Where should these palaces be built? - Micmaths
This problem, posed by Conway and Sloane, is quite simple at first, but much less so towards the end.
This question is also known as Tammes' problem: https://fr.wikipedia.org/wiki/Probl%C...
The book in which I found this problem is Sphere Packings, Lattices and Groups by J. H. Conway and N. J. A. Sloane.
Niel Sloane's website, which lists all the best known solutions, is: http://neilsloane.com/packings/ Note that in the table on this page, the minimum distance between points is denoted by the central angle. For example, for M=6, we can read 90 in the "min separation" column, which means that, viewed from the center, two adjacent points of the octahedron are at right angles to each other.
The article that solves the problem for M=13 and M=14: The Tammes problem for N=14 - Oleg R. Musin, Alexey S. Tarasov - https://arxiv.org/abs/1410.2536
More:
OEIS: https://oeis.org
My video on the Conway knot: • Une énigme de 50 ans résolue : le nœud de ...
Thumbnail: Chloé Bouchaour / chloescope_
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