arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 0904.0826math.HOmath.NT
收藏

关于三角函数有理值的一种新方法

A New Approach to Rational Values of Trigonometric Functions

Gregory P. Dresden

摘要:

众所周知,sin(aπ/b),cos(aπ/b)等,只对少数几个选定的整数a和b是有理数。我们证明了这等价于这样一个事实:只有d = 1,2,3,4和6是Q上2次单位的本原d次单位根.

英文摘要:

It is well known that sin(aπ/b), cos(aπ/b), etc., are only rational numbers for a few select integers a and b. We show that this is equivalent to the fact that only for d = 1,2,3,4, and 6 is the primitive dth root of unity of degree 2 over Q.

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。

↑