You should have Zvezdelina do more videos, I never get bored when she is explaining something.

I cannot get my head around how Zvezdelina can draw all these diagrams so well just by hand. I can't even manage a straight line by hand at all, let alone one which bisects an angle and meets a line at its midpoint.

@timetogetcancer7866

8 жыл бұрын

And then you see them draw a 3d shape

@NikopolAU

8 жыл бұрын

+Castor Quinn quit drinking then

@yali_shanda

8 жыл бұрын

In Soviet Russia, triangles draw you.

@yali_shanda

8 жыл бұрын

+Yali Shanda Or, should I say in this case, Soviet Bulgaria.

@bgezal

8 жыл бұрын

+Castor Quinn Just draw triangles for a couple of decades and you will also become master.

1:00 Nice nod to the Vitosha computer, the first Bulgarian made computer :)

@vailias

8 жыл бұрын

+Scrotie McBoogerball Thank you! I could read the text but didn't know the word. (google translate was of zero help also)

@SparklyRazor

8 жыл бұрын

+Scrotie McBoogerball Ah, I wondered what that was!

@ivayloivggrigorov9959

8 жыл бұрын

+vailias it's also called after a mountain.

@rdreher7380

8 жыл бұрын

+Scrotie McBoogerball Ah that's what it was. I know Russian, so I could read it, and I figured out it was Bulgarian, and the name of a mountain, but I had no idea what the reference was here.

@icyzoneinfo

8 жыл бұрын

I was just going to ask what does the mountain have to do with computers :D

We've learned two things: - the animations are VERY well done - that lady REALLY likes triangles :)

@malinastankova4918

3 жыл бұрын

lol

@Triantalex

8 ай бұрын

false.

Damn you got Question 6 Right!!!

@unounk9415

6 жыл бұрын

in less than 4.5 hours!

@unounk9415

6 жыл бұрын

it took the guy in the main video a YEAR to solve it

@unounk9415

6 жыл бұрын

in less than 4.5 hours! It took the guy in the main video a YEAR to solve it, and the hosts of the competition couldn't solve it in 6 hours

@sobanudlz

5 жыл бұрын

Im still Uno Unk

@hawthornroot

4 жыл бұрын

with a perf score of 7

“Some of his [Euler's] simplest discoveries are of such a nature that one can well imagine the ghost of Euclid saying, 'Why on earth didn't I think of that?'” H. S. M. Coxeter

@Triantalex

8 ай бұрын

??

on which point of a triangle is the hospital located? the medicenter!

@laxpors

8 жыл бұрын

+Kristian Bernardo HA

@SpaghettiFace2

8 жыл бұрын

I would make a similar joke about the circumcenter, but it would just be awkward.

@FernieCanto

8 жыл бұрын

+SpaghettiFace2 I tried to do a circumcenter joke too, but it was cut.

@LosDynasty

8 жыл бұрын

+Fernie Canto I would make a joke about the orthocenter but it's not funny. its unorthodox. ( i tried. bye)

@EvolBob1

8 жыл бұрын

+Kristian Bernardo- Its funny. Its even funnier telling this, especially when I get a blank stare and I'm the only one laughing.Explaining it only makes it worst.

Pete, nice work on the animations, really helps with visualisation

@pmcpartlan

8 жыл бұрын

+Tom D.H Thank you, glad they helped.

@smaakjeks

8 жыл бұрын

+Pete McPartlan Yeah, great job!

@AD173

8 жыл бұрын

+Pete McPartlan Hey, what software do you use for the illustrations? I really need to know!

@xnopyt647

2 жыл бұрын

@@pmcpartlan You are awesome!

@ErikOosterwal

Жыл бұрын

At one point the animations looked like 3D representations with the triangle and medicenter lying on a plane and the circumcenter and orthocenter positioned above and below the plane. In this simulated 3D view it looks like the Euler line is perpendicular to the plane. 🤔

The "Nah just kidding" at 4:00 killed me

@judahdelrio3650

7 жыл бұрын

FliiFe what

@jamesterpaul

7 жыл бұрын

Judah Del Rio ahlie

@sobanudlz

5 жыл бұрын

More like 4:11 ALSO WATCH MY CHANNEL

@screamsinrussian5773

4 жыл бұрын

@@sobanudlz no, go away

@jassenjj

3 жыл бұрын

Did you think of Kristen Wiig? Just kiddin'...

The medicenter is where I have to go after watching this. My head hurts.

