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Math Help - Gauss Bonnet theorem for hyperbolic triangle

  1. #1
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    Gauss Bonnet theorem for hyperbolic triangle

    Hi, i was hoping that someone could help me understand the integration parts of the proof on page 3 of: http://www.maths.manchester.ac.uk/~c.../lecture07.pdf
    Particularly i dont understand where the sqrt(1-x^2) comes from on the integral and the beta and pi - alpha
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  2. #2
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    the half circle is the graph of \sqrt{1-x^2}. To compute
    \int_{\Delta}{\frac{1}{y^2}dxdy}, note the area \Delta is bounded by x=a, x=b and the half circle. So we can compute the integral using iterated integrals by Fubini's theorem, for x from a to b, y from \sqrt{1-x^2} to infinite.
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