勾股定理离散性质的推广和应用—Pythagorean方程和特殊的M角数

An Extension of Pythagorean Equation with Its Application—Pythagorean Equation and Special M-Gonal Numbers

摘要: 采用Pythagorean方程的解决方法,我们得到了一对M角数之差仍然为M角数的连接形式。使用给出的这些明显可计算的普通表达式，我们在两种数组之间建立了一种非凡的连接。从而使得两种数组的平面射影可以成为“局部”拓扑，并且在Desarguesian型拓扑实数射影平面上，自然而然的可以共享许多拓扑椭圆的性质。

Abstract: Based on the solution of Pythagorean Equation, we obtain a relationship that the difference be-tween two M-Gonal numbers is still an M-Gonal number. With this explicit computable expression, we establish a remarkable connection between two pairs of numbers. The projected planes of two pairs of numbers generate partial topological structure. In real Desarguesian projective plane, this structure shares many existing properties of topological ellipsoid naturally.