A179292 Decimal expansion of radius of inscribed sphere of an icosahedron with radius of circumscribed sphere = 1.

7, 9, 4, 6, 5, 4, 4, 7, 2, 2, 9, 1, 7, 6, 6, 1, 2, 2, 9, 5, 5, 5, 3, 0, 9, 2, 8, 3, 2, 7, 5, 9, 4, 0, 4, 2, 0, 2, 6, 5, 9, 0, 5, 8, 8, 3, 0, 9, 2, 6, 4, 8, 0, 1, 7, 5, 4, 9, 5, 5, 7, 7, 5, 0, 0, 8, 4, 3, 8, 6, 4, 4, 9, 7, 1, 7, 3, 7, 1, 1, 6, 7, 9, 3, 0, 2, 7, 2, 9, 9, 4, 8, 4, 8, 7, 0, 8, 7, 1, 3, 7, 8, 5, 2, 8

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Jul 09 2010

Keywords

• nonn
• cons
• easy

Comments

Icosahedron: A three-dimensional figure with 20 equilateral triangle faces, 12 vertices, and 30 edges.

Examples

			0.794654472291766122955530928327594042026590588309264801754955775008438...
		

Links

• Mathforum, Icosahedron
• Wikipedia, Icosahedron
• MathWorld, Icosahedron
• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A010527, A102208, A179290.

Programs

Mathematica

R=1;RealDigits[N[(Sqrt[75+30*Sqrt[5]]/15)*R,175]]

PARI

polrootsreal(45*x^4-30*x^2+1)[4] \\ Charles R Greathouse IV, Sep 02 2024

PARI

sqrt(6/sqrt(5)+3)/3 \\ Charles R Greathouse IV, Sep 02 2024

Formula

Sqrt(75 + 30*sqrt(5))/15.

Extensions

Offset corrected, keyword:cons added by R. J. Mathar, Jul 11 2010