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

Author

Paolo Xausa, Jul 29 2024

Keywords

• nonn
• cons
• easy

Examples

			0.688190960235586769103604790955443839762949668...
		

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.

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.

Programs

Mathematica

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

PARI

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

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