A187798 Decimal expansion of (3-phi)/2, where phi is the golden ratio.

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

Offset: 0

Author

Joost Gielen, Aug 30 2013

Keywords

• nonn
• cons

Comments

This is the height h of the isosceles triangle in a regular pentagon inscribed in the unit circle formed from a diagonal as base and two adjacent pentagon sides. h = sqrt(sqrt(3-phi)^2 - (sqrt(2 + phi)/2)^2) = sqrt(10 - 5*phi)/2 = (3 - phi)/2. - Wolfdieter Lang, Jan 07 2018

Examples

			0.6909830056250525758977065828171809411398454100971185689322756886473697685905...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A001622, A081011, A187426, A226765, A094874, A344212.

Programs

Mathematica

RealDigits[(3 - GoldenRatio)/2, 10, 111][[1]] (* or *)
RealDigits[(5 - Sqrt[5])/4, 10, 111][[1]] (* Robert G. Wilson v, Jan 07 2018 *)

PARI

(5-sqrt(5))/4 \\ Charles R Greathouse IV, Aug 31 2013

Formula

Equals (3-phi)/2 = A094874/2 with phi from A001622.

From Amiram Eldar, Nov 28 2024: (Start)

Equals 1/A344212.

Equals Product_{k>=0} (1 - 1/A081011(k)). (End)

Extensions

Extended by Charles R Greathouse IV, Aug 31 2013