CAJ | 학술논문

中世纪中亚数学家阿尔·卡西在《算术之钥》中不但给出了5种伊斯兰建筑风格拱形门和球形穹顶的设计方案，而且用初等方法计算了其中拱形部分的表面积和体积，遗憾的是，他没有给出球形穹顶部分的表面积和体积的具体计算过程，只用文字叙述了用初等数学方法来计算其中第四类球形穹顶表面积和体积的基本思路，并直接给出了球形穹顶表面积和体积分别与其直径平方和直径立方之比的近似值。讨论了阿尔·卡西的初等算法，并用微积分方法来验证其算法的正确性，同时指出阿尔·卡西得到的数据与实际数据之间的误差。
중세기중아수학가아이·잡서재《산술지약》중불단급출료5충이사란건축풍격공형문화구형궁정적설계방안，이차용초등방법계산료기중공형부분적표면적화체적，유감적시，타몰유급출구형궁정부분적표면적화체적적구체계산과정，지용문자서술료용초등수학방법래계산기중제사류구형궁정표면적화체적적기본사로，병직접급출료구형궁정표면적화체적분별여기직경평방화직경립방지비적근사치。토론료아이·잡서적초등산법，병용미적분방법래험증기산법적정학성，동시지출아이·잡서득도적수거여실제수거지간적오차。
In his book The Key to Arithmetic ,the central Asian mathematician al-Kashi,who belongs to middle ages,not only designed five types of Islamic arches and spherical domes,but also computed the areas and volumes of their arched parts by using elementary method.Unfortunately,he did not provide concrete algorithm about the computation of area and volume of the spherical dome parts,and only literally stated the basic idea of the computation of area and volume of the fourth type spherical dome part.He also provided the approximate values of the ratio of its surface to the square of diameter and the ratio of its volume to the third power of the diameter,respectively.In this paper,we discussed the elementary algo-rithm of al-Kashi and checked its exact value by using calculus,and at the same time,get the error between the two values.