+lai yong hui i know it is my favorite since my school years, though i never had a reason :)
@simonlai31598 жыл бұрын
+Giorgos Chatziioannou (LezantasGR34T) Same. But when I showed these 'triangles' to friend, they don't care about it
@SpaghettiToaster8 жыл бұрын
+lai yong hui Please, everyone knows the octagon is the most holy of shapes.
@dinonid12347 жыл бұрын
I've never been so into geometry as after watching this.
@ndbchannellocustgroveva19525 жыл бұрын
OMG, I'm in love!
@MAFLSTAR7 жыл бұрын
I kinda have a crush on this lady...
@fandomewhisper4 жыл бұрын
Yes
@guidenredhawk3 жыл бұрын
Me too
@StuziCamis8 жыл бұрын
Could you do this with 3-D objects like, say, a triangular-based pyramid?
@erikziak12498 жыл бұрын
You know that you are old when watching this brings up memories which seem to you like being from a time when dinosaurs roamed the earth. I feel so old right now.
@AnalyticalReckoner8 жыл бұрын
Can you use the 3 points on the line to work out the dimensions of the triangle?
@KrazyisSloth8 жыл бұрын
+Omnis Imperator I'm not 100% sure, but I would guess no. Since the distances are always in ratio 1:2, they only information the centres give you is an overall scale. That one piece of information isn't enough to uniquely define a triangle, you'd need three numbers to do that.
@niksxr8 жыл бұрын
+Omnis Imperator easy No, the easiest case is the 3 centers lying on the same point - insta showstopper. When thinking about the other cases, it seems to me that you can figure out the dimensions if you know the centers plus either 1 angle or 1 side length (and which angle/side is meant). Can't prove it though
@MushookieMan3 жыл бұрын
@@niksxr You can rotate, scale, and translate *any* non equilateral triangle so that all three centers coincide with another non-equilateral triangle. Because this gives you almost no information about the triangle, you almost definitely need two pieces of information.
@niksxr3 жыл бұрын
@@MushookieMan thanks, yes. But I think you just need one more defined piece of the triangle to define it all
@MushookieMan3 жыл бұрын
@@niksxr No, you need a minimum of two. If you were given just one angle, for example, the other two angles can take on a whole range of values. But, for any of those potential triangles, you know you can rotate and scale them so their centers lie on the same three points as what you were given. That means you haven't distinguished between all those possibilities.
@SunriseFireberry8 жыл бұрын
For non-Euclidian (positively or negatively curved space) triangles, is the Euler line in some sense straight or are they curved, or do they even have an Euler line at all?
@LordLOC8 жыл бұрын
+TimeAndChance If I remember from my college days properly, I don't believe there is a Euler line at all in non-Euclidian geometry.
@LittlePeng98 жыл бұрын
+TimeAndChance I'm afraid that in non-Euclidean planes the three centers might not even exist (i.e. the lines defining them might not coincide).
@theodorostsilikis40256 жыл бұрын
the center of mass exists for sure,same place with constant curvature,varying place with locally varying curvature
@EtzEchad8 жыл бұрын
Professor Stankova is truly a gifted teacher.
@zeppelin171716 жыл бұрын
she's such a brilliant teacher
@InShortSight8 жыл бұрын
Are there 3 dimensional shape's with similar properties? I ask because the animations make the magic highway look like it creates a Z axis perpendicular to an equilateral triangle which is rotating in 3 dimensional space. It could be cool to see a similar effect on an already 3D shape :3
@szafranizm8 жыл бұрын
What a great easiness of delivering knowlage!
@unvergebeneid8 жыл бұрын
+Mateusz Szafrański For some reason I imagine "knowlage" being pronounced French, while swirling some red wine. "Quelle facilité à délivrer du no-laaaaaage, n'est-ce pas ?"
@Eazoon8 жыл бұрын
Can a similar line be created with a pyramid?
@lbblackburn8 жыл бұрын
Beautiful proofs. This professor explains the proofs very well. I remember a harder proof that the Euler line exists--so I learned something new.
