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There are flying saucers in my math book
Mar. 10th, 2011 01:36 amNo, really, there are. Help.
If you're curious: look for saucers . It's actually a very cool schematic: we want to draw a surface immersed (well, embedded with not many points of intersection) in R^4. So we find a special (multivalued) function of 2 variables, graph it in R^3, so that its partial derivatives form the other two coordinates. The reason we can do this is that the surface is an "exact Lagrangian immersion" into standard C^2, a thing we definitely care about in symplectic geometry. It generalizes, too--the 1D case is just graphing a function and graphing its derivative, etc., but the 1D case is rather uninteresting. Once I realized this I also realized Yasha talked a little about it in the first FARS seminar in the fall, that is, the seminar I've been organizing. Gah.
Also, AAAAGH I have no time before Friday.
If you're curious: look for saucers . It's actually a very cool schematic: we want to draw a surface immersed (well, embedded with not many points of intersection) in R^4. So we find a special (multivalued) function of 2 variables, graph it in R^3, so that its partial derivatives form the other two coordinates. The reason we can do this is that the surface is an "exact Lagrangian immersion" into standard C^2, a thing we definitely care about in symplectic geometry. It generalizes, too--the 1D case is just graphing a function and graphing its derivative, etc., but the 1D case is rather uninteresting. Once I realized this I also realized Yasha talked a little about it in the first FARS seminar in the fall, that is, the seminar I've been organizing. Gah.
Also, AAAAGH I have no time before Friday.
