Timeline for Most intricate and most beautiful structures in mathematics
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2010 at 23:13 | comment | added | Spiro Karigiannis | @Sean: Yup, that is the Hopf fibration. | |
| Dec 17, 2010 at 15:53 | comment | added | Sean Tilson | Thanks, that is really cool. So are they linked like so homepages.wmich.edu/~drichter/hopffibration.htm ? | |
| Dec 17, 2010 at 11:39 | comment | added | Spiro Karigiannis | @Sean: It is both. $\mathbb R^3$ is the union of disjoint circles and a line, any two of which are linked, and one can use this description to also view $\mathbb R^3$ as the disjoint union of tori and a line. | |
| Dec 16, 2010 at 11:52 | comment | added | Daniel Moskovich | Dror Bar-Natan has a beautiful animation of the Hopf fibration: math.toronto.edu/drorbn/Gallery/KnottedObjects/PlanetHopf | |
| Dec 16, 2010 at 4:10 | history | edited | Douglas Zare | CC BY-SA 2.5 |
fixed transposition of superscripts, reordered list
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| Dec 15, 2010 at 0:29 | comment | added | Sean Tilson | @Spiro: do you mean disjoint tori? that is the story i recall. Please ignore me if this is dumb. PS thanks for including your example #4 | |
| Dec 14, 2010 at 21:50 | comment | added | Gil Kalai | I think they also have intricate highly symmetric triangulations. E.g. "Kuhnell's CP^2". They are beautiful and intricate but perhaps not even aiming to be the most beautiful/intricate. (They are quite modest, just 9 vertices.) | |
| Dec 14, 2010 at 19:07 | comment | added | Spiro Karigiannis | @Deanne: You're correct, they're not as intricate as the Mandlebrot set or the Cantor set, but it's amazing to me that one can fill up all of $\mathbb R^3$ completely with disjoint circles (and one line), any two of which are non-trivially linked. [But I deliberately called them beautiful only, not intricate.] | |
| Dec 14, 2010 at 17:06 | comment | added | Deane Yang | I agree that these are among the most beautiful structures in geometry and topology, but I'm not sure that they qualify as being "intricate". | |
| Dec 14, 2010 at 17:02 | comment | added | Spiro Karigiannis | In the interest of full disclosure: I copied and pasted some of this from my own answer to another question: mathoverflow.net/questions/44635/sn-to-sm-to-b-bundle-possible/… | |
| Dec 14, 2010 at 17:02 | history | answered | Spiro Karigiannis | CC BY-SA 2.5 |