A189038 Decimal expansion of (9+sqrt(17))/8.

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

Offset: 1

Author

Clark Kimberling, Apr 15 2011

Keywords

• nonn
• cons
• easy

Comments

Decimal expansion of the shape (= length/width = (9+sqrt(17))/8) of the greater (9/4)-contraction rectangle.

See A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes.

This number - 1, namely w = (1 + sqrt(17))/8 = 0.6403882032..., is the positive real root of 4*x^2 - x - 1, with negative root -(-1 + sqrt(17))/8 = -0.3903882032... = -(w - 1/4). - Wolfdieter Lang, Dec 12 2022

Examples

			1.64038820320220756872767623199675962814339990...
		

Crossrefs

Cf. A188738, A189037.

Programs

Mathematica

r = 9/4; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]

PARI

(sqrt(17)+9)/8 \\ Charles R Greathouse IV, Apr 25 2016