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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 (list; constant; graph; refs; listen; history; text; internal format)
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: A068607 A167004 A259346 * A019827 A269557 A201581

Adjacent sequences:  A239795 A239796 A239797 * A239799 A239800 A239801

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, Mar 27 2014

STATUS

approved

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Last modified May 29 07:20 EDT 2017. Contains 287243 sequences.