@VierfachLP8 жыл бұрын
11:10 Triforce
@hakkbak8 жыл бұрын
:l
@Banzybanz5 жыл бұрын
15 more minutes with this beautiful lady
@danhoenn6 жыл бұрын
Does the euler line give enough information about the triangle it describes to construct a triangle when only given it's euler line? Or is there not enough information inherent in the different points
@SumNutOnU2b5 жыл бұрын
I came here to ask this same question. Although not of the line itself but the three points specifically. Given the line only (as a complete, extended line) then it wouldn't be so. Obviously if you change the triangle but only enlarge or shrink it and keep the same proportions then the line will stay the same but the three centers will shift position along that line. I think if you have only the line segment terminated by the Ortho- and circum- centers then that should be enough to define two triangles (one with the centroid at 1/3 and another with it at 2/3), and having all three would definitively define only one triangle. But it's hard to tell for sure. I tried to Denise a method of working backwards to get the triangle, but I got lost and couldn't get there. I think it can be done though, I just couldn't figure out how
@NoriMori19928 жыл бұрын
Zvezda has such nice printing.
@susclik3 жыл бұрын
The triangle can be described and represented as three points on a line. SO you can draw a line, put points on it and have a triangle.
@unvergebeneid8 жыл бұрын
Well, all triangles whose vertices don't lie on a circle also don't have an orthocentre. It just so happens that there are no such triangles but still.
@AscendingApsolut8 жыл бұрын
funny...
@unvergebeneid8 жыл бұрын
AscendingApsolut No, just a set-theoretically true statement ...
@AscendingApsolut8 жыл бұрын
It doesn't make it less funny.(to me)
@unvergebeneid8 жыл бұрын
AscendingApsolut Well ok, then I'm glad you enjoyed yourself :)
@AscendingApsolut8 жыл бұрын
*;)*
@devjock8 жыл бұрын
Is there a special name for the point halfway between the centroid and the orthocenter on the Euler line? (13:37 unnamed point between G and H)
@theodorostsilikis40256 жыл бұрын
i think its name is bill
@SumNutOnU2b5 жыл бұрын
I wanted to know this too. It ought to have a name but they don't mention it. 🤔
@halyoalex89423 жыл бұрын
Look it up, you may be able to give it a cool name
@therealelement75 Жыл бұрын
9 point circle, center of the circle running through the midpoints of each line, where the altitudes intersect, and the midpoint between the vertices and the orthocenter
@venkybabu81402 жыл бұрын
Just how they produce frequency. Some kind of following Euler lines. So maybe spheres produce frequency on those points for something like earth. That's why tides are in pressure gradients. Mostly stress lines for quakes. When they move.
@scowell7 жыл бұрын
Lots of fun to load up CARMetal and play with this.
@hassanaitoufkir830810 ай бұрын
Beautiful mind
@lidorshimoni54703 жыл бұрын
I so love the pro. Does she write some math books?
@Kram10328 жыл бұрын
Nice proof :)
@aryamankejriwal59597 жыл бұрын
Mind = Blown🎇🎆🎆🎇🎆🎇🎆
@icyzoneinfo8 жыл бұрын
I think she meant "triangle", not "circle" in 1:40
@AgentM1248 жыл бұрын
11:25 triforce! °o°
@soldtobediers5 жыл бұрын
Numbers cannot lie.
@petercoolbaugh68503 жыл бұрын
What is the relation between the largest spheres that could fit within pyramids with the triangle as the base, and the centers as the ceilings?
@themobiusfunction3 жыл бұрын
What's the Euler line for an equaliteral triangle? Is it just a point?
@icrin_8 жыл бұрын
which program was used to do that triangle?
@TheTruthSentMe8 жыл бұрын
+Icaro Vasconcelos I don't know which particular program this is. Though Geogebra can do the same and more.
@ratlinggull22238 жыл бұрын
MS Paint
@wolf10665 жыл бұрын
So glad this extra footage was here. After watching the previous video at kzbin.info/www/bejne/rYerZYCJa9tlabc I had to come looking for this.
