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A243908
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Johannes Kepler's polyhedron inscribing constant.
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1
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7, 0, 1, 6, 3, 9, 7, 0, 0, 3, 7, 0, 3, 3, 9, 2, 1, 4, 2, 8, 2, 8, 4, 0, 5, 4, 3, 5, 1, 5, 7, 4, 4, 6, 2, 7, 4, 7, 2, 6, 8, 4, 2, 0, 1, 4, 2, 3, 9, 2, 9, 7, 3, 6, 9, 2, 9, 0, 2, 1, 8, 1, 4, 1, 3, 4, 8, 9, 1, 9, 8, 8, 9, 8, 3, 3, 7, 8, 5, 0, 3, 6, 1, 6, 9, 5, 0, 2, 8, 2, 7, 2, 2, 7, 8, 2, 5, 5, 9, 2, 5, 4, 7, 4, 1, 9, 5, 2
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OFFSET
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-1,1
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COMMENTS
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Decimal expansion of (5 + 2*sqrt(5))/135.
The finite solid analogy to the plane polygon inscribing constant (A085365).
The five Platonic solids are the tetrahedron, the hexahedron (or cube), the octahedron, the dodecahedron and the icosahedron.
The geometric interpretation is as follows. Begin with a unit sphere. Inscribe a tetrahedron and then inscribe a sphere. Inscribe a cube and then inscribe a sphere. Inscribe an octahedron and then inscribe a sphere. Inscribe a dodecahedron and then inscribe a sphere. Inscribe an icosahedron and then inscribe a sphere. This constant is the radius of this last sphere. Actually, the order in which the five solids are inscribed has no effect on the resulting constant.
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LINKS
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FORMULA
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Equals 1/A211174 = 1/(9*(15 - 6*sqrt(5))).
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EXAMPLE
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0.070163970037033921428284054351574462747268420142392973692902181413489198898...
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MAPLE
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MATHEMATICA
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RealDigits[(5 + 2 Sqrt[5])/135, 10, 100][[1]] (* Wesley Ivan Hurt, Sep 05 2014 *)
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PROG
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(PARI) first(n)=digits(floor(10^(n+1)*(5+2*sqrt(5))/135)) \\ Edward Jiang, Sep 05 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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