m×n矩形的格点平行四边形和正方形的计数

Counting Lattice Point Parallelograms and Lattice Point Squares from m×n Rectangles

通过引入具有性质 E的平行四边形和正方形的概念 ,求出 m× n矩形的内含 i× j矩形 .它具有性质 E的平行四边形 (简称 E平行四边形 )个数 ,又具有性质 E的正方形 (简称 E正方形 )个数 .进而 ,求出 m×

By leading the concept of parallelogrem with property E and the concept of square with property E ,the authors find out the number of parallelograms with property E (parallelogram E for short) and the number of square with property E (square E for short)from inclusive i×j rectangles in m×n rectangles;and then,find out the number of lattice point parallelograms and the number of lattice point squares from m×n rectangles.