThe Scientific World Journal2356-61401537-744X2015-01-01201510.1155/2015/535469535469Pick’s Theorem in Two-Dimensional Subspace of R3Lin Si0College of Science, Beijing Forestry University, Beijing 100083, ChinaIn the Euclidean space R3, denote the set of all points with integer coordinate by Z3. For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick’s Theorem, kIP+1/2BP-1, where BP is the number of lattice points on the boundary of P in Z3, IP is the number of lattice points in the interior of P in Z3, and k is a constant only related to the two-dimensional subspace including P.http://dx.doi.org/10.1155/2015/535469 |
| spellingShingle | Lin Si Pick’s Theorem in Two-Dimensional Subspace of R3 The Scientific World Journal |
| title | Pick’s Theorem in Two-Dimensional Subspace of R3 |
| title_full | Pick’s Theorem in Two-Dimensional Subspace of R3 |
| title_fullStr | Pick’s Theorem in Two-Dimensional Subspace of R3 |
| title_full_unstemmed | Pick’s Theorem in Two-Dimensional Subspace of R3 |
| title_short | Pick’s Theorem in Two-Dimensional Subspace of R3 |
| title_sort | pick s theorem in two dimensional subspace of r3 |
| url | http://dx.doi.org/10.1155/2015/535469 |
| work_keys_str_mv | AT linsi pickstheoremintwodimensionalsubspaceofr3 |