3维勾股数的性质及其计算方法

The Properties of Three-dimensional Pythagorean Triple and its Calculation Method

讨论了3维本原勾股数的几条性质,并根据2维勾股数与3维勾股数的关系,提出了用2维本原勾股数构造3维勾股数的方法和计算公式。从三元数的概念出发,推导出计算3维本原勾股数的公式及其计算结果。利用该方法可以类推出4维、5维甚至更高维勾股数。

In this paper,some properties of the 3D primitive pythagorean triangles were discussed,and on the basis of the relation between the two dimension pythagorean triangles and the 3D pythagorean triangles,a method and a design formula of constructing the 3D pythagorean triangles by utilizing two dimension Primitive pythagorean triangles.A design formula of the 3D primitive pythagorean triangles which is according to the three-ary number was inferred and applied as well.This design formulas can be used to infer the design formulas of four-dimensional pythagorean triangles,five-dimensional pythagorean triangles,and even more dimensional pythagorean triangles