Triangle Centres and the Euler Line (extra footage)

  Рет қаралды 112,064

Numberphile2

Numberphile2

Күн бұрын

Пікірлер: 156
@TheGreatPizzaMasterpiece
@TheGreatPizzaMasterpiece 2 жыл бұрын
Math just never gets old. Thank you, always, for these learning tools!
@shardshunt
@shardshunt 8 жыл бұрын
that was like watching a mystery show. brilliant.
@monocledino
@monocledino 8 жыл бұрын
eyy it's my professor!!
@IMortage
@IMortage 8 жыл бұрын
+Butt McFarts You lucky sob.
@marvelous1358
@marvelous1358 8 жыл бұрын
congrats man. make the most of it.
@tomd1969
@tomd1969 8 жыл бұрын
I love Zvezda.
@1234eg9876
@1234eg9876 8 жыл бұрын
Marvelous demonstration.
@AlwaysLoisLane
@AlwaysLoisLane 6 жыл бұрын
When she said "And that unique point... is the Centroid.", I had a very steep inclination towards saying "I love you"
@Caye2013
@Caye2013 8 жыл бұрын
Thank you for these videos. I'm thinking seriously to support you on Patreon!
@PragyAgarwal
@PragyAgarwal 8 жыл бұрын
How does every person on this channel have a wonderfully pleasant voice and accent !?
@richardgurney1844
@richardgurney1844 3 жыл бұрын
They are chosen specially
@pablolichtig2536
@pablolichtig2536 4 жыл бұрын
This was just beautiful
@DrSegatron
@DrSegatron 8 жыл бұрын
The Euler line looks like a three-dimensional normal to the triangle face.
@melitamann1983
@melitamann1983 8 жыл бұрын
+DrSegatron I can see that, too. It looks like a triangle pierced by the euler line. It becomes really clear when the shape is changing.
@MuradBeybalaev
@MuradBeybalaev 7 жыл бұрын
Such perception delusion is not limited to Euler's line. No worth in pointing it out every time.
@theodorostsilikis4025
@theodorostsilikis4025 6 жыл бұрын
it is,and the proof can be much simple in 3 dimensions
@danhoenn
@danhoenn 6 жыл бұрын
In fact all of the triangles look like a shadow cast onto a piece of paper by an equilateral triangle being rotated about in 3D space!
@albertbirog.1888
@albertbirog.1888 7 жыл бұрын
A wonderful and useful presentation!
@BinaHejazi
@BinaHejazi 7 жыл бұрын
You are the most brilliant but more importantly the sweetest mathematician I have ever seen and all that makes you a MIRACLE!!
@Caye2013
@Caye2013 8 жыл бұрын
What a great mathematician!
@unvergebeneid
@unvergebeneid 8 жыл бұрын
+Caye2013 Leonhard Euler or Zvezdelina Stankova?
@Caye2013
@Caye2013 8 жыл бұрын
+Penny Lane Both hahaha
@simonlai3159
@simonlai3159 8 жыл бұрын
The triangle is the best polygon. I learnt this from vihart
@bluewisdomtriforce
@bluewisdomtriforce 8 жыл бұрын
triangle. triangle triangle triangle triangle triangle
@icrin_
@icrin_ 8 жыл бұрын
+lai yong hui it's even an instrument
@gchatz6480
@gchatz6480 8 жыл бұрын
+lai yong hui i know it is my favorite since my school years, though i never had a reason :)
@simonlai3159
@simonlai3159 8 жыл бұрын
+Giorgos Chatziioannou (LezantasGR34T) Same. But when I showed these 'triangles' to friend, they don't care about it
@SpaghettiToaster
@SpaghettiToaster 8 жыл бұрын
+lai yong hui Please, everyone knows the octagon is the most holy of shapes.
@dinonid1234
@dinonid1234 7 жыл бұрын
I've never been so into geometry as after watching this.
@ndbchannellocustgroveva1952
@ndbchannellocustgroveva1952 5 жыл бұрын
OMG, I'm in love!
@MAFLSTAR
@MAFLSTAR 7 жыл бұрын
I kinda have a crush on this lady...
