Timeline for Kepler conjecture: Are there only two most efficient packings or could there be more than two?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 14 at 7:57 | comment | added | Greg Kuperberg | @SamHopkins - My old paper on this has a counterexample in Figure 6. What should be the optimal circle packing in 2 dimensions isn't "tight" in the sense of Conway and Sloane. Their game with rearrangements of pieces of the plane creates an illusion that the packing has wasted space that can be eliminated. But the "wasted" space isn't actually eliminated, it is carried off to infinity. | |
| Jan 17 at 3:26 | vote | accept | Michael Hardy | ||
| Jan 16 at 23:08 | comment | added | Sam Hopkins | Also in the mentioned paper "Notions of denseness" by Kuperberg (arxiv.org/abs/math/9908003), in the last section he seems to suggest something is wrong with the "tightness" notion from Conway and Sloane, though reading quickly I don't totally grasp what the issue is. | |
| Jan 16 at 22:17 | comment | added | Timothy Chow | @SamHopkins Ah, that would be a plausible question whose answer might be 2. In Conway and Sloane's paper, they call such a thing a uniform packing. The argument in their paper might settle this question given that the Kepler conjecture is now settled, but I'm not 100% sure. | |
| Jan 16 at 22:09 | history | edited | Timothy Chow | CC BY-SA 4.0 |
added 16 characters in body
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| Jan 16 at 22:06 | comment | added | Sam Hopkins | What do you think about: "the CCP and HCP are the only dense sphere packings whose symmetry group acts transitively on the spheres"; is that known to be true/false? | |
| Jan 16 at 22:03 | history | answered | Timothy Chow | CC BY-SA 4.0 |