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A188593 Decimal expansion of (diagonal)/(shortest side) of a golden rectangle. 4
1, 9, 0, 2, 1, 1, 3, 0, 3, 2, 5, 9, 0, 3, 0, 7, 1, 4, 4, 2, 3, 2, 8, 7, 8, 6, 6, 6, 7, 5, 8, 7, 6, 4, 2, 8, 6, 8, 1, 1, 3, 9, 7, 2, 6, 8, 2, 5, 1, 5, 0, 0, 4, 4, 4, 8, 9, 4, 6, 1, 1, 2, 8, 8, 8, 6, 0, 3, 0, 6, 3, 4, 0, 1, 7, 0, 3, 8, 7, 0, 0, 3, 4, 3, 7, 5, 8, 5, 6, 2, 1, 9, 4, 1, 6, 2, 2, 7, 6, 3, 3, 5, 1, 7, 9, 9, 4, 3, 5, 1, 0, 2, 8, 0, 6, 0, 0, 8, 4, 1, 7, 9, 7, 4, 1, 3, 2, 3, 8, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A rectangle of length L and width W is a golden rectangle if L/W = r = (1+sqrt(5))/2. The diagonal has length D = sqrt(L^2+W^2), so D/W = sqrt(r^2+1) = sqrt(r+2).

Largest root of x^4 - 5x^2 + 5. - Charles R Greathouse IV, May 07 2011

This is the case n=10 of (Gamma(1/n)/Gamma(2/n))*(Gamma((n-1)/n)/Gamma((n-2)/n)) = 2*cos(Pi/n). - Bruno Berselli, Dec 13 2012

Edge length of a pentagram (regular star pentagon) with unit circumradius. - Stanislav Sykora, May 07 2014

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10001

Eric Weisstein's World of Mathematics, Golden Rectangle

Eric Weisstein's World of Mathematics, Pentagram

EXAMPLE

1.902113032590307144232878666758764286811397268251...

MATHEMATICA

r = (1 + 5^(1/2))/2; RealDigits[(2 + r)^(1/2), 10, 130]][[1]]

PROG

(PARI) sqrt((5+sqrt(5))/2)

CROSSREFS

Cf. A001622 (decimal expansion of the golden ratio).

Cf. A188594 (D/W for the silver rectangle, r=1+sqrt(2)).

Sequence in context: A221429 A221507 A089481 * A065421 A198556 A261169

Adjacent sequences:  A188590 A188591 A188592 * A188594 A188595 A188596

KEYWORD

nonn,cons,easy

AUTHOR

Clark Kimberling, Apr 04 2011

STATUS

approved

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Last modified March 27 22:02 EDT 2017. Contains 284182 sequences.