Euler's Theorem In Geometry
In geometry, Euler's theorem states that the distance d between the circumcentre and incentre of a triangle can be expressed as
where R and r denote the circumradius and inradius respectively (the radii of the above two circles). The theorem is named for Leonhard Euler, who published it in 1767. However, the same result was published earlier by William Chapple in 1746.
From the theorem follows the Euler inequality:
Read more about Euler's Theorem In Geometry: Proof
Famous quotes containing the words theorem and/or geometry:
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—Albert Camus (1913–1960)
“... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.”
—Louise Bourgeois (b. 1911)