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A200257 Decimal expansion of the circumradius R of cyclic pentagon with sides 2, 3, 5, 7, and 11. 3

%I

%S 5,5,0,6,2,9,9,6,3,8,6,6,8,1,3,1,8,1,9,8,8,4,3,9,5,0,6,3,3,1,3,1,8,8,

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

%U 1,9,7,7,6,2,9,3,6,2,9,1,1,1,8,8,9

%N Decimal expansion of the circumradius R of cyclic pentagon with sides 2, 3, 5, 7, and 11.

%C Note that for cyclic polygon R does not depend on order of sides.

%H Ralph H. Buchholz and James A. MacDougall, <a href="http://dx.doi.org/10.1016/j.jnt.2007.05.005">Cyclic polygons with rational Sides and Area</a>, Journal of Number Theory, Volume 128, Issue 1, January 2008, Pages 17-48.

%H Zak Seidov, <a href="/A200257/a200257.png">Figure showing polygon</a>

%e R = 5.5062996386681...

%t nn=5; L=Sum[Prime[n],{n,nn}]; RealDigits[Re[FindRoot[Sum[ArcSin[Prime[n]/2/R], {n,nn}] == Pi, {R,L/2/Pi}][[1,2]]]]

%K nonn,cons

%O 1,1

%A _Zak Seidov_, Nov 15 2011

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Last modified September 18 18:41 EDT 2021. Contains 347533 sequences. (Running on oeis4.)