If only that had been the reason for modification of some of what the resultant programme did become, the programme would have been slightly sensical. Currently, the programme is one of the confusant programmes that I have observed until now.
When people say they don't understand trigonometry, I think what they meant is that they are uncomfortable with the array of emotions and characteristics shown by the hypotenuse. Many of which are not commonly considered acceptable for Euclidian geometry
"...emotions and characteristics shown by the hypotenuse. Many of which are not acceptable in euclidean geometry" Cool, so I can treat my hypotenueses like the misbehaving teenagers they are!
I never thought a simple shape could be so satisfying until at the end all centers converged as the isosceles triangle slowly became an equilateral one
A bit slow at the start, but just like any other anime it starts quite unexpectedly pulling all the disparate pieces together right near the end. A brilliant show, 10/10 would watch again. I hope there's a sequel.
It wasn't a traditional hand-drawn animation, it was made on a tectronics terminal, which sped up the process immensely. The problem of filming it, however, wasn't resolved that simply.
The Textronix 4051 had a base price of $6000 (more like $30,000 in today's money) and featured a "storage tube" which made the vector image "stick" to the screen until reset. That means it needed no display RAM to hold a bitmap of the current screen. The resolution was 1024x768. The screen was a monochrome single-color phosphor. They are normally green; I don't know if they had white back in the day. I suppose this was made by photographing the screen for each frame. But, to do color, each color would be drawn by itself and photographed separately. They could be combined using filters to expose a color image.
@@jakewartooth Wikipedia for the details. I'd previously learned how memory CRT works because I'm curious and read a lot. I know about photography, and learned about film-era special effects from books and TV shows. It's easier than ever to know things!
7:49 because of the center point appearing to be one a line, and then that yellow feller just hanging out, and they all move with each other against the perimeter of the triangle, this part always looks to me like we are seeing a triangle being rotated in 3D space and the camera is changing locations. But it’s not quite 3D, it’s off by *that* much. Not quite 4D either, but my mind just makes the connection regardless
@@rhyler_3968 Sakura Futaba. Persona 5's Navigator, and all-round best girl in that game, and many others. Gets a solid 3rd place, just after Ramiel and Asuka in the Best Girl overall.
Seriously cool, especially since I remember having worked with the 4051 terminals a little bit in college. There is so much beauty in certain geometric relationships.
Differences between centroid and circumcenter - Centroid always inside triangle, circumcenter can be outside - Line from the midpoint of side of triangle goes to opposing corner for centroid, in circumcenter it is always perpendicular. This is particularly important with obtuse triangles
8:08 Those dots behave very much like they are on a line through the 3'rd dimension perpendicular to the triangle-plane & intersecting the plane at the red points position. (7:50 except for the yellow point for some triangles, that point behaves like it is on the triangle plane & at a different location for those triangles.)
I knew exactly what it was before even searching it, but really I'll watch anything synced to Cruel Angel Thesis. And as a bonus I immediately got recommended to rewatch Propane Genesis Evangelion.
Why didn’t we learn this in trigonometry or geometry? This is such a good way to express so many abstract mathematical concepts, not only intuitively, but quickly too. Thank you for posting this. This is an amazing resource. ❤
There was (is?) a thing literally called sacral geometry which associated physical shapes with philosophical and religious concepts (and sometimes representations of real world objects) and as such was significantly used in design of temples/churches, sigils, and different types of art. So yea it's really not that far off
When geometry comes with its’ proofs, it honestly feels like witchcraft. It actually makes so much sense and it’s so easy but it feels too magical to be this simple.
This video is just like Outside in. They're both videos uploaded a while ago that are centered on some geometric idea, and both inexplicably appear on my recommended every now and then. Great video, 10/10.
Almost shown in the presentation, the incenter is the center of the circle inscribed in a triangle. What they showed is how you find it (where vertex bisectors meet), but they could have shown at the beginning with the moving circle that when it increases in size to the point it is touching all sides of the triangle, it's center is the incenter. Because it's the center of a circle, the incenter is equidistant from all sides of the triangle (the distance is the circle's radius).
