等径球在空间中的最佳堆放法

The Optimization Method of Heaping up Equal Radius Spheres

具体计算J.Kepler的4种堆放法的几何模型的孔隙率,找出了孔隙率与角度的函数关系,对计算孔隙率的精确公式,按带下标函数处理,严格证明了两种1个球切12个球的堆放法是最佳堆放法,和有无限多种与最佳堆放法孔隙率相同的1个球切10个球的堆放法。

The gap rates of Kepler, J's models with four types of heaping up methods were caculated. The functional relation between gap rates and angles was formulatued. A accurate gap rate was formulated based on subscript functions, and two types of 1 externally tangent sphere with 12 spheres were proven to be optimum heaping uo methods. However, there are uncountably infinite optimum mehtods having the same gap rate. They are all types of 1 tangent sphere with 10 spheres.