Euler's theorem in geometry
id:
euler-s-theorem-in-geometry-237-11250768
title:
Euler's theorem in geometry
text:
In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by or equivalently where R and r denote the circumradius and inradius respectively. The theorem is named for Leonhard Euler, who published it in 1765. However, the same result was published earlier by William Chapple in 1746. From the theorem follows the Euler inequality: which holds with equality only in the equilateral case.
brand slug:
wiki
category slug:
encyclopedia
description:
On distance between centers of a triangle
original url:
https://en.wikipedia.org/wiki/Euler%27s_theorem_in_geometry
date created:
date modified:
2023-11-23T15:13:13Z
main entity:
{"identifier":"Q1423818","url":"https://www.wikidata.org/entity/Q1423818"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/c/ca/Euler_theorem2.svg","width":388,"height":378}
fields total:
13
integrity:
15