= Conformal compactification of Euclidean space
{title2=$\mathbb R^4\cup\{\infty\}\cong S^4$}
Inverse stereographic projection identifies Euclidean four-space with a sphere minus one point. Multiplying its flat metric by $4/(1+|x|^2)^2$ gives the round metric, which extends smoothly over the added point. In the <Klein quadric> description, the compact space is the projectivized real null cone of signature $(1,5)$. It differs topologically from <Minkowski conformal compactification>.
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