A188939 Decimal expansion of (7+sqrt(33))/4.

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

Offset: 1

Author

Clark Kimberling, Apr 14 2011

Keywords

• nonn
• cons

Comments

Decimal expansion of the shape (= length/width = (7+sqrt(33))/4) of the greater (7/2)-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.

Examples

			3.1861406616345071649626528670547323295550...
		

Crossrefs

Cf. A188738, A188739.

Programs

Mathematica

r = 7/2; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
RealDigits[(7+Sqrt[33])/4,10,140][[1]] (* Harvey P. Dale, Nov 02 2015 *)

Extensions

Corrected and extended by Harvey P. Dale, Nov 02 2015