@jetx9988 жыл бұрын
At 2:34 there's a sound of a piano key in the back ground, it's also in both the hook number videos, what's going on?!
@apeman52918 жыл бұрын
How do we know that the orthocenter of the little triangle is the circumcenter of the big triangle?
@pooiyx8 жыл бұрын
What is the practical purpose of the orthocentre though? The centroid is the geometric centre, the circumcentre is the centre of the circumcircle, and the incentre is the centre of the incircle. But where does the orthocentre "come from", other than just being the intersection of the 3 altitudes?
@ThichMauXanh3 жыл бұрын
orthocenter is very much related to circumcenter. First thing we know are from this video, orthocenter is circumcenter reflected twice about the medicenter. Second: if you reflect each altitude about the corresponding angle bisector, the three reflections meet at the circumcenter, that's why orthocenter & circumcenter are called "Isogonal Conjugates". Third: when you reflect Orthocenter about the three sides of the triangle, the three reflections all lie on the circumcircle. So in a way you are right, orthocenter is just some derivative of circumcenter.
@DragonMasterClay8 жыл бұрын
So, can we take a triangular prism with a triangular base and stick a sphere in it and around it and poke some lines through it with similar results? I kinda want to try.
@hyrekandragon26657 жыл бұрын
No you need to use a tetrahedron. A shape made.up of 4 triangles. It's also known as a triangular pyramid.
@theodorostsilikis40256 жыл бұрын
don't do it,people who did all died
@YoniMek5 жыл бұрын
Does the tetrahedron have some type of euler surface?
@waverlyseptember48918 жыл бұрын
What I would now like to know is this: do these centres (or other centres) and the Euler line exist for a triangle on a non-euclidean surface, and if so, how does the curvature (whether positive or negative) of the surface affect the centres and Euler line?
@Ethereal-me8 жыл бұрын
+Jane Stacey I'm just guessing here from the top of my head, that they (the centres) will exist and indeed there will be an Euler line. But it will of course follow the curvature, the same way as the medians and all other lines will do. In fact curvature will have nothing to do with it. Take a piece of fabric, draw the shapes and lines and just play with the cloth... :)
@prithwishguha309 Жыл бұрын
Well the SAS similarity was bogus similarity is shown by angle not side length and it's much easier too
@Hinyousha4 жыл бұрын
Does an euler line appears also in Non-Euclidian spaces??
@alanturingtesla7 жыл бұрын
What about a Euler plane surface for pyramids? And is there a Euler pyramid for 4 dimensional "pyramids"?
@rhyswells87257 жыл бұрын
should link a pdf explaining the math behind these videos
@puskajussi378 жыл бұрын
Could a closed line be considered a two angled polygon? Would monogon be a point, a line with one end or an anfinite line with one bend in it?
@lock_ray8 жыл бұрын
+puskajussi37 You can't really have a two-gon in euclidean space, because it just degenerates into a line segment... but on the surface of a sphere you can! You could also think of making a monogon on a sphere but I guess that just degenerates into a great circle... which in this geometry is just equivalent to a straight line. Point is... you need curvature to make these things work properly.
@edwardilie94887 жыл бұрын
can we build a smaller congruent triangle with the 3 centers of the bigger triangle?
@keescanalfp51435 жыл бұрын
nice question. suppose not really a smaller one, but at any case one mirrored about / over the euler line.
@gbear10054 жыл бұрын
Isnt a poont just a representation of a line perpendicular to the plane
@MrGreyprof8 жыл бұрын
13:58 What happens with this 2:1 proof when the triangle "goes" towards an equilateral triangle. Then all the points are on top of each other, and therefore the ratio must be different when that is the case, and just before that is the case as well?? Anyone??
