A374971 Decimal expansion of the apothem (inradius) of a regular heptagon with unit side length.

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

Offset: 1

Author

Paolo Xausa, Jul 26 2024

Keywords

• nonn
• cons
• easy
• changed

Examples

			1.0382606982861682835817694307429201653528601033...
		

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. A374957 (circumradius), A374972 (sagitta), A178817 (area).

Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A174968 (octagon), A375152 (9-gon), A179452 (10-gon), A375191 (11-gon), A375193 (12-gon).

Cf. A178818, A073052, A343058.

Programs

Mathematica

First[RealDigits[Cot[Pi/7]/2, 10, 100]]

PARI

 5/(Pi/7) \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals cot(Pi/7)/2 = A178818/2.

Equals 1/(2*tan(Pi/7)) = 1/(2*A343058).

Equals A374957*cos(Pi/7) = A374957*A073052.

Equals A374957 - A374972.

Largest of the 6 real-valued roots of 448*x^6 -560*x^4 +84*x^2 -1 =0. - R. J. Mathar, Aug 29 2025