Interpret this geometrically

  • Thread starter Daveyboy
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  • #1
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Main Question or Discussion Point

Hi,

I'm trying to get an idea of what this is in my head but I do not have mathematica handy.

f:R1 to R3
|f(t)|=1
and f'(t)f(t)=0

should I just imagine these as being two tangent vectors.
 

Answers and Replies

  • #2
1,013
65
If that is a dot product, you should already know of a common simple curve whose tangent lines are always perpendicular to the position vector of the curve. The fact that the length of the position vector is a constant should tell you that the curve is a subset of a particular common surface.
 
  • #3
58
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Me thinks sphere.
 
  • #4
259
2
Yous thinks right.

Well, circle I think, actually.
 
  • #5
1,013
65
The sphere is the right idea. Note that the curve does not need to be a circle.
 

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