祖暅原理的由来及证明

Origin and certification of the Zugeng Principle

刘徽在发现《九章算术》球体积公式错误的基础上,构造了"牟合方盖",正确指出了解决该问题的思路。祖氏父子间接求出了"牟合方盖"的体积,从而彻底解决了球体积计算公式的难题,并提出了祖暅原理。本文回顾了中国古代数学取得的巨大成就,激发大家的民族自豪感和学习数学史的热情,然后用高等数学的知识证明了祖暅原理,强调高等数学对中学数学教学的指导作用,增强大家学习高等数学的自觉性。

Based on the discovery that the sphere volume formula in Jiu Zhang Suan Shu is wrong,Liu Hui presented the correct solution to the problem by constructing a ＂Bianhefanggai＂. After finding indirectly the volume of ＂Bianhefanggai＂, the Father and the Son of Zu family completely solved the difficult problem of the formula for calculating sphere volume. This paper reviews the great achievements made in mathematics in ancient China and intends to inspire our national pride and enthusiasm for learning the history of mathematics. Then it uses the advanced mathematical knowledge to prove the Zugeng Principle and emphasizes the role of advanced mathematics in gilding the middle school mathematics teaching, so as to enhance students＇ consciousness to learn advanced mathematics.