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bio website installero.com
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May
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revised Average sine of an angle between two rays in a cone
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revised Computing ${\int\limits_{0}^{\chi}\int\limits_{0}^{\chi}\int\limits_{0}^{2\pi}\sqrt{1- \cdots} \, d\phi \, d\theta_1 \, d\theta_2}$?
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May
22
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...
May
22
comment Average sine of an angle between two rays in a cone
Asked another question at last: math.stackexchange.com/questions/147662/…
May
21
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.
May
21
revised Computing ${\int\limits_{0}^{\chi}\int\limits_{0}^{\chi}\int\limits_{0}^{2\pi}\sqrt{1- \cdots} \, d\phi \, d\theta_1 \, d\theta_2}$?
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May
21
asked Computing ${\int\limits_{0}^{\chi}\int\limits_{0}^{\chi}\int\limits_{0}^{2\pi}\sqrt{1- \cdots} \, d\phi \, d\theta_1 \, d\theta_2}$?
May
12
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.
May
12
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.
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revised Average sine of an angle between two rays in a cone
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revised Average sine of an angle between two rays in a cone
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