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 Sep13 awarded Good Question Jul31 awarded Yearling Jun19 awarded Popular Question Feb6 awarded Popular Question Feb10 awarded Nice Question May23 revised Average sine of an angle between two rays in a cone added 190 characters in body May23 revised Computing ${\int\limits_{0}^{\chi}\int\limits_{0}^{\chi}\int\limits_{0}^{2\pi}\sqrt{1- \cdots} \, d\phi \, d\theta_1 \, d\theta_2}$? added 40 characters in body May23 awarded Promoter May22 suggested rejected edit on Average sine of an angle between two rays in a cone May22 comment Average sine of an angle between two rays in a cone Btw, It should be $A^2$ in the equation for the average sine... May22 comment Average sine of an angle between two rays in a cone Asked another question at last: math.stackexchange.com/questions/147662/… May21 comment Computing ${\int\limits_{0}^{\chi}\int\limits_{0}^{\chi}\int\limits_{0}^{2\pi}\sqrt{1- \cdots} \, d\phi \, d\theta_1 \, d\theta_2}$? Thank you! There was definitely a mistake. But I expect both $\theta_1$ and $\theta_2$ to be in $[0,\chi]$. The point is that it's a cone, not a sphere. May21 revised Computing ${\int\limits_{0}^{\chi}\int\limits_{0}^{\chi}\int\limits_{0}^{2\pi}\sqrt{1- \cdots} \, d\phi \, d\theta_1 \, d\theta_2}$? edited body May21 asked Computing ${\int\limits_{0}^{\chi}\int\limits_{0}^{\chi}\int\limits_{0}^{2\pi}\sqrt{1- \cdots} \, d\phi \, d\theta_1 \, d\theta_2}$? May12 comment Average sine of an angle between two rays in a cone In a percolation problem. I'm calculating the average number of bonds in a 3d set of randomly disturbed 1d sticks. I can send you one of my papers. May12 comment Average sine of an angle between two rays in a cone If I'm not mistaken, the last line should be like this: $${=\cos(\phi_1+\phi_2)\,\sin^2\frac{\theta}{2} +\cos(\phi_1-\phi_2)\,\cos^2\frac{\theta}{2}}$$ Thank you for your help! Will see if I can integrate that. May11 awarded Supporter May11 revised Average sine of an angle between two rays in a cone edited title May11 awarded Editor May11 revised Average sine of an angle between two rays in a cone deleted 174 characters in body