Incenter: angle bisectors Circumcenter: perpendicular bisectors of each side Centroid: the lines from the midpoint of a side to the opposite angle Orthocenter: lines perpendicular to the side that go through the opposite angle
I remember when I was taught this in primary school geometry class. Seeing the relationship between circles and triangles for the first time and how I could find the center of any triangle with a compass; I don't think there was a point in my school life that felt as satisfied and made me feel as happy for having learned anything in school as that moment. I was never particularly good at math, I struggled with it all the way up to humble community college, but anything involving geometry and trigonometry always were something special for me
"Alright lads, the fans REALLY want a sequel to Top Gear. What should we name it?" Employee #1: "Top Gear 2!" Employee #2: "Bottom Gear!" Employee #3: "7:19"
I was watching the Soviet stop motion animated film “Tale of Tales”. This piece (Bach’s Prelude in E-flat minor) plays multiple times, and I could not remember where I had heard it before fairly recently until I finally went “ *GASP* THE TRIANGLE VIDEO!!!!”
Incentre: Intersection of angle bisectors. Circumcentre: Intersection of edge perpendicular bisectors. Centroid: Intersection of medians. Orthocentre: Intersection of altitudes.
I used to draw what I just learned were centroids all the time in graphics on a drawing board back in high school & was amazed that the 3 lines always crossed at the same point no matter what shaped triangles I started with & always wondered whether that represented the center of mass of the triangle
Woke up at night because of hives, this video made me fall back to sleep. I would've stayed up as always if I didn't find it, the music is just that good.
Incentre: angle bisectors Circumcentre: perpendicular bisectors Centroid: midpoint to vertex Orthocentre: vertex to closest point including extended lines
You know, I never really liked trigonometry - and still don't - but the elegance of mathematical determinism in pattern generation, especially in geometry, will always have something soothing and satisfying about it. Great video!
Incenter: split each angle in half, find the intersection Circumcenter: the point where all vertices are equidistant Centroid: draw a line from each vertex to the opposite side, find the intersection Orthocenter: draw a line from each vertex perpendicular to the opposite side, find the intersection
oh man this version is so much more relaxing that the evangelion one
I came here just because I saw the evangelion one...
Have to agree with you there
No shit, sherlock
Actually there is another.
th-cam.com/video/8xqskiIehfk/w-d-xo.html
It appears we all are on the same train here then I take it?
This truly feels like we’re watching a restricted video
Pnor
@@asheep7797 in a way, it is
SCP: #### (triangles and shit bro)
@@asheep7797 This genre is what gets me off..
This was originally going to be the ep 26 of evangelion but they thought it was going to be confusing to people and they changed it
If only that had been the reason for modification of some of what the resultant programme did become, the programme would have been slightly sensical. Currently, the programme is one of the confusant programmes that I have observed until now.
@@RokeJulianLockhart.s13ouq your two sentences are some of the most confusant things I've ever had to observe. I like em tho
It's not like it is any less confusing on its own
The acute triangle's dilemma
same Profile Picture
When people say they don't understand trigonometry, I think what they meant is that they are uncomfortable with the array of emotions and characteristics shown by the hypotenuse. Many of which are not commonly considered acceptable for Euclidian geometry
As Someone who dealt with angles and hypotenuses a lot, I hate them both with a burning passion
"...emotions and characteristics shown by the hypotenuse. Many of which are not acceptable in euclidean geometry"
Cool, so I can treat my hypotenueses like the misbehaving teenagers they are!
But trigonometry is amazing, why would you hate it?
@@PrismaticCatastrophism Because it often isn't taught well, instead of being taught how to think, it's taught as what to think
331thliker5thcomtnr
Music is Bach if you hadn't noticed. The prelude of the 8th fugue in the Well Tempered Clavier, in d#. BWV 853
The music for the "Grand Tour" is the 12th prelude, in f. BWV 857
Ok
And
I've been searching for this, thank you so much!
thanks a lot
I never thought a simple shape could be so satisfying until at the end all centers converged as the isosceles triangle slowly became an equilateral one
The all-seeing eye.
Such character development!
I was starting to see the triangle moving in 3D at the end and the video. The points fixed on it moving all along.
Awesome 3D experience of 1970!
I'm glad the triangle AMV led me to this video - I needed to remember how to find these elements of triangles.
