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

1,1

Comments

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

Links

Table of n, a(n) for n=1..85.

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

Example

R = 5.5062996386681...

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]]]]

Crossrefs

Sequence in context: A299625 A021649 A357715 * A236023 A200516 A233383

Adjacent sequences: A200254 A200255 A200256 * A200258 A200259 A200260

Keyword

nonn,cons

Author

Zak Seidov, Nov 15 2011

Status

approved