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A245263
Decimal expansion of the minimum total length of lines tying together the five points of a regular pentagon having unit sides.
1
3, 8, 9, 1, 1, 5, 6, 8, 2, 3, 3, 2, 6, 8, 5, 3, 8, 1, 8, 0, 7, 8, 2, 6, 2, 5, 5, 6, 7, 1, 9, 9, 0, 5, 0, 4, 9, 8, 5, 2, 9, 8, 1, 4, 4, 5, 6, 7, 0, 1, 3, 9, 2, 9, 9, 6, 2, 7, 7, 2, 8, 9, 5, 6, 0, 0, 8, 9, 3, 8, 8, 4, 1, 5, 4, 4, 1, 8, 3, 7, 2, 8, 5, 9, 6, 1, 9, 8, 0, 6, 2, 7, 0, 8, 3, 4, 4, 6, 2, 2, 7
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
Sequence in context: A229372 A357406 A021261 * A016672 A177272 A010630
KEYWORD
nonn,cons
AUTHOR
STATUS
approved