Euler Line

Pronunciation: /ˈɔɪ lər laɪn/ ?

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An Euler line is a line that passes through the orthocenter, centroid, and circumcenter of a triangle.[1] In manipulative 1, the Euler line is the blue line. Click on the blue points in manipulative 1 and drag them to change the figure.

The Euler line was first described by Leonhard Euler in Novi Commentarii academiae scientarum imperialis Petropolitanae 11: 103–123. Since the introduction of the Euler line, many other triangle centers have been found that are on the Euler line, including the center of the 9 point circle.

References

  1. Leonard Eulero. Sovtio Facilis Problematum Quorumdam Geometricorum Difficilimorum, 11: 103–123. Novi Commentarii academiae scientarum imperialis Petropolitanae. (Accessed: 2010-01-27). http://math.dartmouth.edu/~euler/docs/originals/E325.pdf.
  2. Mackay, J. S.. The Triangle and its Six Scribed Circles, pp 97-103. Proceedings of the Edinburgh Mathematical Society, Volume 1. Edinburgh Mathematical Society, 1883. (Accessed: 2010-01-29). http://www.archive.org/stream/proceedingsedin15socigoog#page/n107/mode/1up/search/Euler.
  3. H. S. M. Coxeter, Samuel L. Greitzer. Geometry Revisited , pp 18-20. The Mathematical Association of America, 1967. (Accessed: 2010-01-29).

More Information

  • Kimberling, Clark. Euler Line. 2010-01-29. http://faculty.evansville.edu/ck6/tcenters/class/eulerline.html.

Printed Resources

Cite this article as:


Euler Line. 2010-01-27. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/eulerline.html.

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Revision History


2010-01-29: Added "References" (McAdams, David.)
2009-01-05: Initial version (McAdams, David.)

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