@Triantalex

8 ай бұрын

??

7:13 This really does look like a rotation in 3D rather than some purely 2D transformations. Cool.

@ErikOosterwal

Жыл бұрын

In this perspective it looks like the Euler line is perpendicular to the plane containing the triangle and medicenter.

Wow, I love when such simple geometry can produce such a seemingly magical result! And side-note; the graphics in this video were _awesomely_ done.

Animations were top notch this episode

great animation!

@numberphile

8 жыл бұрын

+Pisces Fool kudos to Pete for that... he did some nice stuff.

"Ooh! Fancy. I can get wild! Oo-ho!"

I could listen to Professor Stankova lecture all day.

This is one of my favorite numberphiles to date. A charming result, presenter, and animations.

my favorite property of the centroid (in Portuguese it's the 'baricentro') is that it's the triangle's center of gravity. this means that a triangle can be balanced on that point

@GenericInternetter

5 жыл бұрын

thanks, capitao obvio

@shambosaha9727

4 жыл бұрын

Barycentre literally means Centre of Mass

@shambosaha9727

4 жыл бұрын

Also, the centroid is the barycentre of just a triangular plate. The barycentre of a triangle-shaped wire is the Spieker centre.

@OptimusPhillip

2 жыл бұрын

*assuming that the weight distribution across the area of the triangle is constant.

anyone else notice during the animations that the Euler line coincides with the 2d projection of a line orthogonal to the plane of the triangle through its centroid? Fascinating.

@ExaltedDuck

8 жыл бұрын

...that is if we perceive the triangle with fixed vertices and rotating in a 3 dimensional space and projecting onto the plane as well.

@schnuffelwuff

8 жыл бұрын

And the Circle is the 2D Representation of a Sphere

@schnuffelwuff

8 жыл бұрын

+Patrick Waldner Okay this one may be wrong

@smaakjeks

8 жыл бұрын

+ExaltedDuck Yep!

@Mathhead2000

8 жыл бұрын

I was about to comment the same thing. They should make a follow-up video on that.

"I can get wild" well that made my day

I really like her accent

These videos makes me fall in love with maths!

I love the videos with helpful animations from Pete McPartlan and I love the videos with Zvezdelina Stankova, so this is absolutely wonderful. Thank you for the gift, Brady.

I really love the way Zvezdelina explains things!

So... Illuminati is Magical?

@theshadowmonster1

8 жыл бұрын

+Fiend Sweg Basically

@cubedude76

8 жыл бұрын

+Fiend Sweg is your icon the shade from warcraft 3?

@EebstertheGreat

8 жыл бұрын

+cubedude76 Yes, it's the beveled Undead Shade icon, which in DotA is used for the Shadow Fiend.

@Cloiss_

8 жыл бұрын

+Fiend Sweg Thats how our 8th grade Geometry class views it (even the teacher)

@ratlinggull2223

8 жыл бұрын

cubedude76 Yup, my icon is pretty much Shade with Shades.

I just thought of 4 new centers for a triangle, using the 4 that were introduced in this video. I haven't thought them through that much, but I'm interested in seeing if there are any weird mathematical properties about these centers. So here we go: 1. Anti-orthocenter: Take the centroid, circumcenter, and incenter of any triangle (that is, all the centers except the orthocenter), and those points will form a new triangle. Repeat the process for the new triangle, and for the next triangle, etc. Hopefully, the triangles should get progressively smaller and converge to a point. That point is the anti-orthocenter. 2. Anti-centroid: Go through the same process that you would to find the anti-orthocenter, but this time use the circumcenter, incenter, and orthocenter (that is, all the centers except the centroid) as your three triangle-forming centers. 3. Anti-circumcenter: Same process as the previous two centers, but this time use the centroid, orthocenter, and incenter (that is, all the centers except the circumcenter) as your three triangle-forming centers. 4. Supercenter: Take the previous three centers of any triangle, and they will form a new triangle. (Actually, I have no idea if they do. It could be the case that the anti-orthocenter, anti-centroid, and anti-circumcenter are always collinear for all I know. That's an open question, and I'm interested in seeing a proof either way.) If they do form a triangle, take the anti-orthocenter, anti-centroid, and anti-circumcenter of that triangle to form another one. Repeat this process ad infinitum. Hopefully, these triangles will also get progressively smaller, and the point they converge to is the supercenter. Questions I'm interested in having answered: For which triangles do these centers exist, and for which triangles do they not? What I already know is that the center in question will not exist if one of the triangles along the way is actually a straight line (which is why there is no anti-incenter in this list), or if the triangles do not get smaller in a way that converge to a point. If the sequence of triangles constructed in calculating any of these centers doesn't converge to a point, what happens to them? Do any of these centers lie on the Euler line? If so, which ones? Is there a group of three of these centers that will always be collinear, provided they exist? Are there two centers (out of the ones I listed and the ones in the video) that are actually the same point in disguise? Are there any weird relationships between the smaller triangles constructed along the way and the original triangle? For example, are they similar? Do they share a common centroid, circumcenter, incenter, or orthocenter? How do the areas and side lengths compare?

