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11
votes
Moments of area of random triangle inscribed in a circle
Let $A_d$ be the area of a triangle whose vertices are chosen uniformly at random from a unit sphere in $\mathbb{R}^d$.
I claim that for $d\ge 2$ and $m\ge 1$:
$$
E(A_d^{2m})=\frac{3}{4^m} \prod _{q …
5
votes
Moments of area of random triangle inscribed in a circle
Though this does not directly address the moments question, I was curious as to whether the full probability distribution for the triangle area could be written in closed form. It turns out that this …