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古代埃及人和巴比伦人都曾經知道計算侧面与底面夹45°的正四角錐的体积,他們的算法用我們的术語来讲,就是所求体积等于底面积乘以高的三分之一;当时的人們甚至还会計算截割这种角锥而得到的錐台的体积,关于古代人们是怎样得到角锥体积計算公式的問题,我們可以作如下的推測:图1所示的立方体ABCDEFGH可以被分割成三个相同的四角錐EABCD,EBFGC和ECDHG,它們的区面部是正方形;对这三个四角錐来說,它們每一个的体积显然都等于底面积乘以高的三分之一。再者,我們可将四个这样的角錐(EABCD)拼成一个侧面与底面夹45°角的正四
Both the ancient Egyptians and the Babylonians knew the volume of the square pyramid with a 45° angle between the side and the bottom. Their algorithm, in our terminology, was that the volume required was equal to the bottom area multiplied by the height of one third; The people will even calculate the volume of the truncated cone obtained by cutting such pyramids. With regard to how the ancient people got the calculation formula of the pyramid volume, we can make the following estimation: The cube ABCDEFGH shown in Figure 1 can be Divided into three identical quadrangular pyramids EABCD, EBFGC and ECDHG, their area faces are square; for each of the three quadrangular pyramids, the volume of each of them is obviously equal to the bottom area multiplied by the height one third. Furthermore, we can combine four such pyramids (EABCD) into a positive four with a 45° angle between the sides and the bottom.