A256720 Decimal expansion of the location of the far bifurcation cusp in the Zeeman catastrophe machine.

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

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

Tim Poston and Ian Stewart, Catastrophe Theory and its Applications, Pitman Publishing Ltd, 1978, Chapter 5, page 76.

Links

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Dan Cross, Zeeman's Catastrophe Machine in HTML 5. [Dead link]

The Nonlinear Dynamics Group at Drexel University, Zeeman's Catastrophe Machine.

Wikipedia, Catastrophe theory.

E. C. Zeeman, Catastrophe Theory, Scientific American, Vol. 234, No. 4 (April 1976), pages 65-70, 75-83.

Index entries for algebraic numbers, degree 2.

Example

2.455667219374799046502040536096042680896241972136288067754970...

Mathematica

RealDigits[(27 + Sqrt[489])/20, 10, 120][[1]] (* Amiram Eldar, Apr 11 2026 *)

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

Adjacent sequences: A256717 A256718 A256719 * A256721 A256722 A256723

Keyword

nonn,cons

Author

Stanislav Sykora, Apr 09 2015

Status

approved