个人笔记

1 弧长 arc length

如上图所示，设$\mathrm{\Delta }S=S_i-S_{i-1}$

• 将弧长近似为线段，由此可得$(\mathrm{\Delta }S{)}^2\approx (\mathrm{\Delta }x{)}^2+(\mathrm{\Delta }y{)}^2$
• 无限细化$S_i$与$S_{i-1}$之间的距离，可得$(ds{)}^2=(dx{)}^2+(dy{)}^2$
• 化简得$ds=\sqrt{1-(\frac{dy}{dx}{)}^2}dx$
• 从$S_0$到$S_n$的总弧长$=\int_a

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