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Moebius Transformations Revealed

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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 http://www.ima.umn.edu/~arnold... background music (from Schumann's Kinderszenen, Op. 15, I) is performed by Donald Betts and available at http://www.musopen.com.

Channel: Education
Uploaded: December 31, 1969 at 4:59 pm
Author: jonathanrogness

Length: 02:34
Rating: 4.70
Views: 1495394

Tags: math  mathematics  mobius  moebius  plane  projection  sphere  stereographic  transformation  transformations  

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Video Comments

JanisChambers (December 31, 1969 at 4:59 pm)
wow.. it truly does help relate the limitation of a 2d mindset vs a 3d.. and inspires us to really wonder what a 4d world would look like.
SaikoFTW (December 31, 1969 at 4:59 pm)
I should have known!! Riemann, that was an interesting and yet very simple answer 8'D A glass sphere!
Bosf10 (December 31, 1969 at 4:59 pm)
Haha i thought it looked like a sphere :Panyway its nice and i love how its made to be easy to understand even for people with NO experience with this section of maths.Calm Down.
morgan1627 (December 31, 1969 at 4:59 pm)
so beau~~beautiful!
Morphimort (December 31, 1969 at 4:59 pm)
...
dawilner (December 31, 1969 at 4:59 pm)
Thank You .
dawilner (December 31, 1969 at 4:59 pm)
Thank You.
phyzome (December 31, 1969 at 4:59 pm)
That was beautifully done, a perfect introduction for those of us with no experience in this section of math.Also, *gorgeous*.
naard (December 31, 1969 at 4:59 pm)
technically isn't black the absorption of all colors by the substance being struck by light, rather than the combination of all colors? i think you are thinking about how, when mixing paint, the colors combine into black...which is caused by the aforementioned condition (the new substance now absorbs all wavelengths).when speaking in terms of actual light (which is not paint, or even like paint) white is the combination of all wavelengths (all colors).beware of thinking too much through analogy.
Avatar2050 (December 31, 1969 at 4:59 pm)
i know i appear to have caused controversy by asking a non linear question it was in relation to the colours of the chakras...some schools of thought are that the spectrum ends in violet and white not magenta...thanks for your answer - interesting that both black and white are a combination of all colours.. thanks mobius is such a wonderful geometrical key..ELohim..

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