A179294 Decimal expansion of radius of inscribed sphere about a regular icosahedron with edge = 1.

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

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

			0.75576131407617073048013370202500139263844478889356105922958289203910...
		

References

• Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §12.4 Theorems and Formulas (Solid Geometry), p. 451.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Dr. Math, Icosahedron.
• Wikipedia, Icosahedron.
• MathWorld, Icosahedron.
• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A010527, A102208, A179290, A179292.

Cf. Platonic solids inradii: A020781 (tetrahedron), A020763 (octahedron), A237603 (dodecahedron).

Programs

Mathematica

RealDigits[(Sqrt[42+18Sqrt[5]]/12), 10, 175][[1]]

PARI

sqrt((7+3*sqrt(5))/6)/2 \\ Stefano Spezia, Jan 27 2025

Formula

Equals sqrt(42 + 18*sqrt(5))/12.

Extensions

Partially rewritten by Charles R Greathouse IV, Feb 03 2011