---
tag: MS263NBTRR
kind: concept
name: Lambert quadrilateral
msc: [51F05, 51M09]
sources:
  - url: https://en.wikipedia.org/wiki/Lambert_quadrilateral
same_as:
  wikidata: Q4117142
  wikipedia: Lambert quadrilateral
---

## Summary

A Lambert quadrilateral is a quadrilateral with three right angles.
Johann Heinrich Lambert studied it in the 1760s in an attempt to prove the [[parallel postulate|2PC3XY0PYZ]].
Its fourth angle is right in [[Euclidean geometry|KRZD96GSVC]] and acute in [[hyperbolic geometry|GN4N94GQ0Z]].
Half of a [[Saccheri quadrilateral|5SJVH0BHJE]], cut along the line joining the midpoints of base and summit, is a Lambert quadrilateral.

## Explanations

### L1 human

Draw a shape with four sides in which three corners are square corners.
On a flat sheet the fourth corner is forced to be square too, so you get a rectangle.
In hyperbolic geometry the fourth corner is sharper than a right angle.
Lambert worked out many consequences of a sharp fourth corner and noticed that they look like geometry on a sphere of imaginary radius.