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1引言课上老师带领我们讨论了在二维空间中,当正方形的相邻两点都是有理点时,其余两点一定也都是有理点.课后老师布置了作业让我们研究在三维空间中,如果一个正方体的一个底面四个顶点都是有理点,相对底面的四个顶点是否都是有理点.结果发现答案是不一定:相对底面的四个顶点都是有理点等价于棱长是有理数.二维空间中正方形顶点的有理性与三维空间中正方体顶点的有理性有显著差异.这使我有兴
1 Introduction The teacher in class leads us to discuss that in the two-dimensional space, when two adjacent points of the square are rational points, the other two points must all be rational points. After class, the teacher arranges the homework so that we can study in three-dimensional space If all four vertices of a bottom surface of a cube are rational points, whether the four vertexes of the bottom surface are rational points or not is not obvious: the four vertices of the bottom surface are both rational points equivalent to the edge length Is a rational number.The rationality of the square vertices in two-dimensional space is significantly different from the rationalness of the cube vertices in the three-dimensional space.