A189089 Decimal expansion of Pi + sqrt(-1 + Pi^2).

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

Offset: 1

Author

Clark Kimberling, Apr 16 2011

Keywords

• nonn
• cons

Comments

Decimal expansion of the shape (= length/width = Pi + sqrt(-1 + Pi^2)) of the greater 2*Pi-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

			6.119780760659150034438472695582931258982600110...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A188738, A189090, A189088.

Programs

Mathematica

r = 2*Pi; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]] (*A189089*)
ContinuedFraction[t, 120]  (*A189090*)
RealDigits[Pi+Sqrt[Pi^2-1],10,150][[1]] (* Harvey P. Dale, Apr 18 2025 *)

PARI

Pi + sqrt(Pi^2-1) \\ Charles R Greathouse IV, Oct 02 2022