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

1,2

Comments

Apart from the first digit the same as A010527.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Regular Polygon.

Wikipedia, Apothem.

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

Example

1.8660254037844386467637231707529361834714026269...

Mathematica

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

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.

Sequence in context: A360167 A046266 A165104 * A010527 A270137 A269846

Adjacent sequences: A375190 A375191 A375192 * A375194 A375195 A375196

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 04 2024

Status

approved