a ^ 2 + b ^ 2 + c ^ 2> = (a + b + c) ^ 2 / 3
<=>
3 (a ^ 2 + b ^ 2 + c ^ 2)> = (a + b + c) ^ 2
<=>
2 (a ^ 2 + b ^ 2 + c ^ 2)> = 2 (ab + bc + ca)
<=>
(Ab) ^ 2 + (bc) ^ 2 + (ca) ^ 2> = 0 (true for all a, b, c)

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