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A256720 Decimal expansion of the location of the far bifurcation cusp in the Zeeman catastrophe machine. 2
2, 4, 5, 5, 6, 6, 7, 2, 1, 9, 3, 7, 4, 7, 9, 9, 0, 4, 6, 5, 0, 2, 0, 4, 0, 5, 3, 6, 0, 9, 6, 0, 4, 2, 6, 8, 0, 8, 9, 6, 2, 4, 1, 9, 7, 2, 1, 3, 6, 2, 8, 8, 0, 6, 7, 7, 5, 4, 9, 7, 0, 9, 2, 1, 2, 0, 1, 1, 8, 8, 0, 4, 8, 4, 7, 7, 2, 3, 7, 4, 8, 9, 5, 1, 2, 0, 1, 4, 6, 9, 5, 3, 6, 6, 3, 5, 7, 5, 1, 9, 1, 1, 4, 3, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Largest root of 10*x^2-27*x+6, equal to (27+sqrt(489))/20 (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 far cusp's distance from the pivot.
REFERENCES
T. Poston and I. Stewart, Catastrophe Theory and its Applications, Pitman Publishing Ltd, 1978, Chapter 5, page 76.
LINKS
The Nonlinear Dynamics Group at Drexel University, Zeeman's Catastrophe Machine
E. C. Zeeman, Catastrophe Theory, Scientific American, April 1976, pages 65-70, 75-83.
EXAMPLE
2.455667219374799046502040536096042680896241972136288067754970...
PROG
(PARI) a=(27+sqrt(489))/20 \\ Use \p 2020, and keep 2000 digits
CROSSREFS
Cf. A256719 (near bifurcation cusp).
Sequence in context: A131813 A083038 A061008 * A091988 A023824 A341744
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Apr 09 2015
STATUS
approved

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Last modified June 13 09:03 EDT 2024. Contains 373383 sequences. (Running on oeis4.)