History of Hermite's constants $\gamma_n$

 Display properties:   number-header: $\gamma_n$-Numbers: []+Numbers:+- params:+    n: '1'+  number: '1'+  comment: $\gamma_{1}=1$, $\gamma_{1}^{\,1}=1$; attained by $\mathbb{Z}$+  equals: HREF{Packing_densities_and_Hermite_numbers_of_the_classical_lattices#Z,1,hermite}+- params:+    n: '2'+  number: '1.154700538379251529018297561003914911295203502540253752037204652967955344605866691387430791171499050'+  comment: $\gamma_{2}=\frac{2}{\sqrt{3}}$, $\gamma_{2}^{\,2}=\frac{4}{3}$; attained+    by the hexagonal lattice $A_2$ CITE{Lagrange}+  equals: HREF{Packing_densities_and_Hermite_numbers_of_the_classical_lattices#A,2,hermite}+- params:+    n: '3'+  number: '1.259921049894873164767210607278228350570251464701507980081975112155299676513959483729396562436255094'+  comment: $\gamma_{3}=2^{1/3}$, $\gamma_{3}^{\,3}=2$; attained by $A_3=D_3$, the+    face-centred cubic lattice CITE{Gauss}+  equals: HREF{Packing_densities_and_Hermite_numbers_of_the_classical_lattices#A,3,hermite}+- params:+    n: '4'+  number: '1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573'+  comment: $\gamma_{4}=\sqrt{2}$, $\gamma_{4}^{\,4}=4$; attained by $D_4$ CITE{KZ}+  equals: HREF{Packing_densities_and_Hermite_numbers_of_the_classical_lattices#D,4,hermite}+- params:+    n: '5'+  number: '1.515716566510398082347259801306445238681283542978141642037505242097453677202058277641176134849431791'+  comment: $\gamma_{5}=2^{3/5}$, $\gamma_{5}^{\,5}=8$; attained by $D_5$ CITE{KZ}+  equals: HREF{Packing_densities_and_Hermite_numbers_of_the_classical_lattices#D,5,hermite}+- params:+    n: '6'+  number: '1.665366355311208639217572725017671513324124095787337672980480482451078485985633426184051324797373192'+  comment: $\gamma_{6}=\frac{2}{3^{1/6}}$, $\gamma_{6}^{\,6}=\frac{64}{3}$; attained+    by $E_6$ CITE{Blichfeldt}+  equals: HREF{Packing_densities_and_Hermite_numbers_of_the_classical_lattices#E,6,hermite}+- params:+    n: '7'+  number: '1.811447328527813343188345746430206375400891762515874710237416262768844934627125673909528787782071557'+  comment: $\gamma_{7}=2^{6/7}$, $\gamma_{7}^{\,7}=64$; attained by $E_7$ CITE{Blichfeldt}+  equals: HREF{Packing_densities_and_Hermite_numbers_of_the_classical_lattices#E,7,hermite}+- params:+    n: '8'+  number: '2'+  comment: $\gamma_{8}=2$, $\gamma_{8}^{\,8}=256$; attained by $E_8$ CITE{Blichfeldt}+  equals: HREF{Packing_densities_and_Hermite_numbers_of_the_classical_lattices#E,8,hermite}+- params:+    n: '24'+  number: '4'+  comment: $\gamma_{24}=4$, $\gamma_{24}^{\,24}=4^{24}$; attained by the Leech lattice+    $\Lambda_{24}$ CITE{CohnKumar}+  equals: HREF{Packing_densities_and_Hermite_numbers_of_the_classical_lattices#Lambda,24,hermite}