论文标题
现代化阿基米德的$π$的构造
Modernizing Archimedes' Construction of $π$
论文作者
论文摘要
阿基米德在他的著名作品《圆圈的测量》中描述了一种测量圆圈及其边界区域的过程。他的工作中隐含的是他的程序定义了这些数量。定义$π$的现代方法避开了他的方法，而是使用更容易合理的论点，但它们涉及不是基本的想法。本文使阿基米德的测量程序从现代角度严格。这样一来，它带来了对三角函数的差异特性的严格和几何处理，成为了介绍性演算过程的权限。
In his famous work, "Measurement of a Circle," Archimedes described a procedure for measuring both the circumference of a circle and the area it bounds. Implicit in his work is the idea that his procedure defines these quantities. Modern approaches for defining $π$ eschew his method and instead use arguments that are easier to justify, but they involve ideas that are not elementary. This paper makes Archimedes' measurement procedure rigorous from a modern perspective. In so doing, it brings a rigorous and geometric treatment of the differential properties of the trigonometric functions into the purview of an introductory calculus course.