The triangle lore is getting crazy
thqnk you it is send the goode energy ur way
A bit slow at the start, but just like any other anime it starts quite unexpectedly pulling all the disparate pieces together right near the end. A brilliant show, 10/10 would watch again. I hope there's a sequel.
You have to wait 55 years and then it'll all come together for the sequel
I like the part where it went:
______________________________
•
Not as good as the manga
what show?
@@lilbop4942 whooosh
It's insane to think that since is back in the 70s, someone animated all this with traditional hand-drawn animation.
It wasn't a traditional hand-drawn animation, it was made on a tectronics terminal, which sped up the process immensely. The problem of filming it, however, wasn't resolved that simply.
@@cancerguy5435 oooh, i see
never really knew what a tectronics terminal is
thanks for the info!
609
699gh*liker3rdcomtnr
There are literally anime in 2023 that is done by hand drawing 🙄
I had an etcha sketch once
Get in the robot, Pythagoras.
I hope this blows up like Outside In. It has the same vibe
I love ancient advanced mathematics videos.
I thought the same exact thing
incredible - especially when you consider the production techniques at the time
The Textronix 4051 had a base price of $6000 (more like $30,000 in today's money) and featured a "storage tube" which made the vector image "stick" to the screen until reset. That means it needed no display RAM to hold a bitmap of the current screen. The resolution was 1024x768.
The screen was a monochrome single-color phosphor. They are normally green; I don't know if they had white back in the day.
I suppose this was made by photographing the screen for each frame. But, to do color, each color would be drawn by itself and photographed separately. They could be combined using filters to expose a color image.
Thank you for this knowledge, but how do you know such things? 🤔 (Sorry for bad English, it is my first and only language)
@@jakewartooth Wikipedia for the details. I'd previously learned how memory CRT works because I'm curious and read a lot. I know about photography, and learned about film-era special effects from books and TV shows.
It's easier than ever to know things!
This is really a cruel angle thesis
Which video of evangelion are you taking about
angle
I could not tell you why I find this animation style so cool to watch. All I can do is say that it is.
old style its cool fashion youngling
The aesthetics of this can't be described by words
ugly just like you, hiding behind that stupid orange profile picture
@@jensjakob7743 Hiding? are the feds after me or something?
sure you can, "nice"
@@caffeine_headacheah, I see u r a man of culture
7:49 because of the center point appearing to be one a line, and then that yellow feller just hanging out, and they all move with each other against the perimeter of the triangle, this part always looks to me like we are seeing a triangle being rotated in 3D space and the camera is changing locations. But it’s not quite 3D, it’s off by *that* much. Not quite 4D either, but my mind just makes the connection regardless
I see it!
It looks like you have a flashlight in front of the triangle and you're moving it around-- like they're plotting the shadow of the triangle
My man, 4d is time. How is it involved here?
you have really great imagination. it really does look 3d
I still wanna say that Ramiel is still best girl. Truly a geometrical waifu
Ramiel is the easygoing version of Futaba Sakura, so yeah, still best girl.
@@RaginKavu who?
@@rhyler_3968 Sakura Futaba. Persona 5's Navigator, and all-round best girl in that game, and many others.
Gets a solid 3rd place, just after Ramiel and Asuka in the Best Girl overall.
child: "mom can we get the center of a triangle?"
mom: "no we have the center of a triangle at home"
center of a triangle at home: 6:57
make it 7:16
LMAO
why did I laugh at this? omg
Way off there, right in the corner
At least it isn’t the circumcenter, which sometimes is outside of the triangle (obtuse triangles)
2:24
Seriously cool, especially since I remember having worked with the 4051 terminals a little bit in college. There is so much beauty in certain geometric relationships.
This is 3Blue1Brown's origin story
Underrated comment
3Blue1Brown lore⁉
His father, 3Brown1Blue
yes
loved watching the triangle move and groove at the end. the circumcenter and orthocenter made it look like it was waving its hands
The Grand Tour felt like a beautiful dance.
Differences between centroid and circumcenter
- Centroid always inside triangle, circumcenter can be outside
- Line from the midpoint of side of triangle goes to opposing corner for centroid, in circumcenter it is always perpendicular. This is particularly important with obtuse triangles
They should really have added those little squares to denote right angles for the circumcenter lines
Putting it into words removes the magic of it.
