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Two quick questions on subspaces (intro to tensor calc)

  1. Dec 25, 2005 #1
    So the parametric equations of a hypersurface in VN
    are

    x^1=acos(u^1)
    x^2=asin(u^1)cos(u^2)
    x^3=asin(u^1)sin(u^2)cos(u^3)
    ...
    x^(N-1)=asin(u^1)sin(u^2)sin(u^3)...sin(u^(N-2))cos(u^(N-1))
    x^N=asin(u^1)sin(u^2)sin(u^3)...sin(u^(N-2))sin(u^(N-1))

    where a is a constant. How do I find the single equation of the hypersurface? And then from this how can it be determined whether the points (1/2a,0,0,...,0) and (0,0,0,...0,2a) are on the same or opposite sides of the surface?

    Any insight will be appreciated. Thanks. I ask another question when this thing is resolved in my mind.
     
  2. jcsd
  3. Dec 26, 2005 #2

    George Jones

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    Staff Emeritus
    Science Advisor
    Gold Member

    Hint: What is the sum of the squares of all the coordinates?

    Regards,
    George
     
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