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

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

Author

Amiram Eldar, Jun 04 2021

Keywords

• nonn
• cons

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).

Examples

			0.60735550374163932719985924360173257727394705341616...
		

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, Moments of Inertia about Selected Axes of Regular Polygons, Right Pyramids on Regular Polygonal Bases, and of the Platonic and Some Archimedian Polyhedra, American Journal of Physics, Vol. 25, No. 7 (1957), pp. 489-490.
• John Satterly, The Moments of Inertia of Some Polyhedra, The Mathematical Gazette, Vol. 42, No. 339 (1958), pp. 11-13.
• Wikipedia, List of moments of inertia.
• Wikipedia, Moment of inertia.
• Wikipedia, Regular dodecahedron.
• Index entries for sequences related to moment of inertia.

Crossrefs

Cf. A000007, A001622, A020761, A020793, A104457.

Other constants related to the regular dodecahedron: A102769, A131595, A179296, A232810, A237603, A239798.

Programs

Mathematica

RealDigits[(95 + 39*Sqrt[5])/300, 10, 100][[1]]

Formula

Equals (95 + 39*sqrt(5))/300.

Equals (28 + 39*phi)/150, where phi is the golden ratio (A001622).