Unit 08: Arc Length and Curvature


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You see coffee cup caustics everywhere!

A video from Summer 2021

Here is the verification of the curvature formula: 
r[t_]:= {x[t], y[t], z[t]}; 
s[t_]:= Sqrt[r'[t].r'[t]];
T[t_]:= r'[t]/s[t];
kappa1[t_]:= Sqrt[T'[t].T'[t]]/s[t]
kappa2[t_]:= Sqrt[Cross[r'[t], r''[t]].Cross[r'[t], r''[t]]]/s[t]^3
Simplify[kappa1[t]^2 == kappa2[t]^2]

A video from Summer 2020

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