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jonathanrogness
Приєднався 2 чер 2007
Moebius Transformations Revealed
A short film depicting the beauty of Moebius Transformations in mathematics. The movie shows how moving to a higher dimension can make the transformations easier to understand.
The full version is available at www.ima.umn.edu/~arnold/moebius/
The background music (from Schumann's Kinderszenen, Op. 15, I) is performed by Donald Betts and available at www.musopen.com.
The full version is available at www.ima.umn.edu/~arnold/moebius/
The background music (from Schumann's Kinderszenen, Op. 15, I) is performed by Donald Betts and available at www.musopen.com.
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Wow I am very impressive with your job. I have developed the same graph with Trigonometric Partitions Equations. ua-cam.com/video/Xd8V9ST1RDg/v-deo.htmlsi=gISfQb2K2XuIMiSi
morbious transformations (really sweet visualization though)
I don't know but is this related? A Line has 2 point on its edge A Square has 4 line on its edge A Cube has 6 square on its edge . . And A Tesseract has 8 Cube on its edge?
Wow, this is so cool!
I dont know whats going on but if this was done with an equation ima just say it ur a genius
So beautiful, thank you, this video changed my life years ago when I first saw it!
hello from 2023
I think this was the video Terrance Tao was talking about in that talk.
Morbius transformations
This has been one of my favorite videos for so long that it is like an old friend. Great choice of music. Schumann Kinderszenen opus 15 number 1 beautifully played by the late Donald Betts.
Wow! Thanks! I'm here from researching the Z-Transform. I needed a concrete visual and THIS is it. THanks!
Casper the friendly ghost is a Moebius 1:02
Кто от Ульянова - ставьте лукас!
Thankyou
Legendary!
I want to pay you money for taking time to build this animation Seriously, I felt spell bound...Thanks so much
This is beautiful indeed
I am here because of this paper: Data augmentation with Mobius transformations
I love having my mind blown so gently.
The greatest video I've seen on mobius transformations
What software can be used to do that?
Anyone here from Terence Taos talk?
hbar / ((27pi) / 13) = 1.61624007e-35 m^2 kg / s photos.app.goo.gl/3KXBCDiV2ECJ2wkr9 photos.app.goo.gl/L2cKcqhLpGntNdjE8 photos.app.goo.gl/pUgd18b2S5ZksnB79 ((27pi) / 13) / c = 2.17645445e-8 kg exactly ((27pi) / 13) * c = 1.9560997e+9 joules exactly (27pi) / 13 = 6.52484628053 momentum exactly
I wonder what Bernhard Riemann would say about this, if he could see this video? I bet his mind would be blown. Back in his day I bet all mathematicians had to imagine and visualise, rather than having a handy animation to do the visualising for them. That's quite mindblowing, really. I mean, maths is hard enough for me to get my head around, let alone having to imagine it all rather than see it. Pairing this with the Schumann is inspired, by the way.
Wow... Purdy colors😱
Alright gang let's see who the Moebius Menace really is! *takes off mask* GASP! Old man Sphere Projection!
In HD: ua-cam.com/video/0z1fIsUNhO4/v-deo.html
A rotation of the Riemann sphere about a horizontal axis does not represent an inversion of the complex plane. It represents an inversion and a rotation (combined). The true sphere representation of an inversion corresponds to reaching through the sphere, pinching the other side, and pulling it through, i.e. literally turning it inside out (inverting it). In the case where the inversion swaps zero and infinity, one would reach directly through the diameter of the sphere, and hence the transformation is equivalent to mirroring across a horizontal plane.
I found your video mate, really love the content. Subbed straight away, We should connect!
Another proof that a picture worth a thousand words, Great job
beauti
jump scare at the end
But what happens when you move part of the sphere below the plane? Right-side up and upside-down?
This is very clear. Thank you !
What pulchritude.
I've come back to this vid over and over across the years. There's something about it that gives me great peace and satisfaction.
Meier brought me here!
Amazingly simple and beautiful!
most stunning video ever seen on youtube
Marvelous.
Wow, this video sure is a good demonstration of the Moebius Transformations. But I think there would be a problem if the figure on the sphere is not a lattice shape when explaining inversion. I did a quick calculation and I came to the conclusion that it would be a true inversion for any kind of figure on the sphere if the sphere and the figure on it is mirrored by a z=r plane(where r is the radius of the sphere) This certainly can not be accomplished by just rotating the sphere
aren't Mobius transformations orientation-preserving?
Came here from Apophysis.
Anyone here from MathPath?
Yep!
Hello there
yaaah
me
ayyyy
This is so great!! What software did you use to animate this :)
Then, put a hypersphere above THAT sphere!
You are a madman and I will have no part of this insanity!
I intend to fund your research into this! :O
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omg i just did archive and saw this on youtube when it was 1st made
...No comments...\o/...<3...
Hello, I would like to make similar animation on my own, but instead of sphere, place different shaped object. I'm not trained in Blender or similar soft. Could someone give me a hint how to easily made something like that (if easily is possible)? Maybe share softwere name, or even project where I could just replace the object?
If you have a little experience in programming, use something like shadertoy.com It's a site that display the webgl result of the fragment shader you created. a fragment shader is simply a program that is executed for each pixel of the screen in this case. The xy coordinate of the pixel are given by gl_FragCoord. you can manipulate all that to give the right color to your pixel