一类四边形的有理距点问题

On Rational Distance Point Problem for Quadrilaterals

摘要:

过指出参考文献中的错误, 说明Steinhaus整距点问题至今仍然是没有解决的公开问题. 利用数域的扩张和Galois群的一些结论, 研究边长的平方为有理数, 且一组对角之和为\frac{2k\pi}{n}的四边形, 其中k

Abstract:

In the present paper, by pointing out some errors in reference [17], we know that the well-known integer distance point problem of Steinhaus is still open. Using the result of Galois extension, we discuss the Steinhaus problem for some quadrilaterals. In fact, we show that for the case of quadrilaterals which the sum of a pair of corner is \frac{2k\pi}{n}, where n\geq 7, k