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Decimal expansion of Pi*sqrt(3)/16.
4

%I #17 Mar 24 2021 09:14:41

%S 3,4,0,0,8,7,3,8,0,7,9,3,9,1,5,8,4,6,9,8,6,3,8,9,6,7,3,3,0,7,9,0,4,1,

%T 9,9,8,0,3,2,6,2,4,2,1,5,1,7,3,8,8,8,5,7,9,1,9,3,5,3,4,2,5,3,8,5,2,7,

%U 3,0,9,6,4,6,1,1,9,1,3,5,3,1,9,0,7,7,3,4,3,5,2,8,9,7,6,1,2,8,1,6,6,0,5,4,1,7

%N Decimal expansion of Pi*sqrt(3)/16.

%C The atomic packing factor (APF) of the diamond cubic crystal lattice and the smallest APF among all crystallographic lattices filled by spheres of the same diameter. The APF of the body-centered-cubic (bcc) lattice packed with spheres of the same diameter is twice this value (see Examples). For other crystal lattices, see the cross-refs.

%H Stanislav Sykora, <a href="/A247446/b247446.txt">Table of n, a(n) for n = 0..2000</a>

%H Steve Sque, <a href="https://www.stevesque.com/diamond/structure/">Structure of Diamond</a> (adapted from 2005 thesis)

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Diamond_cubic">Diamond cubic</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Atomic_packing_factor">Atomic packing factor</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 0.340087380793915846986389673307904199803262421517388857919353425385273...

%e APF of the bcc lattice packed with spheres of the same diameter:

%e 0.680174761587831693972779346615808399606524843034777715838706850770546...

%t RealDigits[Pi*Sqrt[3]/16,10,120][[1]] (* _Vaclav Kotesovec_, Oct 04 2014 *)

%o (PARI) Pi*sqrt(3)/16

%Y Cf. APF's of other crystal lattices: A093825 (hcp,fcc), A019673 (simple cubic).

%K nonn,cons,easy

%O 0,1

%A _Stanislav Sykora_, Sep 29 2014