@idk70168 жыл бұрын
I think the equilateral triangle is only the case, but for the triangles before that it's still 2:1
@fabiant.24857 жыл бұрын
When you have an equilateral triangle the 2:1 relationship is technically still valid. Think of it like this: the distance from the Orthocenter to the Medicenter is always 2 times longer than the distance of the Circumcenter to the Medicenter. Simpler put "CM = 2*OM" or "CM/2 = OM" whichever you prefer. in an equilateral triangle the distances are obviously zero, so the equation goes "0 = 2*0" -> "0 = 0" or "0/2 = 0" -> "0 = 0" which are both true statements, thus the rule is not broken. Now if you were to shift any of the three points of an equilateral triangle in any direction by any Infinitesimal length "X" (a number so small that it is basically 1/∞), then the Orthocenter and Medicenter would move apart the exact same Infinitesimal length "X" and the Circumcenter and Medicenter would move apart exactly half that Infinitesimal length or "X / 2".
@idk70167 жыл бұрын
Kiba Nemial Wow, that does work. Thanks
@jethrojangles95418 жыл бұрын
those freehand straight lines, tho
@Dave.Cooper8 жыл бұрын
Why is the camera continuously moving?
@ozdergekko8 жыл бұрын
A language question about a word that I hear frequently in math/physics context, but cant't get the meaning of. It sounds like "guy" or "guide"; in this video it's used e.g. at 6:04. Help, anyone? spelling? proper uses? thx!
@tamaboyle8 жыл бұрын
+ozdergecko It's "this guy". It's just a colloquial demonstrative pronoun for a thing. en.wiktionary.org/wiki/guy#Etymology_2
@Schindlabua8 жыл бұрын
+ozdergecko seawas! "This guy" = "Der do"
@ozdergekko8 жыл бұрын
Schindlabua jössas, der. jo, eh! pfiat enk, sogt da peda
@GglSux5 жыл бұрын
Hmmm... I don't know if I (or someone else) should be concerned by the fact that this is the fifth time (or sixth... honestly I've lost count) I watch this video. Every time I restart my browser it reloads the "previous session" and I usually start by just closing the old pages that I have already "read/watched" but every time I come to this one I watch it again... And leave it for the next "session"... Maybe I'm in need of an intervention, am I the first "documented case" of "numberphilea" ? :)
@VincentFarrugia8 жыл бұрын
Free Dell advert
@GB-fh5tt2 жыл бұрын
"you realize some coincides are theorems, and then you try to prove them"
@professorpoke4 жыл бұрын
She has a nice handwriting.
@psaini19998 жыл бұрын
Wow
@Xayuap2 жыл бұрын
¿what about their ratio?
@Xayuap2 жыл бұрын
see till the end prior to comment
@abcdef20698 жыл бұрын
i understabnd ED=1/2 AB i dont understand GD=1/2 AG fast
Sorry Pete, but you missed a 'z' on young Zvezda's geometry notes! :p
@jesuspena34605 жыл бұрын
I want to marry her, seriously
@RanEncounter8 жыл бұрын
Illuminati confirmed?
@stumbling8 жыл бұрын
+RanEncounter 3 centres on the Euler line. HALF LIFE 3 CONFIRMED!
@MuradBeybalaev7 жыл бұрын
You aren't gonna last long in a geometry class with that habit.
@dijjit8 жыл бұрын
I knew Zelda emblem was going to show up here
@TheSentientCloud8 жыл бұрын
The Golden triangle seems to have a lot of unique properties involving the Golden ratio itself.. I'm wondering if possibly the Euler line's points lies in a Golden ratio fashion as well...
@gugurlqk3 жыл бұрын
EG BG джи джи биджи
@putu67 жыл бұрын
Excellent presentation. Visit us in South Africa: you will change the image of math.
@abcdef20698 жыл бұрын
more camera focus on the paper, and not on the person, this gives me a headache. this is a main problem with num philes.
@ThichMauXanh3 жыл бұрын
marry me professor.
@NickMC5125 жыл бұрын
I would marry a woman Iike this. I don’t care if she’s older or not. Intelligent, passionate, educated women > all others.
@duongquocthongho21173 жыл бұрын
i love the lady :D
@joannfreedman17945 жыл бұрын
Apparently the tryangle allows spirits to come through from another demention! Jayz and so many in the music industry use this symbol. Satan can use this as an energy feild but so does The LORD! The devil is always trying to userp GOD'S power.