利用gnomons构造本原勾股三元组和具有公共乘子的勾股三元组
Construction of primitive Pythagorean triples and Pythagorean triples with a common multiplier using gnomons
摘要：
传统的用两个自变量的公式构造原始毕达哥拉斯三元组的方法不允许它们的排序。本文对本原毕达哥拉斯三元组的构造提出了新的看法。本文提出了一种用两个因变量构造本原毕达哥拉斯三元组的方法。这使得能够构建原始毕达哥拉斯三元组的有序表。使用有序数据，有可能以一种新的方式解决包含毕达哥拉斯三元组系统的问题，例如欧拉平行六面体的构造，完美长方体的构造，或者用两种颜色着色自然数的问题，这样就没有毕达哥拉斯三元组是单色的（拉姆齐理论的问题之一）。
英文摘要：
The traditional construction of primitive Pythagorean triples by the formulas of two independent variables does not allow their ordering. The paper shows a new view on the construction of primitive Pythagorean triples. A method for constructing primitive Pythagorean triples, based on the use of gnomons equal in area to the squares of the legs from a primitive Pythagorean triple, using two dependent variables, is proposed. This enables the ability to build an ordered table of primitive Pythagorean triples. Working with ordered data, it is possible to approach in a new way the solution of problems that include systems of Pythagorean triples, such as the construction of Eulerian parallelepipeds, the construction of a Perfect Cuboid, or the problem of coloring natural numbers in two colors so that no Pythagorean triple is monochrome (one of the problems of Ramsey theory).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
