王半仙的学习分享

1 弧长 arc length

如上图所示，设$\Delta S=S_i-S_{i-1}$

• 将弧长近似为线段，由此可得$(\Delta S)^2 \approx(\Delta x)^2+(\Delta y)^2$
• 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

Read more