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

[@khanacademy]

@jsaic The power of mathematics is that it can abstract problems from many different domains AND tell us fundamental things about our universe (which may also turn out to be useful). It really is a purer philosophy (not jaded by fuzzy word play) that also turns out to be the core of science and technology. When I first learned about Euler's Line, it gave me goosebumps. Tells me that there is a deep structure to the universe that we are only beginning to catch glimpses of.

[@harshalbanti2120]

Sir why did you take line OFG as transversal or straight line while proving while taking vertical opposite angle you have already considered it is straight line ... In proof off can't be taken straight because we have to proove it

[@GetMeThere1]

Just AWESOME. The next time I have some free time (I'm trying to schedule for sometime in 2015) I'm going to get some good material on this stuff and plunge into it. It really PROFOUNDLY FASCINATES me.... Thanks for bringing this moving information to us, Sal.

[@sweetysureka1573]

yo howz life 12 years laterr

[@GetMeThere1]

@@sweetysureka1573 still plagued by stupid youtube comments.

[@Nikifuj908]

I find it sad that folks see mathematics as a tool to be used in "the real world". That's one aspect of it, but give math some credit as a field of its own. I'd like to see someone list the applications of engineering in math for a change. Mathematics is more than just a tool. It's a pursuit in its own right. I mean, we don't teach performing arts just so people can compete in today's dramatic world; we have performing arts class because performing arts is beautiful.

[@zack_120]

0:28 - NEAT! Unfortunately though the INcenter of this triangle is NOT in the Euler line 😂

[@yulonglian2137]

Hi! Just wanted to put it out there that homothety can be used for a much simpler proof! If anyone wants to find out just search it up online.

[@heesoolee8788]

You should also add that triangle DEF's vertices are made of the three bisecting dots of their respective lines. And that line segment ED is parallel to line segment BD and soon with the other pairs. And the proof with vectors on a graph is much easier.

[@rolfch1p]

Excellent Proof!

[@ohwhererehwho]

Do bubbles observe these trigometric laws of Euler's triangles in 3D? I would think so - which would be quite interesting. Resonance nodes and locations of peaks would also be identified...if the surfaces or wires (strings) were to be uniform along the axes you are defining. Cool extrapolations can be made.

[@suppandi1000]

It was beautiful,sal

[@heesoolee8788]

And can you post a video about how is the circumcenter the orthocenter.

[@anubhavamishra]

Just take simple two similar triangle FOG ~ CIG as vertically opposite angles are equal and FY||CX As FG:CG = 1:2 so OG:GI = 1:2

[@PrashantSingh-rm7zr]

you can't take vertically opposite angles as equal, because they aren't equal untill you prove that OI is a st. line, that's what he was doing in this video

[@ooker777]

in your last video, you said that this line has a magical relationship with Euler's formula. Can you show me what is it Sal? plz plz plz

[@heysiri3327]

This is a nice proof, but do not forget about the very very simple Vertical Angles Property.

[@smitashripad9757]

G is the incentre of FED(also known as the pedal triangle)

[@atinfinityplus]

thank you, sal. however, i remember, while in school, i used to always think "yeah, but...."(meaning, what are all of these things used for in the real world?). i know your main concern is getting the information across, but it's never clear how these things get implemented into the real world. is it helpful in programming, or software engineering, or architecture, game design...? probably, but how?

[@4ltrz555]

Ayy hello. You still alive?

[@radekmartin6328]

Do they teach this in High School?

[@mukulkumar8611]

No

[@abhinavlathwal7508]

This is taught to us by our maths teacher in 9th class

[@Scalifs]

This looks very interesting but I'm not old enough to know half the vocabulary Sal says :[

[@ericj199]

old enough now?