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A256719
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Decimal expansion of the location of the near bifurcation cusp in the Zeeman catastrophe machine.
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2
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1, 4, 0, 4, 0, 7, 1, 4, 8, 3, 4, 8, 3, 0, 0, 8, 7, 2, 6, 8, 1, 2, 1, 8, 4, 2, 8, 4, 5, 7, 6, 4, 6, 8, 7, 0, 6, 8, 0, 8, 0, 1, 1, 3, 5, 7, 2, 8, 6, 8, 9, 7, 0, 1, 4, 3, 1, 0, 2, 6, 2, 8, 7, 7, 4, 8, 6, 3, 7, 0, 0, 4, 8, 6, 4, 2, 3, 0, 6, 5, 5, 2, 5, 0, 7, 7, 6, 6, 7, 3, 2, 0, 0, 9, 6, 1, 8, 8, 1, 3, 5, 3, 6, 5, 0
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OFFSET
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1,2
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COMMENTS
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Positive root of 6*x^2-7*x-2, equal to (7+sqrt(97))/12 (Poston 1978).
Applies to the 'classical' Zeeman machine with a disk of diameter 1 and the distance between the pivot and the fixed point equal to 2. With respect to the pivot, the near and far bifurcation cusps are located on opposite side the fixed point. This constant is the near cusp's distance from the pivot.
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REFERENCES
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T. Poston and I. Stewart, Catastrophe Theory and its Applications, Pitman Publishing Ltd, 1978, Chapter 5, page 76.
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LINKS
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Stanislav Sykora, Table of n, a(n) for n = 1..2000
D. Cross, Zeeman's Catastrophe Machine in HTML 5
The Nonlinear Dynamics Group at Drexel University, Zeeman's Catastrophe Machine
Wikipedia, Catastrophe theory
E. C. Zeeman, Catastrophe Theory, Scientific American, April 1976, pages 65-70, 75-83.
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FORMULA
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Satisfies 3*a*(2*a-1)=2*(2*a+1).
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EXAMPLE
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1.40407148348300872681218428457646870680801135728689701431...
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MATHEMATICA
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RealDigits[(7 + Sqrt[97])/12, 10, 111][[1]] (* Robert G. Wilson v, Apr 20 2015 *)
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PROG
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(PARI) a=(7+sqrt(97))/12 \\ Use \p 2020, and keep 2000 digits
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CROSSREFS
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Cf. A256720 (far bifurcation cusp).
Sequence in context: A345450 A098002 A241658 * A343722 A035622 A112919
Adjacent sequences: A256716 A256717 A256718 * A256720 A256721 A256722
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KEYWORD
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nonn,cons
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AUTHOR
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Stanislav Sykora, Apr 09 2015
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STATUS
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approved
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