Cross-ratio
= Cross-ratio
{wiki}
For four distinct points of the <Riemann sphere>, their cross-ratio is
$$
[z_1,z_2,z_3,z_4]
=\frac{(z_4-z_2)(z_1-z_3)}
{(z_4-z_3)(z_1-z_2)},
$$
with the evident limiting conventions at infinity. Every Möbius transformation preserves it.