cp's OEIS Frontend

A343851 Decimal expansion of the solution to the Heilbronn triangle problem for seven points in a unit square.

%I A343851 #40 Dec 24 2024 11:35:17
%S A343851 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,
%T A343851 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,
%U A343851 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
%N A343851 Decimal expansion of the solution to the Heilbronn triangle problem for seven points in a unit square.
%C A343851 The Heilbronn triangle problem: find an arrangement of n points in a convex region such that the minimum area among triangles formed by three of the points is maximized.
%C A343851 The seven-point configuration in the square was found by Comellas and Yebra and proved optimal by Chen and Zeng.
%D A343851 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.16, p. 527.
%H A343851 Liangyu Chen and Zhenbing Zeng, <a href="https://doi.org/10.1007/978-3-642-21046-4_11">On the Heilbronn Optimal Configuration of Seven Points in the Square</a>, Automated Deduction in Geometry, Springer-Verlag, 2011, pp. 196-224.
%H A343851 Francesc Comellas and J. Luis A. Yebra, <a href="https://doi.org/10.37236/1623">New Lower Bounds for Heilbronn Numbers</a>, Electronic Journal of Combinatorics, 9 (2002).
%H A343851 Erich Friedman, <a href="https://erich-friedman.github.io/packing/heilbronn">The Heilbronn Problem for Squares</a>.
%H A343851 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeilbronnTriangleProblem.html">Heilbronn Triangle Problem</a>.
%H A343851 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>.
%F A343851 This is the smallest positive root of 152x^3 + 12x^2 - 14x + 1.
%e A343851 0.08385900900751340663796674354476...
%t A343851 First@ RealDigits@ N[Root[152x^3+12x^2-14x+1, x, 2], 105]
%o A343851 (PARI) polrootsreal(152*x^3+12*x^2-14*x+1)[2]
%Y A343851 Cf. A248866 (discrete Heilbronn triangle problem).
%K A343851 nonn,cons
%O A343851 0,2
%A A343851 _Jeremy Tan_, May 03 2021