Your Geometry teacher probably already told you all about it one morning when you weren't paying attention, but a basically Möbius Transformation is "a map of the complex plane to itself in which a point "z" is mapped to a point "w" by w=(az+b)/(cz+d), where a,b,c, and d are complex numbers and ad-bc does not equal zero."
Got that? There's going to be a pop quiz on this tomorrow, so pay attention.
Propers to tdj and his beautiful blog for the lesson. posted by chuckdarwin at 2:16 AM on June 26, 2007
For a brief moment while watching that I completely understood curvature of space, relativity, and quantum theory. Then I lost it, poof! What a post. Blowed my mind. thanks. posted by Blingo at 2:56 AM on June 26, 2007
So can he show us what a Möbius transform looks like when applied to 3D objects? I'd like to see how a complex model looks as it's turned inside out. posted by Tzarius at 5:34 AM on June 26, 2007
Fantastic. For number theory fans, Mobius transformations are crucial to the theory of modular forms -- sort of a higher-dimensinal version of trigonometry in which the zoo of transformations of the plane depicted in this video replaces simple translations of the line. posted by escabeche at 6:00 AM on June 26, 2007
I am currently studying for a PhD qualifying examination in analysis, the field where most students first encounter these types of Moebius transformations.
The animation was very pretty, and a good depiction of what's going on. posted by King Bee at 6:16 AM on June 26, 2007
Only loosely related, but you can find a couple of classic math videos on Google now: Outside In (sphere eversions) and Not Knot (hyperbolic knot complements).
Thanks, Wolfdog. Cheers, everybody; this is mainly down to me having such a shower of smart-arses on my f-list. posted by chuckdarwin at 6:45 AM on June 26, 2007
Ever since that Björk thread, every time I see an "o" with an umlaut over it, I see a little surprised face.
Very nice. Thanks. posted by OmieWise at 7:02 AM on June 26, 2007
Beautiful - thank you!
Would that this had existed when I was trying (and mostly failing) to learn such things. posted by speug at 7:37 AM on June 26, 2007
that was really lovely. i think the part of my brain that likes ayn rand just had an orgasm. posted by es_de_bah at 8:20 AM on June 26, 2007
i think the part of my brain that likes ayn rand just had an orgasm.
That's so disgusting in so many ways that I feel like I need a shower. posted by OmieWise at 8:35 AM on June 26, 2007
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Got that? There's going to be a pop quiz on this tomorrow, so pay attention.
Propers to tdj and his beautiful blog for the lesson.
posted by chuckdarwin at 2:16 AM on June 26, 2007