@fandomewhisper
@fandomewhisper 4 жыл бұрын
Yes
@guidenredhawk
@guidenredhawk 3 жыл бұрын
Me too
@StuziCamis
@StuziCamis 8 жыл бұрын
Could you do this with 3-D objects like, say, a triangular-based pyramid?
@erikziak1249
@erikziak1249 8 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.
@AnalyticalReckoner
@AnalyticalReckoner 8 жыл бұрын
Can you use the 3 points on the line to work out the dimensions of the triangle?
@KrazyisSloth
@KrazyisSloth 8 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.
@niksxr
@niksxr 8 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
@MushookieMan
@MushookieMan 3 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.
@niksxr
@niksxr 3 жыл бұрын
@@MushookieMan thanks, yes. But I think you just need one more defined piece of the triangle to define it all
@MushookieMan
@MushookieMan 3 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.
@SunriseFireberry
@SunriseFireberry 8 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?
@LordLOC
@LordLOC 8 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.
@LittlePeng9
@LittlePeng9 8 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).
@theodorostsilikis4025
@theodorostsilikis4025 6 жыл бұрын
the center of mass exists for sure,same place with constant curvature,varying place with locally varying curvature
@EtzEchad
@EtzEchad 8 жыл бұрын
Professor Stankova is truly a gifted teacher.
@zeppelin17171
@zeppelin17171 6 жыл бұрын
she's such a brilliant teacher
@InShortSight
@InShortSight 8 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
@szafranizm
@szafranizm 8 жыл бұрын
What a great easiness of delivering knowlage!
@unvergebeneid
@unvergebeneid 8 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 ?"
@Eazoon
@Eazoon 8 жыл бұрын
Can a similar line be created with a pyramid?
@lbblackburn
@lbblackburn 8 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.
@VierfachLP
@VierfachLP 8 жыл бұрын
11:10 Triforce
@hakkbak
@hakkbak 8 жыл бұрын
:l
@Banzybanz
@Banzybanz 5 жыл бұрын
15 more minutes with this beautiful lady
@danhoenn
@danhoenn 6 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
@SumNutOnU2b
@SumNutOnU2b 5 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
@NoriMori1992
@NoriMori1992 8 жыл бұрын
Zvezda has such nice printing.
@susclik
@susclik 3 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.
@unvergebeneid
@unvergebeneid 8 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.
@AscendingApsolut
@AscendingApsolut 8 жыл бұрын
funny...
@unvergebeneid
@unvergebeneid 8 жыл бұрын
AscendingApsolut No, just a set-theoretically true statement ...
@AscendingApsolut
@AscendingApsolut 8 жыл бұрын
It doesn't make it less funny.(to me)
@unvergebeneid
@unvergebeneid 8 жыл бұрын
AscendingApsolut Well ok, then I'm glad you enjoyed yourself :)
@AscendingApsolut
@AscendingApsolut 8 жыл бұрын
*;)*
@devjock
@devjock 8 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)
@theodorostsilikis4025
@theodorostsilikis4025 6 жыл бұрын
i think its name is bill
@SumNutOnU2b
@SumNutOnU2b 5 жыл бұрын
I wanted to know this too. It ought to have a name but they don't mention it. 🤔
@halyoalex8942
@halyoalex8942 3 жыл бұрын
Look it up, you may be able to give it a cool name
@therealelement75
@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
@venkybabu8140
@venkybabu8140 2 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.
@scowell
@scowell 7 жыл бұрын
Lots of fun to load up CARMetal and play with this.
@hassanaitoufkir8308
@hassanaitoufkir8308 10 ай бұрын
Beautiful mind
@lidorshimoni5470
@lidorshimoni5470 3 жыл бұрын
I so love the pro. Does she write some math books?
@Kram1032
@Kram1032 8 жыл бұрын
Nice proof :)
@aryamankejriwal5959
@aryamankejriwal5959 7 жыл бұрын
Mind = Blown🎇🎆🎆🎇🎆🎇🎆
@icyzoneinfo
@icyzoneinfo 8 жыл бұрын
I think she meant "triangle", not "circle" in 1:40
@AgentM124
@AgentM124 8 жыл бұрын
11:25 triforce! °o°
@soldtobediers
@soldtobediers 5 жыл бұрын
Numbers cannot lie.
