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Curvature of a sphere

  1. Jan 28, 2008 #1
    I am attempting to prove the following relation between the curvature K of a sphere of radius R and the area A of a geodesic circle of radius a.

    K = [tex]lim_{a\rightarrow 0}[/tex] [tex]\frac{\pi\cdot a^{2}-A}{a^{4}}[/tex] [tex]\frac{12}{\pi}[/tex]

    I'm off by a factor of 4 (i.e. I have 3 in the numerator instead of 12) and I think it might have something to do with my calculation of the area A. I found:

    A = [tex]\pi[/tex] R[tex]^{2}[/tex]sin[tex]^{2}[/tex][tex]\frac{a}{R}[/tex]

    Where did I go wrong?
     
    Last edited: Jan 28, 2008
  2. jcsd
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