论文标题
一种新的完整算法，用于不可约二芬太汀毕达哥拉斯三角形（IDPTS）
A new complete algorithm for Irreducible Diophantine Pythagorean Triangles (IDPTs)
论文作者
论文摘要
众所周知，侧面长度为3、4和5的三角形是直角的。欧几里得是第一个提供一个用于生成其他具有整数侧长度的右角三角形的公式。 在本文中，我提出了一种新颖的算法，以生成具有整数侧长的所有可能的直角三角形，其中三个侧长没有共同的除数。该算法基于假设和其他两个方面最大的长度差异。我还证明了这种算法的完整性：它产生了所有可能的三角形，只有这样的三角形。
It is well known that a triangle with side lengths 3, 4 and 5 is right-angled. Euclid was the first to give a formula for generating other right-angled triangles with integer side lengths. In this text, I present a novel algorithm to generate all possible right-angled triangles with integer side lengths, in which the three side lengths have no common divisor. The algorithm is based on the difference in length between the hypothenuse and the largest of the two other sides. I also prove the completeness of this algorithm: it generates all possible such triangles and nothing but such triangles.