@petercoolbaugh6850
@petercoolbaugh6850 3 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?
@themobiusfunction
@themobiusfunction 3 жыл бұрын
What's the Euler line for an equaliteral triangle? Is it just a point?
@icrin_
@icrin_ 8 жыл бұрын
which program was used to do that triangle?
@TheTruthSentMe
@TheTruthSentMe 8 жыл бұрын
+Icaro Vasconcelos I don't know which particular program this is. Though Geogebra can do the same and more.
@ratlinggull2223
@ratlinggull2223 8 жыл бұрын
MS Paint
@wolf1066
@wolf1066 5 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.
@jetx998
@jetx998 8 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?!
@apeman5291
@apeman5291 8 жыл бұрын
How do we know that the orthocenter of the little triangle is the circumcenter of the big triangle?
@pooiyx
@pooiyx 8 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?
@ThichMauXanh
@ThichMauXanh 3 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.
@DragonMasterClay
@DragonMasterClay 8 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.
@hyrekandragon2665
@hyrekandragon2665 7 жыл бұрын
No you need to use a tetrahedron. A shape made.up of 4 triangles. It's also known as a triangular pyramid.
@theodorostsilikis4025
@theodorostsilikis4025 6 жыл бұрын
don't do it,people who did all died
@YoniMek
@YoniMek 5 жыл бұрын
Does the tetrahedron have some type of euler surface?
@waverlyseptember4891
@waverlyseptember4891 8 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-me
@Ethereal-me 8 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
@prithwishguha309 Жыл бұрын
Well the SAS similarity was bogus similarity is shown by angle not side length and it's much easier too
@Hinyousha
@Hinyousha 4 жыл бұрын
Does an euler line appears also in Non-Euclidian spaces??
@alanturingtesla
@alanturingtesla 7 жыл бұрын
What about a Euler plane surface for pyramids? And is there a Euler pyramid for 4 dimensional "pyramids"?
@rhyswells8725
@rhyswells8725 7 жыл бұрын
should link a pdf explaining the math behind these videos
@puskajussi37
@puskajussi37 8 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_ray
@lock_ray 8 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.
@edwardilie9488
@edwardilie9488 7 жыл бұрын
can we build a smaller congruent triangle with the 3 centers of the bigger triangle?
@keescanalfp5143
@keescanalfp5143 5 жыл бұрын
nice question. suppose not really a smaller one, but at any case one mirrored about / over the euler line.
@gbear1005
@gbear1005 4 жыл бұрын
Isnt a poont just a representation of a line perpendicular to the plane
@MrGreyprof
@MrGreyprof 8 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??
@idk7016
@idk7016 8 жыл бұрын
I think the equilateral triangle is only the case, but for the triangles before that it's still 2:1
@fabiant.2485
@fabiant.2485 7 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".
@idk7016
@idk7016 7 жыл бұрын
Kiba Nemial Wow, that does work. Thanks
@jethrojangles9541
@jethrojangles9541 8 жыл бұрын
those freehand straight lines, tho
@Dave.Cooper
@Dave.Cooper 8 жыл бұрын
Why is the camera continuously moving?
@ozdergekko
@ozdergekko 8 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!
@tamaboyle
@tamaboyle 8 жыл бұрын
+ozdergecko It's "this guy". It's just a colloquial demonstrative pronoun for a thing. en.wiktionary.org/wiki/guy#Etymology_2
@Schindlabua
@Schindlabua 8 жыл бұрын
+ozdergecko seawas! "This guy" = "Der do"
@ozdergekko
@ozdergekko 8 жыл бұрын
Schindlabua jössas, der. jo, eh! pfiat enk, sogt da peda
@GglSux
@GglSux 5 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" ? :)
@VincentFarrugia
@VincentFarrugia 8 жыл бұрын
Free Dell advert
@GB-fh5tt
@GB-fh5tt 2 жыл бұрын
"you realize some coincides are theorems, and then you try to prove them"
@professorpoke
@professorpoke 4 жыл бұрын
She has a nice handwriting.
