A277390 Decimal expansion of 5-2*sqrt(5)+sqrt(25-10*sqrt(5))-sqrt(5-2*sqrt(5)).

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

Offset: 1

Author

Martin Renner, Oct 12 2016

Keywords

• nonn
• cons

Comments

Largest radius of five circles tangent to a circle of radius 1.

A quartic integer with minimal polynomial x^4 - 20x^3 + 10x^2 + 20x + 5. - Charles R Greathouse IV, Oct 12 2016

Examples

			1.42591999815959135206...
		

Links

• Eric W. Weisstein: Steiner chain. From MathWorld. A Wolfram Web Resource.
• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. A176394 (three circles), A014176 (four circles).

Programs

Mathematica

RealDigits[5-2*Sqrt[5]+Sqrt[25-10*Sqrt[5]]-Sqrt[5-2*Sqrt[5]],10,120][[1]] (* Harvey P. Dale, May 20 2021 *)

PARI

s=sqrt(5); t=5-2*s; sqrt(25-10*s)+t-sqrt(t) \\ Charles R Greathouse IV, Oct 12 2016

Formula

tan(Pi/5)*(tan(Pi/5)+sqrt(1+tan(Pi/5)^2)).