---
tag: 09ASMRMD67
kind: concept
name: Cross-ratio
aliases: [cross-ratio, double-ratio, anharmonic-ratio]
msc: [30C35]
sources:
  - url: https://en.wikipedia.org/wiki/Cross-ratio
    locator: lead section
same_as:
  wikidata: Q899539
  wikipedia: Cross-ratio
---

## Summary

The cross-ratio is a number made from four points of a line, or of the Riemann sphere, see the [[definition|05MW7MPRBS]].
It does not change under [[Möbius transformations|0SG74WBFA2]] and, more generally, under projective transformations.