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A188582 Decimal expansion of sqrt(2) - 1. 0
4, 1, 4, 2, 1, 3, 5, 6, 2, 3, 7, 3, 0, 9, 5, 0, 4, 8, 8, 0, 1, 6, 8, 8, 7, 2, 4, 2, 0, 9, 6, 9, 8, 0, 7, 8, 5, 6, 9, 6, 7, 1, 8, 7, 5, 3, 7, 6, 9, 4, 8, 0, 7, 3, 1, 7, 6, 6, 7, 9, 7, 3, 7, 9, 9, 0, 7, 3, 2, 4, 7, 8, 4, 6, 2, 1, 0, 7, 0, 3, 8, 8, 5, 0, 3, 8, 7, 5, 3, 4, 3, 2, 7, 6, 4, 1, 5, 7, 2, 7, 3, 5, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

"In his Book 'The Theory of Poker,' David Sklansky coined the phrase 'Fundamental Theorem of Poker,' a tongue-in-cheek reference to the Fundamental Theorem of Algebra and Fundamental Theorem of Calculus from introductory texts on those two subjects. The constant [sqrt(2) - 1] appears so often in poker analysis that we will in the same vein go so far as to call it 'the golden mean of poker,' and we call it 'r' for short. We will see this value in a number of important results throughout this book."

If a triangle has sides whose lengths form an harmonic progression in the ratio 1/(1 - d):1:1/(1 + d) then the triangle inequality condition requires that d be in the range 1 - sqrt(2) < d < sqrt(2) - 1. - Frank M Jackson, Oct 01 2013

REFERENCES

Bill Chen and Jerrod Ankenman, The Mathematics of Poker, Chpt 14 - You Don't Have To Guess: No-Limit Bet Sizing, pg. 153, ConJelCo, LLC, Pittsburgh PA 2006.

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 396 and 486.

LINKS

Table of n, a(n) for n=0..103.

FORMULA

sqrt(2)-1 = exp(asinh(cos(Pi))) = exp(asinh(-1)). - Geoffrey Caveney, Apr 23 2014

EXAMPLE

= 0.414213562373095048801688724209698078569671875376948073...

MATHEMATICA

RealDigits[ Sqrt[2] - 1, 10, 111][[1]]

CROSSREFS

Cf. A002193, A014176, A020807, A120731.

Sequence in context: A156896 A002193 A020807 * A230077 A055190 A155781

Adjacent sequences:  A188579 A188580 A188581 * A188583 A188584 A188585

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Apr 04 2011

STATUS

approved

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Last modified July 28 14:27 EDT 2014. Contains 245000 sequences.