Pick's Theorem in two-dimensional subspace of ℝ3. Si L - ScientificWorldJournal (2015) Bottom Line: In the Euclidean space ℝ(3), denote the set of all points with integer coordinate by ℤ(3).For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick's Theorem, k(I(P) + (1/2)B(P) - 1), where B(P) is the number of lattice points on the boundary of P in ℤ(3), I(P) is the number of lattice points in the interior of P in ℤ(3), and k is a constant only related to the two-dimensional subspace including P. View Article: PubMed Central - PubMed Affiliation: College of Science, Beijing Forestry University, Beijing 100083, China. ABSTRACTIn the Euclidean space ℝ(3), denote the set of all points with integer coordinate by ℤ(3). For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick's Theorem, k(I(P) + (1/2)B(P) - 1), where B(P) is the number of lattice points on the boundary of P in ℤ(3), I(P) is the number of lattice points in the interior of P in ℤ(3), and k is a constant only related to the two-dimensional subspace including P. No MeSH data available. © Copyright Policy - open-access Related In: Results  -  Collection getmorefigures.php?uid=PMC4352900&req=5 .flowplayer { width: px; height: px; } Mentions: For example, in Figure 1, I(P) = 60, B(P) = 15. Then, the area of the polygon is A(P) = 60 + 15 − 1 = 74.

Pick's Theorem in two-dimensional subspace of ℝ3.

Si L - ScientificWorldJournal (2015)

Related In: Results  -  Collection

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Mentions: For example, in Figure 1, I(P) = 60, B(P) = 15. Then, the area of the polygon is A(P) = 60 + 15 − 1 = 74.

Bottom Line: In the Euclidean space ℝ(3), denote the set of all points with integer coordinate by ℤ(3).For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick's Theorem, k(I(P) + (1/2)B(P) - 1), where B(P) is the number of lattice points on the boundary of P in ℤ(3), I(P) is the number of lattice points in the interior of P in ℤ(3), and k is a constant only related to the two-dimensional subspace including P.

View Article: PubMed Central - PubMed

Affiliation: College of Science, Beijing Forestry University, Beijing 100083, China.

ABSTRACT
In the Euclidean space ℝ(3), denote the set of all points with integer coordinate by ℤ(3). For any two-dimensional simple lattice polygon P, we establish the following analogy version of Pick's Theorem, k(I(P) + (1/2)B(P) - 1), where B(P) is the number of lattice points on the boundary of P in ℤ(3), I(P) is the number of lattice points in the interior of P in ℤ(3), and k is a constant only related to the two-dimensional subspace including P.

No MeSH data available.