Let K be an algebraic number field. We investigate the K-rational distance problem and prove that there are infinitely many nonisomorphic cubic number fields and a number field of degree n for every $n\geq 2$ in which there is a point in the plane of a unit square at K-rational distances from the four vertices of the square.

中文翻译：

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K-有理距离问题的注释

让ķ是一个代数数域。我们调查ķ- 有理距离问题并证明有无穷多个非同构三次数域和一个度数域n对于每个 $n\geq 2$ 其中单位正方形的平面上有一点在ķ- 到正方形四个顶点的有理距离。