Incenter, Orthocenter, Circumcenter, CentroidDate: 01/05/97 at 21:25:17 From: Kristy Beck Subject: Euler line I have been having trouble finding the Euler line on a triangle. If you would explain to me, I would be most grateful! Thank you, Kristy Beck Date: 01/06/97 at 01:51:53 From: Doctor Pete Subject: Re: Euler line The Euler line of a triangle is the line which passes through the orthocenter, circumcenter, and centroid of the triangle. The orthocenter is the intersection of the triangle's altitudes. The circumcenter is the center of the circumscribed circle (the intersection of the perpendicular bisectors of the three sides). The centroid is the intersection of the three medians of the triangle. There's also the incenter, which is the intersection of the angle bisectors of the triangle. -Doctor Pete, The Math Forum NEWSGROUP DISCUSSIONS For proofs involving the center of gravity and the circumcenter of a triangle, see Eileen Steven's question sent to the newsgroup geometry-pre-college, and Eileen Schoaff's answer: http://mathforum.org/kb/message.jspa?messageID=1077584 http://mathforum.org/kb/thread.jspa?forumID=128&threadID=351544 For some properties of the orthocenter of a triangle, see Michael Keyton's posting to the newsgroup geometry-puzzles: http://mathforum.org/kb/message.jspa?messageID=1084283 ON THE WEB: TRIANGLE CENTERS Prof. Clark Kimberling's page of Triangle Centers provides a listing, with links to descriptions and illustrations, of 20th-century triangle centers, including: Schiffler Point, Exeter Point, Parry Point, congruent isoscelizers point, Yff Center of Congruence, isoperimetric point and equal detour point, Ajima-Malfatti Points, Apollonius Point, Morley Centers, Hofstadter Points, and equal parallelians points; and some classical triangle centers: centroid, incenter, circumcenter, orthocenter, Fermat Point, nine-point center, symmedian (or Lemoine) point, Gergonne point, Nagel point, Mittenpunkt, Spieker center, Feuerbach point, isodynamic points, and Napoleon points. http://faculty.evansville.edu/ck6/encyclopedia/ -Doctor Sarah, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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