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A239798
Decimal expansion of the midsphere radius in a regular dodecahedron with unit edges.
14
1, 3, 0, 9, 0, 1, 6, 9, 9, 4, 3, 7, 4, 9, 4, 7, 4, 2, 4, 1, 0, 2, 2, 9, 3, 4, 1, 7, 1, 8, 2, 8, 1, 9, 0, 5, 8, 8, 6, 0, 1, 5, 4, 5, 8, 9, 9, 0, 2, 8, 8, 1, 4, 3, 1, 0, 6, 7, 7, 2, 4, 3, 1, 1, 3, 5, 2, 6, 3, 0, 2, 3, 1, 4, 0, 9, 4, 5, 1, 2, 2, 4, 8, 5, 3, 6, 0, 3, 6, 0
OFFSET
1,2
COMMENTS
In a regular polyhedron, the midsphere is tangent to all edges.
Apart from leading digits the same as A019863 and A019827. - R. J. Mathar, Mar 30 2014
FORMULA
Equals phi^2/2, phi being the golden ratio (A001622).
Equals (3+sqrt(5))/4.
Equals lim_{n->oo} A000045(n)/A066983(n). - Dimitri Papadopoulos, Nov 23 2023
EXAMPLE
1.30901699437494742410229341718281905886015458990288143106772431135263...
MAPLE
Digits:=100: evalf((3+sqrt(5))/4); # Wesley Ivan Hurt, Mar 27 2014
MATHEMATICA
RealDigits[GoldenRatio^2/2, 10, 105][[1]] (* Vaclav Kotesovec, Mar 27 2014 *)
PROG
(PARI) (3+sqrt(5))/4
CROSSREFS
Cf. A001622,
Midsphere radii in Platonic solids:
A020765 (tetrahedron),
A020761 (octahedron),
A010503 (cube),
A019863 (icosahedron).
Sequence in context: A167004 A287632 A259346 * A019827 A329284 A269557
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, Mar 27 2014
STATUS
approved