Euler line | Special properties and parts of triangles | Geometry | Khan Academy

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The magic and mystery of the Euler Line
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Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.
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[@nodariel]

Once again I have learnt something incredible from your video. Fantastic.

[@TheMoo1231]

forgot to mention about the 2:1 ratios....

[@Ferrus91]

This is the best actual proof I have seen. Uses line traversals and centroid properties to simply derive the statement. Pretty sure Khan could do this proof without confusing anyone. :)

[@GetMeThere1]

Who needs religion when you can have this? As a matter of fact, who needs orgasms when you can have this? This sort of stuff stirs me to the core of my being....for me it's the most moving and satisfying sort of thing I've ever experienced. Why did nobody show me these things in school???

[@StefanS117MC]

i often ask my self: why is our world following so simple rules?

[@commanderoftheenhancementation]

this video is helpful

[@jeromebando5216]

this is really really nice and good to watch and easiest to understand.

[@AlderDragon]

I think the length from the orthocenter to the centroid is actually exactly twice as long as the distance from the centroid to the circumcenter.

[@coolsteven2]

This is amazing! I stumbled upon this video. GET OUT Triangles are more amazing than I thought they were.

[@jetpaq]

i have to say,i thought same thing..but its hard to criticize the mastah!hehehe *bows* all hail Sal!!! king of Teach!

[@Madgod112]

GIMP hint: if you hold shift while clicking in different places with the brush tool, it will draw a line from where you last clicked. I'm not sure if you know this and there's some reason you're not doing it, but I figured I'll post it here anyway.

[@sebaschan-uwu]

But the real question is, does this work when using a scalene obtuse triangle and does it still work even though the altitude intersecting point is outside the circle

[@Buoy2]

what's the relationship between the euler line and the triangle? Is there some kind of symmetry?

[@Kashif_Javaid]

Sal, how come you are not using triangle, line, circle etc tool for your geometry playlist?

[@laputahayom]

@TheHdulcimerguy he means that the circle goes thourgh nine spical points analogous to the centroid.

[@ROBIN-db1je]

Thank you sooo much

[@Waranle]

Thank you Sal

[@XecutionStyle]

What is the significance of the Euler line? Is there one, or is it just like the Euler identity there to mock us.

[@gorjanec1]

i think that e^(πi)+1=0 is a much more prettyer equation

[@utubedkf]

There's an interesting progam called GeoGebra that can be used to show these three points. (just google for GeoGebra to find it -- looks like links are disabled for these comments)

[@gokor356]

i wonder if eulers line intersecting one of the sides of the triangle is somehow related to the phi ratio. hmm...

[@tristoncriswell3254]

no

[@dhruvlamba5299]

Nice work

[@nybotheveg]

@XecutionStyle euler did amazing things just to troll use.

[@gamingtec101]

Great video. M9

[@DeependraSingh1]

GamingTec101 m8 👍🏻👍🏻

[@Mmouse_]

"Circumcentu̲r" ... what?

[@gabrielignacio.x]

what kind of magic is this D:

[@DashDart]

@GetMeThere1 yea sure but that's just one of the 6.5 billion people on earth. Sure that is great and really inspiring that he apparently avoided orgasm for the sake of mathematics and i agree that he was a true genius...but still, you know, it's a bit too far into saying.... but anyways...i totally respect your views on that and i don't mean to offend you or anything..i am just saying what i feel :)

[@Ilikemeows]

Could have used this a year ago :(

[@DashDart]

@GetMeThere1 hehe...same here dude... but i wouldn't go as far as saying "who needs orgasms"...because orgasms are the reason human beings exist in this earth(well this is too dramatic but still...its a thought) but either ways...it stirs me too...it feels so overwhelming and exciting that for a while you can't help but smile like a douche :) and i don't care about that as long as i love mathematics, all seems well :) Cheers Bidit from Nepal

[@Ilikemeows]

@GetMeThere1 That orgasm part is a bit too far dont you think? Lol, im kidding, if math or just intellectual stuff stimulates interest in you, its a gift; you appreciate knowledge.

[@Cashman9111]

and the incenter is left alone :(

[@GetMeThere1]

@DashDart : The well-known modern mathematician Paul Erdos claimed to live most of his adult life without orgasms--because they ruffled his thinking enough to detract from his mathematics.

[@StefanS117MC]

though, sex is pretty cool ...and god, too

[@TheMoo1231]

Too far lol