Steinmetz solid

牟合方盖是由中国古代数学家刘徽首先发现并采用的一种用于计算球体体积的方法，牟合方盖的体积跟内接球体体积的比为。采用的模型像一个牟合的方形盒子，故称为牟合方盖。The steinmetz solid is a method for calculating the volume of a sphere first discovered and adopted by the ancient Chinese mathematician Liu Hui. The ratio of the volume of the steinmetz solid to the volume of the inner sphere is . And the model used is like a muhe square box, it is called Steinmetz solid.如果将两个半径相等，相互垂直的圆柱体重叠，那么相交部分就是牟合方盖。由于这种特殊的构造方式，做出牟合方盖的横截面，那么在横截面上牟合方盖的被截取部分为正方形，并且正方形始终与其内切球被截取的圆相切。其面积比为。由于每个横截面的面积之比均为，那么根据祖暅原理（或称卡瓦列利原理），最终就有体积比为。If two cylinders of equal radius and perpendicular to each other are overlapped, then the intersecting part is a steinmetz solid. Because of this special construction, the cross section of the mulch square cover is made, so that the intercepted part of the mulch square cover is square in the cross section, and the square is always tangent to the circle with which the inner cutting ball is int