The Question of Counting for Intersection Points （交点的计算问题）.pdf

正 N 边形形内对角线 交点的计数问题 The Question of Count for Intersection Points of Inner Diagonal Lines of Regular N Polygon 海南省海南中学：许伦博 指导老师：贺航飞 完成时间：2008 年 8 月 23 日星期六 The Question of Counting for Intersection Points of Inner Diagonal Lines of Regular N Polygon XU Lunbo (Hainan Senior High School, Hainan) Instruction Teacher: HE Hangfei 【Abstract 】 In the early 1980s of twenty century, Professor Zhang Zhongfu, an expert in graph theory, raised a question in his research[1]: how many points of intersection of diagonal lines are there inside a regular N polygon, hoping to find out a formula of count. It has been more than 20 years since the question was raised, which has aroused the interest of quite a lot of experts, scholars and those who love mathematics, but still remains unsolved. When N is an odd number, proposition 1 can be derived from formula of counting based on proposition 2, which can also be verified by the programme the author has made. Proposition 1: when N is an odd number, there is no concurrence of 3 or more than 3 diagonal lines of regular N polygon. Proposition 2: when N is an odd number, the number of intersection points of inner diagonal lines of regular N polygon is: 4 1 a C n − n (− 1n)( − 2)( 3) n n 24 But when N is an even number, it becomes quite complicated. When N are some special even numbers refe