cp's OEIS Frontend

A341906 Decimal expansion of the moment of inertia of a solid regular dodecahedron with a unit mass and a unit edge length.

%I A341906 #18 Sep 30 2023 13:14:32
%S A341906 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,
%T A341906 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,
%U A341906 4,3,8,6,9,9,9,5,8,1,3,0,3,5,9,0,5,4,0
%N A341906 Decimal expansion of the moment of inertia of a solid regular dodecahedron with a unit mass and a unit edge length.
%C A341906 The moments of inertia of the five Platonic solids were apparently first calculated by the Canadian physicist John Satterly (1879-1963) in 1957.
%C A341906 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.
%C A341906 The corresponding values of c for the other Platonic solids are:
%C A341906 Tetrahedron: 1/20 (= A020761/10).
%C A341906 Octahedron: 1/10 (= A000007).
%C A341906 Cube: 1/6 (= A020793).
%C A341906 Icosahedron: (3 + sqrt(5))/20 (= A104457/10).
%H A341906 P. K. Aravind, <a href="https://doi.org/10.1119/1.16787">Gravitational collapse and moment of inertia of regular polyhedral configurations</a>, American Journal of Physics, Vol. 59, No. 7 (1991), pp. 647-652.
%H A341906 Frédéric Perrier, <a href="https://web.archive.org/web/20211003110410/https://www.ipgp.fr/sites/default/files/archimedeani_200115.pdf">Moments of inertia of Archimedean solids</a>, 2015.
%H A341906 John Satterly, <a href="https://doi.org/10.1119/1.1934519">Moments of Inertia about Selected Axes of Regular Polygons, Right Pyramids on Regular Polygonal Bases, and of the Platonic and Some Archimedian Polyhedra</a>, American Journal of Physics, Vol. 25, No. 7 (1957), pp. 489-490.
%H A341906 John Satterly, <a href="https://www.jstor.org/stable/3608345">The Moments of Inertia of Some Polyhedra</a>, The Mathematical Gazette, Vol. 42, No. 339 (1958), pp. 11-13.
%H A341906 Wikipedia, <a href="https://en.wikipedia.org/wiki/List_of_moments_of_inertia">List of moments of inertia</a>.
%H A341906 Wikipedia, <a href="https://en.wikipedia.org/wiki/Moment_of_inertia">Moment of inertia</a>.
%H A341906 Wikipedia, <a href="https://en.wikipedia.org/wiki/Regular_dodecahedron">Regular dodecahedron</a>.
%H A341906 <a href="/index/Mo#moment_of_inertia">Index entries for sequences related to moment of inertia</a>.
%F A341906 Equals (95 + 39*sqrt(5))/300.
%F A341906 Equals (28 + 39*phi)/150, where phi is the golden ratio (A001622).
%e A341906 0.60735550374163932719985924360173257727394705341616...
%t A341906 RealDigits[(95 + 39*Sqrt[5])/300, 10, 100][[1]]
%Y A341906 Cf. A000007, A001622, A020761, A020793, A104457.
%Y A341906 Other constants related to the regular dodecahedron: A102769, A131595, A179296, A232810, A237603, A239798.
%K A341906 nonn,cons
%O A341906 0,1
%A A341906 _Amiram Eldar_, Jun 04 2021