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joeyjokester
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Homework Statement
I am given this parametrization of the mobius band:
F(s,t) = (cos(t)+s*cos(t)*cos(t/2), sin(t)+s*sin(t)*cos(t/2), s*sin(t/2))
Let F1 be F restricted to (0,2*pi) X (-1,1).
Let F2 be F restricted to (-pi,pi) X (-1,1).
let N1 be the unit normal field determined by F1
let N2 be the unit normal field determined by F2
The question reads:
Compute the unit normal field for N1, N2 at the points (0,1,0) and (0,-1,0).
Homework Equations
N(t) = (dF/ds X dF/dt)/ ||dF/ds X dF/dt||
The Attempt at a Solution
I am unsure how to begin on this. I am looking for a starting block. Obviously I want to plug in the point before taking cross products? How do I do this when F(s,t) takes 2 parameters, but I am given a point of the form (x,y,z). This is troublesome. I have computed the partials dF/ds and dF/dt, but I don't know what to do with them.. I don't want to take this nasty cross product.
thanks