@psaini1999
@psaini1999 8 жыл бұрын
Wow
@Xayuap
@Xayuap 2 жыл бұрын
¿what about their ratio?
@Xayuap
@Xayuap 2 жыл бұрын
see till the end prior to comment
@abcdef2069
@abcdef2069 8 жыл бұрын
i understabnd ED=1/2 AB i dont understand GD=1/2 AG fast
@postbodzapism
@postbodzapism 8 жыл бұрын
There are more than 200 triangle centers
@stigcc
@stigcc 7 жыл бұрын
relike868p Really?
@scowell
@scowell 7 жыл бұрын
en.wikipedia.org/wiki/Encyclopedia_of_Triangle_Centers
@venkateshbabu5623
@venkateshbabu5623 6 жыл бұрын
Saturn turn is the e. The Euler numbers mess.
@quantiplex
@quantiplex 8 жыл бұрын
Sorry Pete, but you missed a 'z' on young Zvezda's geometry notes! :p
@jesuspena3460
@jesuspena3460 5 жыл бұрын
I want to marry her, seriously
@RanEncounter
@RanEncounter 8 жыл бұрын
Illuminati confirmed?
@stumbling
@stumbling 8 жыл бұрын
+RanEncounter 3 centres on the Euler line. HALF LIFE 3 CONFIRMED!
@MuradBeybalaev
@MuradBeybalaev 7 жыл бұрын
You aren't gonna last long in a geometry class with that habit.
@dijjit
@dijjit 8 жыл бұрын
I knew Zelda emblem was going to show up here
@TheSentientCloud
@TheSentientCloud 8 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...
@gugurlqk
@gugurlqk 3 жыл бұрын
EG BG джи джи биджи
@putu6
@putu6 7 жыл бұрын
Excellent presentation. Visit us in South Africa: you will change the image of math.
@abcdef2069
@abcdef2069 8 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.
@ThichMauXanh
@ThichMauXanh 3 жыл бұрын
marry me professor.
@NickMC512
@NickMC512 5 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.
@duongquocthongho2117
@duongquocthongho2117 3 жыл бұрын
i love the lady :D
@joannfreedman1794
@joannfreedman1794 5 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.
Cow-culus and Elegant Geometry - Numberphile
22:00
Numberphile
Рет қаралды 148 М.
The Foundation of Mathematics - Numberphile
15:11
Numberphile2
Рет қаралды 109 М.
黑天使被操控了#short #angel #clown
00:40
Super Beauty team
Рет қаралды 41 МЛН
快乐总是短暂的!😂 #搞笑夫妻 #爱美食爱生活 #搞笑达人
00:14
朱大帅and依美姐
Рет қаралды 15 МЛН
黑天使只对C罗有感觉#short #angel #clown
00:39
Super Beauty team
Рет қаралды 22 МЛН
Do you love Blackpink?🖤🩷
00:23
Karina
Рет қаралды 23 МЛН
Weber's Law - Numberphile
9:03
Numberphile
Рет қаралды 988 М.
Beautiful Trigonometry - Numberphile
12:07
Numberphile
Рет қаралды 825 М.
All possible pythagorean triples, visualized
16:58
3Blue1Brown
Рет қаралды 3,9 МЛН
Squares & Triangles (EXTRA FOOTAGE #1)
6:13
Numberphile2
Рет қаралды 64 М.
Untouchable Numbers - Numberphile
8:09
Numberphile2
Рет қаралды 153 М.
The Return of the Legend of Question Six - Numberphile
16:04
Numberphile2
Рет қаралды 2,1 МЛН
Nash Embedding Theorem - Numberphile
13:42
Numberphile2
Рет қаралды 373 М.
A Miraculous Proof (Ptolemy's Theorem) - Numberphile
38:28
Numberphile
Рет қаралды 1 МЛН
Times Tables, Mandelbrot and the Heart of Mathematics
13:37
Mathologer
Рет қаралды 2,8 МЛН
黑天使被操控了#short #angel #clown
00:40
Super Beauty team
Рет қаралды 41 МЛН