A375067 Decimal expansion of the apothem (inradius) of a regular pentagon with unit side length.

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

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Regular Polygon.

Wikipedia, Apothem.

Index entries for algebraic numbers, degree 4.

Formula

Equals cot(Pi/5)/2 = A019952/2.

Equals 1/(2*tan(Pi/5)) = 1/(2*A019934).

Equals sqrt(1/4 + 1/(2*sqrt(5))).

Equals (1/2)*csc(Pi/5)*cos(Pi/5) = A300074*A019863.

Equals A300074 - A375068.

Equals A131595/30. - Hugo Pfoertner, Jul 30 2024

Example

0.688190960235586769103604790955443839762949668...

Mathematica

First[RealDigits[Cot[Pi/5]/2, 10, 100]]

Prog

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

Crossrefs

Cf. A300074 (circumradius), A375068 (sagitta), A102771 (area).

Cf. apothem of other polygons with unit side length: A020769 (triangle), A020761 (square), A010527 (hexagon), A374971 (heptagon), A174968 (octagon), A375152 (9-gon), A179452 (10-gon), A375191 (11-gon), A375193 (12-gon).

Cf. A019934, A019952, A019863, A131595.

Sequence in context: A365125 A088608 A323984 * A176104 A011481 A212480

Adjacent sequences: A375064 A375065 A375066 * A375068 A375069 A375070

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 29 2024

Status

approved