A method for conic approximation by polynomial curves of odd degree n with approximation order 2n was presented by Floater (1997). A half circle approximation is obtained from the special case of the conic approximation method. In this paper we show that the coefficients of the polynomial curve of odd degree approximating the half circle in the power basis are related to entries of a particular row of a Bernoulli's triangle. We obtain the scaling factor which makes the radial error function equi-oscillate five times, and the Hausdorff distance between the half circle and the polynomial approximation curve.

中文翻译：

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半圆的参数多项式逼近的性质

一种用于二次曲线近似由奇次的多项式曲线方法Ñ与逼近阶2 Ñ用浮子（1997）提出。从圆锥近似方法的特殊情况获得半圆近似。在本文中，我们证明了幂次方近似于半圆的奇数级多项式曲线的系数与伯努利三角形的特定行的条目有关。我们获得了使径向误差函数等次振荡五次的比例因子，以及半圆和多项式逼近曲线之间的Hausdorff距离。