Cross-ratio with second point mapped to zero
= Cross-ratio with second point mapped to zero
{title2=$r=(z_1-z_4)(z_2-z_3)/[(z_1-z_2)(z_4-z_3)]$}
This <cross-ratio> convention is the value of $z_3$ under the <Möbius transformation> sending $z_1,z_2,z_4$ to $1,0,\infty$. It is one minus the convention $(z_1-z_3)(z_2-z_4)/[(z_1-z_2)(z_3-z_4)]$. Exchanging the first two points replaces $r$ by $1-r$. For four points in cyclic order on a circle, this convention gives $r<0$ and $1-r>1$.