三角形丢番图问题的一个较简单的解法,其中从顶点开始平分对边的直线可以合理地表示
An easier solution of a Diophantine problem about triangles, in which those lines from the vertices which bisect the opposite sides may be expressed rationally
摘要:
这是从莱昂哈德·欧拉的拉丁文原文“Solutio facilior problematis Diophantei circa triangulum,in quo rectae ex angulis latera opposita bisecretariat rationaliter exprimantur”的英文翻译。欧拉证明了存在边长为整数的三角形,使得边长与对顶角的平分线的长度为整数,并给出了构造一类这样的三角形的一般方法。
英文摘要:
This is an English translation from the Latin original of Leonhard Euler's ``Solutio facilior problematis Diophantei circa triangulum, in quo rectae ex angulis latera opposita bisecantes rationaliter exprimantur''. In this paper, Euler proves that there exist triangles with integer length sides such that the length of the bisectors of the sides to the opposite angles are integer valued, and he gives a general method for making a certain class of such triangles.
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。