@non-inertialobserver946

5 жыл бұрын

Very interesting

1:14 ooh fancy I can get wild ooOoOoh

This was figured out how LONG ago, and people are still wowed by it. Cause Math and Science ROCK!

Wow Brady! The editing and animation has really improved! Keep up the great work!!

This is arguably my favorite numberphile video. I love number theory but would to see more geometry, trigonometry, and calculus videos.

is it bad that i see the triangles and the lines as 3 dimensional ?

@emilysofiadelatorremartin524

8 жыл бұрын

i don't think so

@Hilko26

8 жыл бұрын

+Watchable No I had it too. It's just an automatic process of your brain trying to comprehend the things happening on the 2d screen.

@moazzamak

8 жыл бұрын

+Watchable It's worse then I expected. I'm afraid you have "The knack" :P

@Satchboy71

8 жыл бұрын

+Watchable When they moved the lines around it really did look three dimensional. The Euler line looked like the Z axis of sorts.

@CryZe92

8 жыл бұрын

+Watchable No, because once you have at least 4 points, a 3-dimensional projection can be clearly defined. So the 3 vertices of the triangle plus the additional center point form a 3-dimensional projection, making it look like it would be 3-dimensional.

greetings from Bulgaria! Great video Zvezdelina amd Brady!

I am in love ! And I am not even a Mathmatician !!! This is awesome ! Ms. Stankova is also so awesome !

That was some great and pertinent geometry animation. Excellent job! Thanks

centroid wins for me, can't have a centre that lies outside of the shape.

@justahker3988

8 жыл бұрын

+JackSwatman Incentre also can't lie outside the shape.

@tylerborgard8805

8 жыл бұрын

+JackSwatman If the center can't be outside the shape, then what about the center of a donut?

@Tumbolisu

8 жыл бұрын

+Tyler Borgard Not fair, that's a concave object.

@NotQuiteFirst

8 жыл бұрын

rekt

@JackSwatman

8 жыл бұрын

+Tyler Borgard I don't feel that totally nullifies my statement but it was very clever and unarguably true

That is elegant! I love to learn new concepts and see where they apply.

I love the Numberphile videos! They get the most fascinating people in them Thank you!

Love the animations, well done!

Fantastic stuff, thoroughly enjoyed this!! One of the things I recently learnt while reviewing analytic geometry is the theorem of Ceva. The cevians - medians, altitudes and angle bisectors are concurrent.

Ah ah, beautiful! Everybody would probably enjoy to have a teacher like that, she's turning simple Maths facts into fascinating questions and wonders. Just like James Grime ;-)

Brilliant Zvezdelina and Brady. Geometry is such a nice discipline.

I need a wife that will look at me like this woman looks at triangles.

@syedwaleedshah2830

5 жыл бұрын

well you gotta start drawing triangles on your body then , eh ?

@rafciopranks3570

5 жыл бұрын

What would be the sum of their angles?

@nicxtrem21

5 жыл бұрын

Imagine if she'd date food-writing glass-structure geometry genius guy

@mienzillaz

4 жыл бұрын

Any update?;)

@fishsauce2221

4 жыл бұрын

Was going to make a triangle joke but I didnt come up with anything.

Great presentation and great animation!!

Zvezdelina is awesome. Love her videos. Thanks Brady!

Usually, I watch Np to hear interesting things not heard before. This time it was a time machine taking me back 25-30 years and it was gooood.

I'm so happy I found this, I'm learning it in school rn and I've been having trouble

This is one of my favorite numberphile videos

I like the centroid as it is the center of mass, however my favourite center is the nine-point center. It also lies on the Euler line, btw. It is the midpoint of the orthocenter and the circumcenter, although that isn't the definition.

