title: Pick's Theorem in two-dimensional subspace of ℝ3.
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.
authors: College of Science, Beijing Forestry University, Beijing 100083, China.
authors: Lin
authors: 0000-0003-0003-0763
authors: L
authors: Si