Geodesic
Journey to the edge of chaos
Matematičeskoe obrazovanie, no. 4 (2024), pp. 26-36 
V. N. Novikov. Journey to the edge of chaos. Matematičeskoe obrazovanie, no. 4 (2024), pp. 26-36. http://geodesic.mathdoc.fr/item/MO_2024_4_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For arbitrary simplices, it is shown that for a fixed volume, the maximum perimeter is achieved with sets of edges consisting of only two or three groups of edges of the same length. Analogues of the Euler and Roucher inequalities are found. The main results of the work were reported at the World Congress “Theory of Systems, Algebraic Biology, Artificial Intelligence: mathematical foundations and applications”, 23-30.06.2023 at the topological section.

[1] V. N. Novikov, “O neravenstvakh v tetraedre”, Matematicheskoe obrazovanie, 2021, no. 2(98), 18–27

[2] R. E. Schwartz, The 5 Electron Case of Thomson's Problem, 2018, arXiv: 1001.3702v5 [math.MG] | MR

[3] Lajos Laszlo, On the Grace-Danielsson inequality for tetrahedra, 2018, arXiv: 1805.08435v1 [math.MG] | MR