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 A220351 Decimal expansion of (3*sqrt(3)+sqrt(7))/10. 2
 7, 8, 4, 1, 9, 0, 3, 7, 3, 3, 7, 7, 1, 2, 2, 2, 4, 7, 1, 0, 8, 3, 9, 5, 4, 7, 7, 8, 1, 5, 6, 8, 7, 7, 5, 2, 6, 5, 3, 8, 6, 7, 4, 9, 4, 4, 5, 1, 3, 5, 9, 2, 0, 6, 4, 5, 3, 5, 7, 5, 5, 3, 9, 7, 5, 5, 6, 8, 6, 7, 8, 7, 3, 9, 5, 6, 6, 8, 3, 7, 3, 9, 0, 0, 3, 8, 3, 1, 4, 4, 6, 7, 4, 6, 2, 8, 9, 3, 3, 7, 6, 4, 1, 9, 4, 3, 0, 0, 2, 5, 8, 4, 7, 1, 7, 5, 7, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Smith & Smith conjecture that this is the Steiner ratio rho_3, the least upper bound on the ratio of the length of the Steiner minimal tree to the length of the minimal tree in dimension 3. Diaconis & Graham offer \$1000 for proof (or disproof) of this conjecture. This is an algebraic number of degree 4; the minimal polynomial is 25x^4 - 17x^2 + 1. REFERENCES Persi Diaconis and R. L. Graham, Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks, Princeton University Press, 2011. See pp. 212-214. Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.6 Steiner Tree Constants, p. 504. LINKS Table of n, a(n) for n=0..118. Warren D. Smith and J. MacGregor Smith, On the Steiner ratio in 3-space, Journal of Combinatorial Theory, Series A 69:2 (1995), pp. 301-332. Index entries for algebraic numbers, degree 4 FORMULA (3*sqrt(3)+sqrt(7))/10. EXAMPLE 0.7841903733771222471083954778156877526538674944513592064535755... MATHEMATICA RealDigits[(3*Sqrt[3]+Sqrt[7])/10, 10, 120] // First (* Jean-François Alcover, May 27 2014 *) PROG (PARI) (3*sqrt(3)+sqrt(7))/10 (PARI) polrootsreal(25*x^4 - 17*x^2 + 1)[4] \\ Charles R Greathouse IV, Jan 05 2016 CROSSREFS Cf. A010527. Sequence in context: A091683 A359009 A092157 * A220863 A330161 A197823 Adjacent sequences: A220348 A220349 A220350 * A220352 A220353 A220354 KEYWORD nonn,cons AUTHOR Charles R Greathouse IV, Dec 11 2012 EXTENSIONS Formula and name simplified by Jean-François Alcover, May 27 2014 STATUS approved

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Last modified September 13 22:05 EDT 2024. Contains 375910 sequences. (Running on oeis4.)