---
tag: 4TWY53TBKK
kind: concept
name: Coplanarity
msc: [51N10, 51A05]
sources:
  - url: https://en.wikipedia.org/wiki/Coplanarity
same_as:
  wikidata: Q543533
  wikipedia: Coplanarity
---

## Summary

A set of points is coplanar when some plane contains all of them.
Any three points are coplanar, so the notion first says something for four or more points.
It is the next step after [[collinearity|0AFNNTRTJE]], and in space it is tested by a vanishing determinant.

## Explanations

### L1 human

Points are coplanar if a flat sheet can pass through all of them.
Three points always fit on a sheet, like a three-legged stool that never wobbles.
Four points may not: the corners of a tetrahedron are not coplanar.
The four corners of a square are coplanar, and so are any points of the floor of a room.