Talk:Hermite constant

New material?

Bacher, Roland (2008). "A new inequality for the Hermite constants". International Journal of Number Theory. 4 (3): 363–386. doi:10.1142/S1793042108001390.

66.177.56.143 (talk) 13:57, 14 July 2008 (UTC)[reply]

"Linearly in n"?

The article says that "the Hermite constant grows linearly in n as n becomes unbounded", but the "estimates" are clearly exponential and not linear! --Erel Segal (talk) 12:29, 19 July 2015 (UTC)[reply]

Basis vectors for the 2D lattice with Hermite constant = 4/3?

I don't know if I'm just dense and missed something, but what exactly IS the 2D lattice with a Hermite constant of 4/3? Can't be the square or hexagonal, right? BagLuke (talk) 06:03, 6 October 2023 (UTC)[reply]

It's sqrt(4/3), not 4/3, and the answer is in the article. Eigenbra (talk) 17:04, 6 October 2023 (UTC)[reply]

Confusion on the 2D Hermite constant

I'm confused. A fundamental region of a hexagonal lattice is a 120 degree rhombus. When the area of such a rhombus is 1, the resulting side lengths are not 2/sqrt(3). Instead, the length is sqrt(2/sqrt(3)). Am I incorrect in thinking that the shortest distance between 2 points in the lattice is supposed to be 2/sqrt(3)? BagLuke (talk) 20:02, 7 October 2023 (UTC)[reply]