It makes me smile each times she says "it better". I don’t know her but I can imagine how good she is as a funny lovely teacher for kids. Thank you. Love it.
at a glance, after watching the rotation animations in the beginning, I'd say every triangle is equilateral, but not in the literal numberphile sense... more like... it describes a plane, and it's "eccentricity" is the amount that plane has been rotated/skewed/squished/whatever before projecting onto 2D. Likewise, Euler's line appears to be perpendicular to the triangle's original plane. My intuition is to try to prove something via linear algebra re: the orthogonality of euler's line to the triangle in some basis.
There is one thing which is difficult to grasp : I mean how can you say that the distance between the vertex and orthocentre will get halved...i mean this is quite intuitive but is there some very short proof(or even a prompt reply) which makes me to believe that..... P.S. awesome video by the way (Y)
And there is one more thing I am curious to know about : actually i was trying to prove it by myself but i was unable to do so...is there some other easy proof which does not require the medial triangle and is easy for a beginner to come up with?...Thanks a lot in advance.
Thank you so much! May I please know what program you used for the interactive triangles? It would be a great help if I used them and tried it out on my own!
I used a program called Geogebra (free!) to do it. On the calculator, you want to go into the geometry mode and get rid of the grid and axes in the settings.
What about the equilateral triangle? In an equilateral triangle, the orthocentre, the centroid, and the circumcentre all coincide. If three points coincide, are they collinear?
What a great question! I can safely say that they are not noncollinear (sorry for the double negative). Since they coincide, there are actually an infinite number of lines that would pass through all of them simultaneously. It would seem that the term collinear loses its usefulness in describing the relationship between the centroid, circumcenter, and orthocenter of an equilateral triangle...
@@kcmathhelp The explanation and the animation is awesome. Could you please let me know whether you had to pay any license fee to Geogebra for using their software for making videos for TH-cam channel..?
It makes me smile each times she says "it better". I don’t know her but I can imagine how good she is as a funny lovely teacher for kids. Thank you. Love it.
Lovely proof with excellent quality of both presentation and production.
at a glance, after watching the rotation animations in the beginning, I'd say every triangle is equilateral, but not in the literal numberphile sense... more like... it describes a plane, and it's "eccentricity" is the amount that plane has been rotated/skewed/squished/whatever before projecting onto 2D. Likewise, Euler's line appears to be perpendicular to the triangle's original plane. My intuition is to try to prove something via linear algebra re: the orthogonality of euler's line to the triangle in some basis.
Presentation couldnt be better!
Thank you for the great video!
Great explanation, flawless.
Excellent👌
This was so clear! Outstanding!
Nice work
Great explanation thank you
There is one thing which is difficult to grasp : I mean how can you say that the distance between the vertex and orthocentre will get halved...i mean this is quite intuitive but is there some very short proof(or even a prompt reply) which makes me to believe that.....
P.S. awesome video by the way (Y)
Great Work...Excellent...
Can You tell me the name of the application you used here????please,...
Geogebra
Neatly done -- with nothing more than Euclidean geometry.
And there is one more thing I am curious to know about : actually i was trying to prove it by myself but i was unable to do so...is there some other easy proof which does not require the medial triangle and is easy for a beginner to come up with?...Thanks a lot in advance.
Outstanding!
Do you use facebook or twitter?
Brilliant
Thank you so much!
May I please know what program you used for the interactive triangles? It would be a great help if I used them and tried it out on my own!
I used a program called Geogebra (free!) to do it. On the calculator, you want to go into the geometry mode and get rid of the grid and axes in the settings.
@@kcmathhelp thank you!
great explanation thank you mam
What about the equilateral triangle? In an equilateral triangle, the orthocentre, the centroid, and the circumcentre all coincide. If three points coincide, are they collinear?
What a great question! I can safely say that they are not noncollinear (sorry for the double negative). Since they coincide, there are actually an infinite number of lines that would pass through all of them simultaneously. It would seem that the term collinear loses its usefulness in describing the relationship between the centroid, circumcenter, and orthocenter of an equilateral triangle...
@@kcmathhelp Yes, you’re right. The collinearity of two or more points implies the uniqueness of the line that contains the points. Thanks.
What a terrific video! What software do you use to do the proofs?
Thanks! I used Geogebra for the geometry and Camtasia to capture my screen and edit the video.
@@kcmathhelp The explanation and the animation is awesome.
Could you please let me know whether you had to pay any license fee to Geogebra for using their software for making videos for TH-cam channel..?
thanks!
Salute!!!
Great content.....thanks:)
WHICH SOFTWARE YOU USE ???
Geogebra!
Great!