A375151 Decimal expansion of the circumradius of a regular 9-gon with unit side length.

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

Offset: 1

Author

Paolo Xausa, Aug 01 2024

Keywords

• nonn
• cons
• easy
• changed

Examples

			1.46190220008154362611637720668314585193675283...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Regular Polygon.
• Wikipedia, Regular polygon.
• Index entries for algebraic numbers, degree 6.

Crossrefs

Cf. A375152 (apothem), A375153 (sagitta), A256853 (area).

Cf. circumradius of other polygons with unit side length: A020760 (triangle), A010503 (square), A300074 (pentagon), A374957 (heptagon), A285871 (octagon), A001622 (10-gon), A375190 (11-gon), A188887 (12-gon)

Cf. A019879, A121602, A272488.

Programs

Mathematica

First[RealDigits[Csc[Pi/9]/2, 10, 100]]

PARI

 5/sin(Pi/9) \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals csc(Pi/9)/2 = A121602/2.

Equals 1/(2*sin(Pi/9)) = 1/A272488.

Equals A375152/cos(Pi/9) = A375152/A019879.

Equals A375152 + A375153.

Largest of the 6 real-valued roots of 3*x^6-9*x^4+6*x^2-1=0. - R. J. Mathar, Aug 29 2025