Euler Line

Pronunciation: /ˈɔɪ.lər laɪn/ Explain

Click on the blue points and drag them to change the figure. Of the three points, which are always inside the triangle? Manipulative 1 - Euler Line Created with GeoGebra.

An Euler line is a line that passes through the orthocenter, centroid, and circumcenter of a triangle.[2] In manipulative 1, the Euler line is the red line. 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. McAdams, David E.. All Math Words Dictionary, euler line. 2nd Classroom edition 20150108-4799968. pg 73. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Leonard Eulero. Sovtio Facilis Problematum Quorumdam Geometricorum Difficilimorum. 11: 103–123. Novi Commentarii academiae scientarum imperialis Petropolitanae. Last Accessed 7/9/2018. http://math.dartmouth.edu/~euler/docs/originals/E325.pdf.
3. Mackay, J. S.. The Triangle and its Six Scribed Circles. pp 97-103. www.archive.org. Proceedings of the Edinburgh Mathematical Society, Volume 1. Edinburgh Mathematical Society. 1883. Last Accessed 7/9/2018. http://www.archive.org/stream/proceedingsedin15socigoog#page/n107/mode/1up/search/Euler.
4. Coxeter, H.M.S. and Greitzer, S.L.. Geometry Revisited. 1st edition. pp 18-20. The Mathematical Association of America. 1967. Last Accessed 7/9/2018. Buy the book

More Information

• Kimberling, Clark. Euler Line. faculty.evansville.edu. 1/29/2010. http://faculty.evansville.edu/ck6/tcenters/class/eulerline.html.

Cite this article as:

McAdams, David E. Euler Line. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/e/eulerline.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/29/2010: Added "References". (McAdams, David E.)
1/5/2009: Initial version. (McAdams, David E.)