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%I #16 Oct 27 2023 10:39:33
%S 5,5,5,9,0,5,2,1,1,4,1,6,5,8,8,7,0,4,8,2,6,2,9,5,5,5,0,6,9,6,5,9,3,0,
%T 2,2,9,6,1,3,8,6,1,1,8,1,9,7,4,7,4,4,6,6,3,4,1,2,6,9,4,6,1,6,7,4,5,3,
%U 0,8,4,4,4,3,9,2,8,6,7,8,2,2,2,8,5,2,5,9,4,2,4,9,4,8,5,4,8,4,7,4,1,1
%N Decimal expansion of smallest disk radius for which six equal disks can cover the unit disk.
%C The largest disk that can be covered by six unit disks has radius 1/r = 1.79886782...
%C Piezas (see Mathematics Stack Exchange link) notes that the minimal polynomials for both this constant and A133077 have unsolvable Galois groups.
%H Erich Friedman, <a href="https://erich-friedman.github.io/packing/circovcir">Circles Covering Circles</a>
%H Jeremy Tan, <a href="https://math.stackexchange.com/questions/2651575/what-is-the-exact-value-of-the-radius-in-the-six-disks-problem/2652796#2652796">What is the exact value of the radius in the Six Disks Problem?</a>, Mathematics Stack Exchange, Feb 15 2018
%H Jeremy Tan, <a href="https://gitlab.com/parclytaxel/Dounreay/-/blob/ad1bc7b5464573483288153556aeb7e74a918e90/packing-covering/dcp/progs/6.py">Python/Singular program</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DiskCoveringProblem.html">Disk Covering Problem</a>
%H <a href="/index/Al#algebraic_18">Index entries for algebraic numbers, degree 18</a>
%F r is the smallest positive root of 7841367r^18 - 33449976r^16 + 62607492r^14 - 63156942r^12 + 41451480r^10 - 19376280r^8 + 5156603r^6 - 746832r^4 + 54016r^2 + 3072.
%e 0.55590521141658870482629555069659...
%t First@ RealDigits@ N[Root[7841367x^18 -33449976x^16 +62607492x^14 -63156942x^12 +41451480x^10 -19376280x^8 +5156603x^6 -746832x^4 +54016x^2 +3072, x, 3], 102]
%o (PARI) polrootsreal(7841367*x^18 -33449976*x^16 +62607492*x^14 -63156942*x^12 +41451480*x^10 -19376280*x^8 +5156603*x^6 -746832*x^4 +54016*x^2 +3072)[3]
%Y Cf. A133077 (five disks).
%K nonn,cons
%O 0,1
%A _Jeremy Tan_, Feb 16 2018
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