毕达哥拉斯三角形的17个元素
The Seventeen Elements of Pythagorean Triangles
摘要：
这是毕达哥拉斯三角形的17个元素的详尽研究，从这样的元素何时是无理数，有理数或整数的角度来看。对于这17个元素中的每一个，给出了它们的完整性、合理性或非合理性的精确条件。这17个元素是：内切圆的半径，外接圆的半径，与三角形的三条边相切的三个外圆的三个半径，三个高度的长度，三个内角平分线的长度，三个外角平分线的长度，以及三个中线的长度。
英文摘要：
This is an exhaustive study of the seventeen elements of Pythagorean triangles, from the point of view of when such an element is an irrational number, a rational number, or an integer. For each of these 17 elements,precice conditions for their integrality,rationality, or irrationality; are given. These 17 elements are:The radius of the incircle, the radius of the circumscribed circle,the three radii of the three exterior circles tangential to the three lines containing the triangles'sides, the lengths of the three heights, the lenghts of the three internal angle bisectors, the lengthe of the three external angle bisectors, and the lengths of the three medians.
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。
