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### Course: Geometry (all content)>Unit 4

Lesson 8: Bringing it all together

# Euler line

The magic and mystery of the Euler Line. Created by Sal Khan.

## Want to join the conversation?

• What is the 9 point circle?
• @ bodickstein whatever wikipedia is a great source for all sorts of information thus liberating students from only learning from textbooks or relying completely on teachers. And even though a lot of people don't like Wikipedia because anyone has the ability to edit it, you'll see that if something get's put in that shouldn't be there the staff immediately corrects this.
• WOW!
This video was awesome!
What else did this guy Euler do?
He seems to be a really smart person!
• Can you show us a video on how to draw a triangle with the Euler line? I sure could use that because my every attempt fails, when I am using a straight edge ruler and protractor. It just doesn't add up... some line is always off the center, or I get an arc as opposed to a line, if there is such a thing as Euler arc!... Of course if I draw it freehand I can make it look any way I like, I can even make it look like in this presentation and say it's true.

And sometimes the centroid or the orthocenter is outside my triangle. What type of triangle is best for demonstrating this relationship with Euler line? Isosceles triangle? So that all the concurrencies (centroid, circumcenter, orthocenter) sit within the triangle? What angles would you use for that triangle?...
• I made this program using the Khan Academy CS platform which allow you to plot the Euler line and see how it changes as the triangle changes (for example, if you make an equilateral triangle).
• While graphing triangles, what do we mean when we say that the triangle is centred at a point, say (2,3)? Is this point the centroid, circumcentre, orthocentre or the 9-point centre?
• I was always taught the center refers to where the median lines meet. Later I was introduced to the centroid which is the same as the center. If you think about this intuitively, it is the center of the area of the triangle and its center of mass (if it had a consistent thickness). You can cut out any triangle and balance it on its center (centroid). When you divide the triangle into three smaller triangles using the centroid as the common vertex, all smaller triangles have the same area.
• Neat stuff, but I'm curious about its applications. Does the Euler line find use in science, engineering, or any other discipline? Excepting mathematics, of course =)
• Is the orthocenter outside of the triangle for an obtuse triangle?
(1 vote)
• yes it is in fact. for more info check out sals triangle vidoes.
• This was very specific but is it possible to get the Euder line on an angle bisector, if possible how?
(1 vote)
• Yes,but only if the triangle is isoceles or equilateral.