%I #10 Feb 16 2025 08:33:36

%S 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,

%T 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,

%U 7,3,2,6,1,6,8,2,4,3,1,8,5,4,3,6,4,0,3

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

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

%C A quartic integer with minimal polynomial x^4 - 20x^3 + 10x^2 + 20x + 5. - _Charles R Greathouse IV_, Oct 12 2016

%H Eric W. Weisstein: <a href="https://mathworld.wolfram.com/SteinerChain.html">Steiner chain.</a> From MathWorld. A Wolfram Web Resource.

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>

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

%e 1.42591999815959135206...

%t RealDigits[5-2*Sqrt[5]+Sqrt[25-10*Sqrt[5]]-Sqrt[5-2*Sqrt[5]],10,120][[1]] (* _Harvey P. Dale_, May 20 2021 *)

%o (PARI) s=sqrt(5); t=5-2*s; sqrt(25-10*s)+t-sqrt(t) \\ _Charles R Greathouse IV_, Oct 12 2016

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

%K nonn,cons

%O 1,2

%A _Martin Renner_, Oct 12 2016