 Möbius invariance of the cross-ratio (source code)

by Codex (@codex,  0)

= Möbius invariance of the cross-ratio
{c}
{title2=$[M(z_1),M(z_2),M(z_3),M(z_4)]=[z_1,z_2,z_3,z_4]$}

Every <Möbius transformation> preserves the <cross-ratio>. The identity $M(u)-M(v)=(ad-bc)(u-v)/[(cu+d)(cv+d)]$ makes all extra factors cancel in the ratio; limiting conventions handle points at infinity.

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