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<a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

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

RealDigits[(E+Sqrt[E^2-4])/2, 10, 150][[1]] (* Harvey P. Dale, Oct 17 2013 *)

Corrected by Harvey P. Dale, Oct 17 2013

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_Clark Kimberling (ck6(AT)evansville.edu), _, Apr 15 2011

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allocated for Clark Kimberling

Decimal expansion of (e+sqrt(-4+e^2))/2.

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

1,1

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

2.2796103731105126266020168769161733623002084362...

r = E; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]

N[t, 130]

RealDigits[N[t, 130]][[1]]

ContinuedFraction[t, 120]

Cf. A188738, A189040, A189041.

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nonn,cons

Clark Kimberling (ck6(AT)evansville.edu), Apr 15 2011

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allocated for Clark Kimberling

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