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Math Help - Euler characteristic of a compact surface

  1. #1
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    Exclamation Euler characteristic of a compact surface

    Determine the Euler characteristic of the compact surface M in R^3 defined by:

    M = {(x,y,z) in R^3; (sqrt(x^2+y^2) - 2006)^2=2(1-z^2)}.

    ------------------------

    So I figured I should use Gauss-Bonnet but how?
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  2. #2
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    this one is a surface of revolution with the z axis as the center. Let y = 0 and x >=0 we get (x-2006)^2 + 2z^2 = 2, an ellipse. So M is homeomorphic to a tori, thus it's Euler characteristic is 0.
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