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[几何] 彭赛列闭合三角形顶点参数化

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hbghlyj Posted 2025-4-24 01:29 |Read mode
对于任何内切于单位圆 $\mathbb{T}$ 并外切于以 $f, g$ 为焦点的椭圆的彭赛列三角形族,其顶点 $z_1, z_2, z_3$ 的初等对称多项式参数化为
\[
z_1 + z_2 + z_3 = f + g + \lambda \overline{f} \, \overline{g}
\]
\[
z_1 z_2 + z_2 z_3 + z_3 z_1 = fg + \lambda (\overline{f} + \overline{g})
\]
\[
z_1 z_2 z_3 = \lambda
\]
其中 $\lambda$ 是沿单位圆 $\mathbb{T}$ 变化的参数。
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2025-6-6 13:27 GMT+8

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