Steiner平面分割空间问题的推广

Generalization of the Problem of the Steiner Plane Partition Space

Steiner平面分割空间问题是一个古老、诱人的问题.本文引入了D变换,对Steiner直线分割平面问题进行了推广,获得了文中的三个预备定理.在此基础上,对Steiner平面分割空间问题进行了更深入的讨论,获得了三个定理.Steiner平面分割空间问题的结果是这三个定理的特例。文中的定理1、定理2也都可作为定理的极端情形.

The problem of the Steiner plane partition space is both old and attractive. In this paper, D transformation is introduced and the problem of the Steiner straight partition plane is generalized and three preparation theorems are derived. On basis of it, the problem of the Steiner plane partition space is deeply discussed and thus three theorems are derived. So the special case of the three theorems is the result of the problem of the Steiner plane partition space. Theorems I and II also may be regarded as the special case of theorem III.