Upward unit normal to an upper circular cone
= Upward unit normal to an upper circular cone
{title2=$n=(-x_1,-x_2,x_3)/(\sqrt2\,x_3)$}
On $x_3^2=x_1^2+x_2^2$ with $x_3>0$, the <gradient> of the defining function gives a normal proportional to $(-x_1,-x_2,x_3)$. Its <Euclidean norm> is $\sqrt2\,x_3$, proving the displayed normalization. This upward normal lies on the boundary of the <Lorentz cone>, so <self-duality of a second-order cone> makes its pairing with every point of the closed upper cone nonnegative.