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

Author

Paolo Xausa, Jul 29 2024

Keywords

• nonn
• cons
• easy

Examples

			0.1624598481164531630779357061075672324774517357607...
		

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.

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.

Programs

Mathematica

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

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

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