8:08 Those dots behave very much like they are on a line through the 3'rd dimension perpendicular to the triangle-plane & intersecting the plane at the red points position. (7:50 except for the yellow point for some triangles, that point behaves like it is on the triangle plane & at a different location for those triangles.)
IIRC that's called the Euler line.
@@rwall514 and the yellow dot?
@@Miguel_Noether that's only on the Euler Line if it's an isosceles triangle.
Four points, four dimensions.
@@Luckingsworth Euler teserac?
I personally want to thank the algorithm for bringing me here after the NGE parody.
I bet anyone who got here without seeing the anime openings must be very confused by the comments
I knew exactly what it was before even searching it, but really I'll watch anything synced to Cruel Angel Thesis.
And as a bonus I immediately got recommended to rewatch Propane Genesis Evangelion.
Why didn’t we learn this in trigonometry or geometry? This is such a good way to express so many abstract mathematical concepts, not only intuitively, but quickly too.
Thank you for posting this. This is an amazing resource. ❤
wait i thought you already learn about the orthocenters, incenters, and circumcenters in geometry
We did
you just never paid attention
I never learned those either
@@user-ys8bs1jd2r bold assumption
3:07 when Ramiel shoots an energy beam at your military facility
Never thought triangles would be so interesting
And they made it mesmerizing to watch and listen
Ah yes my favorite TH-cam video genre, shape lore
Every so often TH-cam’s algorithm has a brain fart and then we get this
Geometry is truly the closest thing to witchcraft in this universe
What about witchcraft? That seems pretty close to witchcraft in my opinion
@@serifbeta7069 yeah but it's not in this universe
@@ultrio325 there were literally witches in the bible.
@@JosiahRobert14 There's heavy debate on whether the Bible arc is canon or if it's a one off
There was (is?) a thing literally called sacral geometry which associated physical shapes with philosophical and religious concepts (and sometimes representations of real world objects) and as such was significantly used in design of temples/churches, sigils, and different types of art.
So yea it's really not that far off
I wanted The Grand Tour segment to last much longer.
man I just got this totally randomly in my home page wtf???? its 12 years old!
When geometry comes with its’ proofs, it honestly feels like witchcraft. It actually makes so much sense and it’s so easy but it feels too magical to be this simple.
its' ?
I often see "it's" for "its" but this is different.
@@JohnDlugosz rude
@@JohnDlugosz tbf he's turkish
Almost 3 am and I am relaxing to this, so satisfying... damn
I could literally recreate this shot for shot in Desmos
Crazy how far math animations have come
This video is just like Outside in. They're both videos uploaded a while ago that are centered on some geometric idea, and both inexplicably appear on my recommended every now and then. Great video, 10/10.
I could literally watch this forever, it's so good
I've learned more about triangles from this than I have ever learned in math class
thank you
This is giving me art teacher brings in the large tv because we’re watching a film vibe.
This movie had such an excellent point
Almost shown in the presentation, the incenter is the center of the circle inscribed in a triangle. What they showed is how you find it (where vertex bisectors meet), but they could have shown at the beginning with the moving circle that when it increases in size to the point it is touching all sides of the triangle, it's center is the incenter. Because it's the center of a circle, the incenter is equidistant from all sides of the triangle (the distance is the circle's radius).
This looks like something I’d find in the back of my high school’s computer lab and I mean that in the best way possible
This video reminded me of a geometry test I have to take tomorrow, thank you obscure video from 12 years ago, I will not forget this
Honestly i just come to this video for the music
I learned centroid and didn't know there were other ways to represent it. Very good simple instructional video perfect for visual learners
Incenter: angle bisectors
Circumcenter: perpendicular bisectors of each side
Centroid: the lines from the midpoint of a side to the opposite angle
Orthocenter: lines perpendicular to the side that go through the opposite angle
I remember when I was taught this in primary school geometry class. Seeing the relationship between circles and triangles for the first time and how I could find the center of any triangle with a compass; I don't think there was a point in my school life that felt as satisfied and made me feel as happy for having learned anything in school as that moment. I was never particularly good at math, I struggled with it all the way up to humble community college, but anything involving geometry and trigonometry always were something special for me
This fascinates me for some odd reason. Guess it just goes to show how beautiful and how perfect a shape can really be.
