Limits...
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.

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.


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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.


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

Si L - ScientificWorldJournal (2015)

© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4352900&req=5

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.