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math214:hw12

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math214:hw12 [2020/04/26 08:23]
pzhou 		math214:hw12 [2026/02/21 14:41] (current)
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 Here is a picture, and the {{ :math214:geodesics.nb.zip |Mathematica program}} to make that picture (FYI, you can [[https://software.berkeley.edu/mathematica | use Mathematica for free]] as Berkeley student!) In the program, I fixed the initial point, and varies shooting angle, and the peak height.  Here is a picture, and the {{ :math214:geodesics.nb.zip |Mathematica program}} to make that picture (FYI, you can [[https://software.berkeley.edu/mathematica | use Mathematica for free]] as Berkeley student!) In the program, I fixed the initial point, and varies shooting angle, and the peak height. 
 {{ :math214:bending.png |}}  {{ :math214:bending.png |}} 
 +
 +And here is a video: {{ :math214:zoom_0.mp4 | varying the bumps and angles. }}
  
 2. Let $S$ be the submanifold of $\R^3$, that arises as the graph of $x^2 - y^2$. Compute the second fundamental form of $S$ at $x=0, y=0$.  2. Let $S$ be the submanifold of $\R^3$, that arises as the graph of $x^2 - y^2$. Compute the second fundamental form of $S$ at $x=0, y=0$. 
math214/hw12.1587889383.txt.gz · Last modified: 2026/02/21 14:44 (external edit)

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