A375068 Decimal expansion of the sagitta of a regular pentagon with unit side length.

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

Offset

0,2

Links

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

Eric Weisstein's World of Mathematics, Regular Polygon.

Eric Weisstein's World of Mathematics, Sagitta.

Index entries for algebraic numbers, degree 4.

Formula

Equals tan(Pi/10)/2 = sqrt(1-2/sqrt(5))/2 = A019916/2.

Equals A300074 - A375067.

Equals A179050/5 = sqrt(A229760)/10. - Hugo Pfoertner, Jul 30 2024

Minimal polynomial: 80*x^4 - 40*x^2 + 1. - Amiram Eldar, May 14 2026

Example

0.1624598481164531630779357061075672324774517357607...

Mathematica

First[RealDigits[Tan[Pi/10]/2, 10, 100]]

Prog

(PARI) tan(Pi/10)/2 \\ Charles R Greathouse IV, Feb 04 2025
(PARI) polrootsreal(80*x^4-40*x^2+1)[3] \\ Charles R Greathouse IV, Feb 04 2025

Crossrefs

Cf. A300074 (circumradius), A375067 (apothem), A102771 (area).

Cf. sagitta of other polygons with unit side length: A020769 (triangle), A174968 (square), A375069 (hexagon), A374972 (heptagon), A375070 (octagon), A375153 (9-gon), A375189 (10-gon), A375192 (11-gon), A375194 (12-gon).

Cf. A019916, A179050, A229760.

Sequence in context: A358089 A010493 A395063 * A175286 A061496 A125115

Adjacent sequences: A375065 A375066 A375067 * A375069 A375070 A375071

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 29 2024

Status

approved