

A239798


Decimal expansion of the midsphere radius in a regular dodecahedron with unit edges.


6



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
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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


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000
Wikipedia, Platonic solid


FORMULA

Equals phi^2/2, phi being the golden ratio (A001622).
Also (3+sqrt(5))/4.


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 A269557 A201581
Adjacent sequences: A239795 A239796 A239797 * A239799 A239800 A239801


KEYWORD

nonn,cons,easy


AUTHOR

Stanislav Sykora, Mar 27 2014


STATUS

approved