The animation at 7:15 looks like as we had a equilateral triangle rotating in 3D space with a orthogonal line (perpendicular to a plane the triangle lies on) led trough the medicenter. So when all the centres collapse it's like we're looking at the triangle "from the top".

really good video & animation ... excellent presentation from Zvezdelina Stankova, also excellent freehand diagram drawing skills

I love the equilateral triangle, it is the most beautiful and symmetric shape to me

Витоша (pronounced vitosha) was the first Bulgarian computer built in 1962-1963 on the basis of a cultural agreement between the Romanian and Bulgarian academies of science.

My mother Joanna Stoicheva Ivanova knew Zvezdelina in the 7th grade. They were in the same Bulgarian school in Ruse. They both had maximum points on the final exam(and another boy). But now my mother is a psychology teacher with 400$ monthly salary (because Bulgaria corruption ect.) and Zvezdelina is having hundreds of thousands of views from America... Поздрави от България!

@user-zb8tq5pr4x

6 жыл бұрын

Zvezdelina is getting less from this video than your mum

This is so awesome!

For any triangle it is possible to construct a circle which passes through the midpoint of each edge, the foot of each altitude, and the midpoint of the line segment from each vertex to the orthocentre. The centre of this circle is called the nine-point centre, and it is another centre which lies on the triangle's Euler line.

Fantastic. I'm having fond memories of my high school geometry class. 😊

Just now I've seen this video,congratulations for the perfect pronunciation !

My favorite video so far.

:D I loved learning about the different centres of a triangle in 9th grade geometry. Awesome!

Fascinating. Thank you.

My favorite video video in a while

3:44 except when you are dealing with an equaliteral triangle

My favourite Numberphile video.

Zvezda is so good, I love her work

6:06 when the drugs kick in great video

Very solid and rigorous proof there, dancing a triangle about graphically

Very nice. Mind expanded.

Nice touch with "Vitosha" on the computer :) My aunt worked on this computer back in 1961.

very very well done! very entertaining! i can't wait to show it to my daughters!

Eulearned a ton of information from this video, and I hope to see Zvezdelina Stankova again!

I like the new style for the animations!

This is fantastic!

yep, best handwriting I've seen on numberphile.

Weird how you see the moving triangle as 3D. Is there a name for that like pareidolia?

@hatchetxrip

6 жыл бұрын

The dissociation between vision-for-perception and vision-for-action

@crackedemerald4930

6 жыл бұрын

We are used to 3d space, if we see a 2d object in 2d space that resembles a projection, outline or structure of a 3d object, we are going to see a 3d object

i really love the way of teaching ... thank you mam

Amazing animations!

loving the fancy graphics!

Another great video and a much enjoyed nod to my home country with the 'Витоша' computer ;) Браво!

i want to see more of this kind of geometric math, it was very fun.

Thanks , it helped a lot!

This is an amazing video!

The technology's sound is killing me 😂 But ma'am you are fantastic and I enjoy learning from you.

Beautiful.

Question: Given the three "centers" is it possible to determine the triangle that generated them? If not, what is the class of triangles that may have generated them? What is the situation in the degenerative cases where two or all three of the "centers" coincide? Any thoughts?

Really going all in on the animation huh? I love it. I wish I could do something like this when teachers ask for proofs.

Numberphile never seize to amaze me.

There's one more centre called EXCENTRE .. where two external bisectors and one internal bisector of a triangle are concurrent . It holds a special property too : INCENTRE (corresponding to internal angle bisector) and EXCENTRE of a triangle are Harmonic Conjucates of each other ;)

Very well explained! And very interesting! :D

This is one of the many reasons triangles are the coolest.

5:15 , love she has a favourite (and her explanation as well is so cool)

The line looks like it always runs perpendicular to an equilateral triangle directly from the center, when they move it around you can see it. and the direction of the 2d "highway" is just based on your 3d perspective.

Whoa... so you can literally represent a triangle in 1-dimensional space just by measuring the movement of dots along the line!? Amazing! I wonder if that exists for other shapes as well.

So, if I break my leg, do I go to the orthocenter or is it better to go to the medicenter for a full check up?

@mayabartolabac

3 жыл бұрын

Neither. You should go to the circumcenter because it's most likely the closest point to you.

This was the best thing I have ever seen.

Useful and interesting with great presentation; thank you : -)

this is beautiful

I love this episode

This is super cool!

zvezdelina stankova.... your handwriting is awesome

Congratulations on question 6 ma'am👏👏