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Decimal expansion of r_9, the 9th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_9.
7

%I #17 Feb 11 2025 09:14:49

%S 6,3,7,5,5,5,9,7,7,2,3,1,9,4,5,7,9,3,4,9,1,3,1,7,1,6,7,7,3,9,9,0,9,5,

%T 9,6,7,3,7,5,7,0,8,4,2,4,5,7,4,0,1,8,7,4,0,6,7,0,8,5,4,5,6,5,6,7,3,3,

%U 1,8,1,1,5,9,9,4,0,6,8,7,3,7,5,7,5,0,4,1,7,1,6,6,0,0,7,3,3,3,7,7,4,9

%N Decimal expansion of r_9, the 9th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_9.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 62.

%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.

%F First root of x^4 - 10x^2 - 8x + 9.

%e 0.637555977231945793491317167739909596737570842457401874067...

%t RealDigits[Root[x^4 - 10x^2 - 8x + 9, x, 1], 10, 102] // First

%o (PARI) polrootsreal(x^4-10*x^2-8*x+9)[1] \\ _Charles R Greathouse IV_, Feb 11 2025

%Y Cf. A246723 (r_1), A246724 (r_2), A246725 (r_3), A246726 (r_4), A246727 (r_5), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246729 (r_8).

%K nonn,cons,easy,changed

%O 0,1

%A _Jean-François Alcover_, Sep 02 2014