OFFSET
1,1
LINKS
Jean-François Alcover, Pentagon Steiner tree. After James C. Bergquist.
Herman P. Robinson, Mathematical Constants. p. 182.
FORMULA
(7*sqrt(3)-sqrt(15))/12 + sqrt(18-6*sqrt(5))/3 + (1+sqrt(5))*sqrt(10-2*sqrt(5))/8 + sqrt(5+2*sqrt(5))/2 = sqrt(17+7*sqrt(5)+sqrt(6*(65+29*sqrt(5))))/2.
EXAMPLE
3.891156823326853818078262556719905049852981445670139299627728956...
MATHEMATICA
(7*Sqrt[3]-Sqrt[15])/12 + Sqrt[18-6*Sqrt[5]]/3 + (1+Sqrt[5])*Sqrt[10-2*Sqrt[5]]/8 + Sqrt[5+2*Sqrt[5]]/2 // RealDigits[#, 10, 101] & // First
PROG
(PARI) sqrt(polrootsreal(x^4-17*x^3+29*x^2-13*x+1)[4]) \\ Charles R Greathouse IV, Jul 15 2014
(PARI) polrootsreal(x^8-17*x^6+29*x^4-13*x^2+1)[8] \\ Charles R Greathouse IV, Oct 27 2023
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jul 15 2014
STATUS
approved