E^(n)空间中几个几何体体积间的关系

Relationship between the volume of some geometries in E^(n) space

探索了n维欧式空间中,当空间维数n为奇数和偶数时两个球体体积公式之间的相互转化.并利用这两个公式研究了n维空间中同底等高的圆锥、半球和圆柱体的体积之比,进而通过引入体积函数的概念,利用它的齐次性性质证明了n维欧式空间中同底等高的锥体和柱体体积之比为1:n.

Researched the two volume formulas of sphere in Enspace when n is odd and even.The two formulas can be transformed into each other by means of integral.The ratio of the volume of the cone,hemisphere and cylinder was obtained by using the two formulas.Finally by introducing the concept of volume function and using its homogeneous property,the proposition was proved that the volume ratio of cone and column which are of same bottom and equal height inn ？ dimensional space is1： n.