发表机构
Tel-Aviv University; University of Toronto（特拉维夫大学; 多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对边位于格点间中点的单模多边形，提出了类似 Pick 定理的面积公式，用内部格点数和顶点数表示面积。
AI 中文摘要
给定平面上顶点位于格点上的多边形，Pick 定理用其内部格点数 I 和边界格点数 B 表示其面积 A：A = I + B/2 - 1。我们考虑平面上边位于格点之间中点的多边形。对于这样的单模多边形，我们用其内部格点数 I 和顶点数 V 表示其面积 A：A = I - V/8 + 1/2。
英文摘要
Given a polygon in the plane with vertices on lattice points, Pick's theorem expresses its area A in terms of the number I of lattice points in its interior and the number B of lattice points in its boundary: A = I + B/2 - 1. We consider polygons in the plane whose edges are halfway between lattice points. For such a polygon that is also unimodular, we express its area A in terms of the number I of lattice points in its interior and the number V of its vertices: A = I - V/8 + 1/2 .
Comments15 pages, 17 figures
