---
tag: KRZD96GSVC
kind: concept
name: Euclidean geometry
msc: [51M05, 51M04]
sources:
  - url: https://en.wikipedia.org/wiki/Euclidean_geometry
same_as:
  wikidata: Q162886
  wikipedia: Euclidean geometry
---

## Summary

Euclidean geometry is the geometry of the [[Euclidean plane|0XW7V9ZZ05]] and of [[Euclidean space|0XPR1E85W0]]: the study of points, lines, distances and angles in a flat space.
It can be built synthetically from axioms, as in [[Euclid's Elements|83WHDAV68J]] and [[Hilbert's axioms|KM1FB8XZ2R]], or analytically with coordinates in $\R^n$.
Its characteristic axiom is the [[parallel postulate|2PC3XY0PYZ]]; dropping it leads to [[absolute geometry|VKFPCSRNDH]] and to [[non-Euclidean geometry|SPCYMFN5V2]].

## Explanations

### L1 human

Euclidean geometry is the geometry of a flat sheet of paper that goes on forever.
Straight lines, circles, triangles and their measures are its objects.
Through a point outside a line there is exactly one line parallel to it, and the angles of a triangle add up to $180^\circ$.
For example, a triangle with sides $3$, $4$ and $5$ has a right angle, by the [[Pythagorean theorem|0VP3A1290K]].