A375152 Decimal expansion of the apothem (inradius) of a regular 9-gon with unit side length.

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

Offset: 1

Author

Paolo Xausa, Aug 01 2024

Keywords

• nonn
• cons
• easy
• changed

Examples

			1.3737387097273111393808320132488363588759362995854...
		

Links

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

Crossrefs

Cf. A375151 (circumradius), A375153 (sagitta), A256853 (area).

Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A179452 (10-gon), A375191 (11-gon), A375193 (12-gon).

Cf. A019879, A019918, A019968.

Programs

Mathematica

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

PARI

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

Formula

Equals cot(Pi/9)/2 = A019968/2.

Equals 1/(2*tan(Pi/9)) = 1/(2*A019918).

Equals A375151*cos(Pi/9) = A375151*A019879.

Equals A375151 - A375153.

Largest of the 6 real-valued roots of 192*x^6 -432*x^4 +132*x^2 -1=0. - R. J. Mathar, Aug 29 2025