基于平均数的椭圆周长近似公式

Approximate Formula of Perimeter of Ellipse Based on Average

椭圆是圆锥曲线之一,在工程制图与机械加工中,常常需要计算椭圆的周长.本文利用调和平均数构造了一个近似计算椭圆周长的公式,并结合算术平均数、几何平均数以及均方根平均数方法,通过加权组合得到一个形式简单的高精度近似公式.数值实例验证了该公式的有效性.

Ellipse is one of conic curves.In engineering drawing and machining,it is often necessary to calculate the perimeter of ellipse.An approximate formula for calculating ellipse circumference is constructed by using harmonic average in this paper.Combining arithmetic average,geometric average and square root average,a new simple and high accurate approximation formula is obtained by weighted combination.Numerical examples verify the effectiveness of the proposed method.