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A341906
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Decimal expansion of the moment of inertia of a solid regular dodecahedron with a unit mass and a unit edge length.
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2
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6, 0, 7, 3, 5, 5, 5, 0, 3, 7, 4, 1, 6, 3, 9, 3, 2, 7, 1, 9, 9, 8, 5, 9, 2, 4, 3, 6, 0, 1, 7, 3, 2, 5, 7, 7, 2, 7, 3, 9, 4, 7, 0, 5, 3, 4, 1, 6, 1, 6, 5, 0, 1, 0, 8, 2, 1, 8, 8, 3, 3, 0, 8, 5, 7, 0, 0, 3, 4, 3, 8, 6, 9, 9, 9, 5, 8, 1, 3, 0, 3, 5, 9, 0, 5, 4, 0
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OFFSET
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0,1
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COMMENTS
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The moments of inertia of the five Platonic solids were apparently first calculated by the Canadian physicist John Satterly (1879-1963) in 1957.
The moment of inertia of a solid regular dodecahedron with a uniform mass density distribution, mass M, and edge length L is I = c*M*L^2, where c is this constant.
The corresponding values of c for the other Platonic solids are:
Icosahedron: (3 + sqrt(5))/20 (= A104457/10).
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LINKS
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FORMULA
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Equals (95 + 39*sqrt(5))/300.
Equals (28 + 39*phi)/150, where phi is the golden ratio (A001622).
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EXAMPLE
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0.60735550374163932719985924360173257727394705341616...
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MATHEMATICA
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RealDigits[(95 + 39*Sqrt[5])/300, 10, 100][[1]]
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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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