# 19 Fresh Euler Line

Euler Line lineThe Euler line of a triangle is a line going through several important triangle centers including the orthocenter circumcenter centroid and center of the nine point circle Euler Line mathopenref eulerline htmlIn the 18th century the Swiss mathematician Leonhard Euler noticed that three of the many centers of a triangle are always collinear that is they always lie on a straight line This line has come to be named after him the Euler line His name is pronounced the German way oiler

mathworld wolfram Triangles Triangle LinesThe Euler line intersects the Soddy line in the de Longchamps point and the Gergonne line in the Evans point The isogonal conjugate of the Euler line is the Jerabek hyperbola Casey 1893 Vandeghen 1965 Euler Line djoyce java Geometry eulerline htmlThe Euler Line of a Triangle It s amazing how much geometry there is in the lowly triangle Consider the triangle ABC below colored magenta Several interesting points and lines can be constructed and they all move as you drag about a vertex A B or C of the triangle mathwords e euler line htmEuler Line The line segment that passes through a triangle s orthocenter centroid and circumcenter These three points are collinear for any triangle In addition the distance from the orthocenter to the centroid is twice the distance from the circumcenter to the centroid

khanacademy Triangles Bringing it all togetherClick to view6 12So it s cool enough that these three special points are on the Euler line but there s actually four special points And actually there s a few more than that are kind of interesting So that orange point right over there is the center of the nine point circle Euler Line mathwords e euler line htmEuler Line The line segment that passes through a triangle s orthocenter centroid and circumcenter These three points are collinear for any triangle In addition the distance from the orthocenter to the centroid is twice the distance from the circumcenter to the centroid the knot triangle EulerLine shtmlThe Euler Line and the 9 Point Circle This is a continuation of The Altitudes and the Euler line page towards the end of which we established existence of the Euler line In any triangle three remarkable points circumcenter centroid and orthocenter are collinear that is lie on the same line Euler s line

### Euler Line Gallery

stock vector cartoon portrait of leonhard euler 281908391, image source: www.shutterstock.com

matlab_7_6, image source: blogs.mathworks.com

physics_bowling_48, image source: real-world-physics-problems.com

eulerd1, image source: www.cs.kent.ac.uk

EulerTimeline, image source: eulerarchive.maa.org

wire 1078391 1501884048 357_634x796, image source: www.dailymail.co.uk

Unicorn_(PSF), image source: commons.wikimedia.org

444px Western_US_electrical_power_transmission_map, image source: en.wikipedia.org

maclaurin%2Bseries, image source: kenschenck.blogspot.com

th?id=OGC, image source: www.mathcurve.com

3 circle venn diagram to download or modify online 1024x709, image source: creately.com

image005, image source: www.monografias.com

touret a meuler et ponceuse stationnaire 240 w 240 w silverline L 149211 1316138_1, image source: www.manomano.fr

Fourier_Series, image source: claesjohnson.blogspot.com

photo_27799, image source: en.tengrinews.kz

1200px Cartesian coordinate system, image source: es.wikipedia.org

convertir, image source: historiaybiografias.com