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What's the angle at infinity?

  1. Feb 4, 2009 #1
    Suppose we have the following shape in the complex plane: The EXTERIOR of the semi-infinite strip bounded by 0 < y < 1 and x > 0. The two physical angles making up the rectangle have interior angles of 3*pi/2 and thus exterior angles of -pi/2.

    Now, because the sum of the exterior angles of a polygon have to sum to 2pi, we can claim that the exterior angle at infinity is simply 2pi - (-pi/2 - pi/2) = 3pi.

    However, I'm having trouble justifying this geometrically. I've looked at projecting the surface onto the Riemann sphere, but the exterior angle at infinity simply seems to be either pi or -pi. I see no reason why it has to do an additional orbit of 2pi.
  2. jcsd
  3. Feb 4, 2009 #2


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    How many non-overlapping triangles can you determine in the polygon? Each triangle contains sum of the interior angles being [tex]\pi[/tex] radians.
  4. Feb 4, 2009 #3
    How do you imagine triangles on an infinite domain? I don't see how this helps...
    Last edited: Feb 4, 2009
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