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A341906
Decimal expansion of the moment of inertia of a solid regular dodecahedron with a unit mass and a unit edge length.
2
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
OFFSET
0,1
COMMENTS
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:
Tetrahedron: 1/20 (= A020761/10).
Octahedron: 1/10 (= A000007).
Cube: 1/6 (= A020793).
Icosahedron: (3 + sqrt(5))/20 (= A104457/10).
LINKS
P. K. Aravind, Gravitational collapse and moment of inertia of regular polyhedral configurations, American Journal of Physics, Vol. 59, No. 7 (1991), pp. 647-652.
Frédéric Perrier, Moments of inertia of Archimedean solids, 2015.
John Satterly, The Moments of Inertia of Some Polyhedra, The Mathematical Gazette, Vol. 42, No. 339 (1958), pp. 11-13.
Wikipedia, Moment of inertia.
FORMULA
Equals (95 + 39*sqrt(5))/300.
Equals (28 + 39*phi)/150, where phi is the golden ratio (A001622).
EXAMPLE
0.60735550374163932719985924360173257727394705341616...
MATHEMATICA
RealDigits[(95 + 39*Sqrt[5])/300, 10, 100][[1]]
CROSSREFS
Other constants related to the regular dodecahedron: A102769, A131595, A179296, A232810, A237603, A239798.
Sequence in context: A021900 A351401 A273413 * A365163 A195432 A196915
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 04 2021
STATUS
approved