A343851 Decimal expansion of the solution to the Heilbronn triangle problem for seven points in a unit square.
0, 8, 3, 8, 5, 9, 0, 0, 9, 0, 0, 7, 5, 1, 3, 4, 0, 6, 6, 3, 7, 9, 6, 6, 7, 4, 3, 5, 4, 4, 7, 6, 0, 5, 5, 6, 8, 4, 4, 3, 2, 4, 7, 6, 8, 1, 9, 1, 6, 1, 4, 9, 8, 5, 2, 6, 1, 2, 3, 0, 0, 8, 8, 5, 6, 6, 2, 4, 3, 5, 0, 9, 5, 3, 5, 7, 5, 2, 4, 4, 8, 3, 9, 7, 6, 5, 5, 8, 6, 0, 3, 9, 8, 9, 6, 0, 8, 5, 3, 7, 1, 2
Offset: 0
Examples
0.08385900900751340663796674354476...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.16, p. 527.
Links
- Liangyu Chen and Zhenbing Zeng, On the Heilbronn Optimal Configuration of Seven Points in the Square, Automated Deduction in Geometry, Springer-Verlag, 2011, pp. 196-224.
- Francesc Comellas and J. Luis A. Yebra, New Lower Bounds for Heilbronn Numbers, Electronic Journal of Combinatorics, 9 (2002).
- Erich Friedman, The Heilbronn Problem for Squares.
- Eric Weisstein's World of Mathematics, Heilbronn Triangle Problem.
- Index entries for algebraic numbers, degree 3.
Crossrefs
Cf. A248866 (discrete Heilbronn triangle problem).
Programs
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Mathematica
First@ RealDigits@ N[Root[152x^3+12x^2-14x+1, x, 2], 105]
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PARI
polrootsreal(152*x^3+12*x^2-14*x+1)[2]
Formula
This is the smallest positive root of 152x^3 + 12x^2 - 14x + 1.
Comments