I'm a centroid fan myself, but I think that the incenter also works fine in most cases
Same vibes as outside in, but damn i cant not think of the evangelion opening after that one video
you know that you're super bored when YT algorithm didn't show you this video, and u willingly watching this video
yeah...
so if this is the anime then i’m assuming the manga is just all the animations drawn as figures proved by mathematical formulas
"Alright lads, the fans REALLY want a sequel to Top Gear. What should we name it?"
Employee #1: "Top Gear 2!"
Employee #2: "Bottom Gear!"
Employee #3: "7:19"
I was watching the Soviet stop motion animated film “Tale of Tales”. This piece (Bach’s Prelude in E-flat minor) plays multiple times, and I could not remember where I had heard it before fairly recently until I finally went “ *GASP* THE TRIANGLE VIDEO!!!!”
Evangelion aside this is seriously impressive for 1976!
ehhhhh what do u mean? the animation is pretty simple
Star wars released one year later
This is a video I like to watch on sleepless nights.
I will forever be haunted by the knowledge that someone defined the center of a triangle like 2:24 (or 7:14).
Right???
That’s only on Obtuse triangles though. You’ll be insane if you saw right triangles. It’s on the hypotenuse
This is really a “trust me it gets super good in season 27” one
As an AutoCAD user, I find this quite funny way of doing this. I had found early on, to obtain the CenterPoint of each line using a drafting compass.
this makes understand each centre of triangles much more effective than any other method of teaching
от развязки мурашки по коже😶 лучшее в мире кинематографа
as a math student i can say that this is a new kind of Art
this video made me fall asleep for 6 hours straight, no joke. good video!
same
pancake
Incentre: Intersection of angle bisectors.
Circumcentre: Intersection of edge perpendicular bisectors.
Centroid: Intersection of medians.
Orthocentre: Intersection of altitudes.
I used to draw what I just learned were centroids all the time in graphics on a drawing board back in high school & was amazed that the 3 lines always crossed at the same point no matter what shaped triangles I started with & always wondered whether that represented the center of mass of the triangle
I can’t watch this without inabakumori being played in my head
Woke up at night because of hives, this video made me fall back to sleep. I would've stayed up as always if I didn't find it, the music is just that good.
Incentre: angle bisectors
Circumcentre: perpendicular bisectors
Centroid: midpoint to vertex
Orthocentre: vertex to closest point including extended lines
7:20 when you want to watch more of Top Gear but Top Gear has three new people besides James, Jeremy and Richard
The music to this is excellent!
this feels strangely calm and relaxing
Geometry is Zen, when explained and visualized like this. Incredible video.
This is oddly satisfying
no triangles were harmed in the making of this video
People need to watch this before entering the Bermuda Triangle
This video generates such strange and unknown emotions...
I had not realized that the circumcenter, centroid, and orthocenter were colinear. The more you know
This video is from 12 years ago and still in my recommendation :D
dude i've watched too much analog horror, I was tensed up waiting for a jumpscare that never came lol
Soooo relatable
Maybe the jumpscare was the knowledge we acquired along the way...
I live here now. This plays in the back of my mind at all times
Thanks for the subbed version!
This is almost unsettling for some reason that I can't pinpoint
That part where something happened - I felt that.
this is my favorite thing i’ve ever seen in my life
Nice anime
This was absolutely mesmerizing to watch. It felt like I was day dreaming
You know, I never really liked trigonometry - and still don't - but the elegance of mathematical determinism in pattern generation, especially in geometry, will always have something soothing and satisfying about it. Great video!
Theres something strangely nostalgic about old educational videos with this kind of music and quality. Like a nostalgia for somewhere ive never been
Congratulations!
Omedetou!!
This is like an adhd sensory video for adults
The ending with the equaliateral triangle gave me chills
Incenter: split each angle in half, find the intersection
Circumcenter: the point where all vertices are equidistant
Centroid: draw a line from each vertex to the opposite side, find the intersection
Orthocenter: draw a line from each vertex perpendicular to the opposite side, find the intersection
this is what the inside of my mind looks like at all hours of the day
I got BWV 853 but I’m looking for this particular recording 🙏🙏🙏
This was amazing!!
Hi!💕
You alive?
this is such a beautiful way to intuit what these centers mean!