---
tag: 0YYT36R4YD
kind: concept
name: Conformal map
aliases: [conformal-mapping, angle-preserving-map]
msc: [30C35]
sources:
  - url: https://en.wikipedia.org/wiki/Conformal_map
    locator: lead section
same_as:
  wikidata: Q850275
  wikipedia: Conformal map
---

## Summary

A conformal map is a map that preserves angles and their orientation at each point, but not necessarily lengths, see the [[definition|0VHNKP1N3K]].
In the plane, the conformal maps on an open set are the [[holomorphic|0DG0Z72CQD]] functions with a derivative that is never zero.