A094887 Decimal expansion of phi*sqrt(2), where phi = (1+sqrt(5))/2.

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

Offset: 1

Author

N. J. A. Sloane, Jun 15 2004

Keywords

• cons
• nonn

Comments

An algebraic number with minimal polynomial x^4 - 6x^2 + 4. - Charles R Greathouse IV, Mar 25 2014

The rhombus with diagonals phi*sqrt(2) and sqrt(2) is the unique golden rhombus -- by definition, the ratio of the diagonals of a golden rhombus is phi -- whose area is also phi (the golden ratio). - Rick L. Shepherd, Apr 10 2017

Examples

			2.28824561127073719...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 1..1000
• MathWorld, Golden Rhombus
• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. A001622 (phi), A002193 (sqrt(2)).

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2)*(1 + Sqrt(5))/2; // G. C. Greubel, Sep 27 2018

Mathematica

RealDigits[GoldenRatio Sqrt[2],10,120][[1]] (* Harvey P. Dale, Jan 24 2016 *)

PARI

sqrt(3+sqrt(5)) \\ Charles R Greathouse IV, Mar 25 2014