Pick's Theorem in Two-Dimensional Subspace of R3. (23rd February 2015) - Si, Lin
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 .