Möbius Transformations Revealed [HD]

Möbius Transformations Revealed is a short video by Douglas Arnold and Jonathan Rogness which depicts the beauty of Möbius transformations and shows how moving to a higher dimension reveals their essential unity. It was one of the winners in the 2007 Science and Visualization Challenge and was featured along with the other winning entries in the September 28, 2007 issue of journal Science. The video, which was first released on YouTube in June 2007, has been watched there by more than a million and a half viewers and classified as a Top Favorite of All Time first in the Film & Animation category and later in the Education category. It was selected for inclusion in the MathFilm 2008 DVD, published by Springer.

credit: Möbius Transformations Revealed was built primarily using POV-Ray with some help from Mathematica. The soundtrack is a performance of "Von fremden Ländern und Menschen" ("Of Foreign Lands and Peoples") from Robert Schumann's Kinderszenen, Op. 15. The pianist is Donald Betts.

source: http://www.ima.umn.edu/~arnold/moebius/

• Category

  Science & Technology

[shpongledmonk]

This is such a powerful idea. It has totally changed the way I look at space, time, and the nature of finite vs infinite.

[djxatlanta]

- wake and bake and take in the universe. =) I've got a bunch of really cool science and math visualizations on a hard drive hooked up to my living room widescreen TV. When I feel like "contemplating" the universe, they look pretty sweet in HD.

[onresonance]

terence tao mentioned this video in his 2009 induction ceremony speech, which is why i came here. i like how simply this is explained.

[NattyDread91]

This is beautiful

[AntonPetrunin]

"Möbius Transformation sends EACH point on the plane to the corresponding point."

This statement is formally wrong. Either one has to remove "each" form the sentence or add "including infinity".

[Patricia Gassmann]

Cool vid.btw im on my moms account.

[Kigen Ekeson]

Sweet!

[333666666]

This is like salvia, without the humiliating YouTube videos after.

[MrCavitysChessCorner]

Insanely awesome. Projects like these are why I get up in the morning. I'm getting trained (lectured thrice a week) to work in a hyperbolic geometry lab. Needless to say I'm excited to do this kind of work.

Geodesics baby!!!!!

[Dhaval Patel]

awesome



[okita1]

love it man, thanks for sharing.

[JouLesConduit]

excellent