

A188582


Decimal expansion of sqrt(2)  1.


4



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
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OFFSET

0,1


COMMENTS

"In his Book 'The Theory of Poker,' David Sklansky coined the phrase 'Fundamental Theorem of Poker,' a tongueincheek 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
This constant is the 6th smallest radius r<1 for which a compact packing of the plane exists, with disks of radius 1 and r.  JeanFrançois Alcover, Sep 02 2014, after Steven Finch.


REFERENCES

Bill Chen and Jerrod Ankenman, The Mathematics of Poker, Chpt 14  You Don't Have To Guess: NoLimit 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.
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 62.


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



