A375193 Decimal expansion of the apothem (inradius) of a regular 12-gon with unit side length.

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

Offset: 1

Author

Paolo Xausa, Aug 04 2024

Keywords

• nonn
• cons
• easy

Comments

Apart from the first digit the same as A010527.

Examples

			1.8660254037844386467637231707529361834714026269...
		

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 2.

Crossrefs

Cf. A188887 (circumradius), A375194 (sagitta), A178809 (area).

Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A375067 (pentagon), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A375152 (9-gon), A179452 (10-gon), A375191 (11-gon).

Cf. A019884, A019913, A019973, A332133, A375069.

Programs

Mathematica

First[RealDigits[Cot[Pi/12]/2, 10, 100]]

PARI

sqrt(3)/2 + 1 \\ Charles R Greathouse IV, Feb 05 2025

Formula

Equals cot(Pi/12)/2 = (2 + sqrt(3))/2 = A019973/2.

Equals 1/(2*tan(Pi/12)) = 1/(2*A019913).

Equals A188887*cos(Pi/12) = A188887*A019884.

Equals A188887 - A375194.

Equals A332133^2 = 2 - A375069. - Hugo Pfoertner, Aug 04 2024