论文标题
表现出平均横截面固定值的区域
Regions exhibiting stationary values of average cross section
论文作者
论文摘要
引入了最大化平均横截面通过形状内的点的问题。这个想法扩展到任意维度。但是，除非横截面穿过形状的质心，否则平均横截面体积无法最大化。因此，我们专注于平均横截面的固定值的形状。提出了一个平均横截面的新型公式。固定形状的方程是得出的，并通过代数解，数值分析和图形显示来讨论一般特征。检查了2、3和5维的固定形状的特殊特性。
The problem of maximizing the average cross section through a point within a shape is introduced. This idea is extended into arbitrary dimensions. However, the average cross sectional volume cannot be maximized unless the cross sections pass through the centroid of the shape. Therefore, we focus on the shapes with stationary values of average cross section. A novel formula for average cross section in any dimension is presented. The equation of the stationary shape is derived and the general characteristics are discussed through algebraic solution, numerical analysis, and interpretation with graphical display. The special properties of the stationary shapes in 2, 3, and 5 dimension is examined.
