Wikipedia:Reference desk/Archives/Mathematics/2023 May 27
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May 27
[edit]How many unit hyperballs can touch a unit hypersphere simultaneously without overlap(s)?
[edit]Is it pi**2*2 round down? And the surface hypervolume of the unit hyperhypersphere round down for five dimensions and so on? Sagittarian Milky Way (talk) 16:06, 27 May 2023 (UTC)
- The number of unit spheres that can simultaneously touch another unit sphere is the Kissing number. The article has numbers (sometimes just a range) for dimensions up to 24. AndrewWTaylor (talk) 17:12, 27 May 2023 (UTC)
- So the 2, 2pi (~6.28), 4pi (~12.57), 2pi^2 (~19.74) thing completely collapses after enough degrees of freedom (I didn't know that number shrinks forever after ~33.07 for dimension 7) Sagittarian Milky Way (talk) 18:53, 27 May 2023 (UTC)