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在人民教育出版社出版的“高級中学課本平面几何”中,在用圓內接正多边形用边数加倍的方法,所得一列正多边形周長的極限来定义了圓周長之后,下面有一个注意,說:“实际上,只要从圓的任意一个內接多边形(不一定要是內接正多边形)出發,用任何方法(不一定用边数加倍的方法)使它的边数無限增加,各边無限縮短,那末这些多边形的周長也有一个
In “The Plane Geometry of High School Textbooks” published by the People’s Education Publishing House, after using the method of doubling the number of edges of a regular polygon in a circle to define the circumference of a column of regular polygons to define the circumference, there is a note below. Say: "Actually, as long as starting from any inscribed polygon of a circle (not necessarily an inscribed regular polygon), its number of edges is infinitely increased by any method (not necessarily by doubling the number of edges), and the edges are infinite. Shortened, then there is also a perimeter of these polygons