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所谓整数几何,是指几何图形中的某些基本量(边长、周长、角度、面积等)为整数的几何问题.把古老的平面几何与整数的有关知识综合起来命题,是近年来初中数学竞赛试题中的一种常见题型.本文举例说明四类整数几何问题的解法,供读者参考. 一、计数问题 几何计数是整数几何问题中的主要题型,解这类问题常用的方法有穷举法、不等式法、构造法、格点法等.
The so-called integer geometry refers to the geometric problem that some basic quantities (side length, perimeter, angle, area, etc.) in geometric figures are integers. The integration of ancient planar geometry and related knowledge of integers is the proposition in recent years. A common question in mathematics contest questions. This article illustrates the solution of four types of integer geometry problems for readers’ reference. I. Counting problems Geometric counting is the main problem in integer geometry problems. Common methods for solving such problems are Exhaustion method, inequality method, construction method, lattice method, etc.