The area of a spherical triangle (sphere radius $a$ ) is given by spherical deficit $ (A+B+C-\pi)$ times $ a^2 $ when enclosed between great circular arcs.

If tangential curvature radii are $ Rg_a, Rg_b, Rg_c$ what is the area of the spherical triangle enclosed between small circles? Positive if apex angle reduces with respect to a geodesic.

  • $\begingroup$ If I intersect a sphere with a plane (not through the origin!) then the result is a circle of some radius $R$ lying on the sphere. Is this $R$ what is meant by 'tangential curvature radii'? $\endgroup$ – Semiclassical Sep 9 '16 at 17:11
  • $\begingroup$ Yes, tangential radius of curvature $Rg$. Changed sphere radius symbol to $a$ to remove the ambiguity. $\endgroup$ – Narasimham Sep 9 '16 at 17:26

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