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

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

Offset: 1

Author

Zak Seidov, Nov 15 2011

Keywords

• nonn
• cons

Comments

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

Examples

			R = 5.5062996386681...
		

Links

• Ralph H. Buchholz and James A. MacDougall, Cyclic polygons with rational Sides and Area, Journal of Number Theory, Volume 128, Issue 1, January 2008, Pages 17-48.
• Zak Seidov, Figure showing polygon

Programs

Mathematica

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]]]]