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A237603 Decimal expansion of the inscribed sphere radius in a regular dodecahedron with unit edge. 5
1, 1, 1, 3, 5, 1, 6, 3, 6, 4, 4, 1, 1, 6, 0, 6, 7, 3, 5, 1, 9, 4, 3, 7, 5, 0, 3, 9, 4, 8, 6, 9, 4, 9, 3, 7, 5, 8, 8, 3, 1, 5, 0, 3, 6, 9, 8, 8, 6, 4, 8, 7, 7, 7, 2, 6, 0, 1, 2, 0, 8, 0, 0, 3, 9, 9, 8, 4, 8, 9, 6, 2, 0, 5, 6, 5, 5, 6, 5, 9, 7, 5, 8, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Equals phi^2/(2*xi), where phi is the golden ratio (A001622, 2*cos(Pi/5)) and xi is its associate (A182007, 2*sin(Pi/5)).

LINKS

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

Wikipedia, Platonic solid

FORMULA

Equals A001622^2/A182007 = (cos(Pi/5))^2/sin(Pi/5) = A019863^2/A019845 = cos(Pi/5)*cotan(Pi/5) = A019863*A019952 = 1/sin(Pi/5) - sin(Pi/5) = A019845^(-1) - A019845 = sqrt(250+110*sqrt(5))/20.

EXAMPLE

1.1135163644116067351943750394869493758831503698864877726012080...

MATHEMATICA

RealDigits[ Cos[Pi/5]^2 / Sin[Pi/5], 10, 111][[1]] (* Or *)

RealDigits[ Sqrt[5/8 + 11/(8 Sqrt[5])], 10, 111][[1]] (* Robert G. Wilson v, Feb 28 2014 *)

PROG

(PARI) sqrt(250+110*sqrt(5))/20

CROSSREFS

Cf. A001622, A182007, A019863, A019863, A019952.

Cf. Platonic solids inradii: A020781 (tetrahedron), A020763 (octahedron), A179294 (icosahedron).

Sequence in context: A199616 A173973 A061649 * A073365 A065077 A118788

Adjacent sequences:  A237600 A237601 A237602 * A237604 A237605 A237606

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, Feb 25 2014

STATUS

approved

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Last modified March 27 02:45 EDT 2017. Contains 284144 sequences.