重要极限$\underset{x\to 0}{lim}\frac{sinx}{x}=1$的一种证明新方法

A New Method for Proving the Fundamental Limit $\underset{x\to 0}{lim}\frac{sinx}{x}=1$

摘要: 借助“割圆术”，根据圆内接正多边形的周长逼近圆的周长，结合正弦函数定义，给出了重要极限$\underset{x\to 0}{lim}\frac{sinx}{x}=1$ 的一种新的证明方法，为开展重要极限实践教学提供一个新颖的、富含历史底蕴的视角。

Abstract: A new proof of the fundamental limit $\underset{x\to 0}{lim}\frac{sinx}{x}=1$ is proposed in this paper by using the method of circle division, which derives an approximation of the circumference from the perimeter of a regular polygon inscribed in a circle. This proof method provides a novel and historically rich teaching perspective for the fundamental limit.