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%I #20 Apr 01 2022 09:14:14
%S 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,
%T 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,
%U 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
%N Decimal expansion of the location of the near bifurcation cusp in the Zeeman catastrophe machine.
%C Positive root of 6*x^2-7*x-2, equal to (7+sqrt(97))/12 (Poston 1978).
%C 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.
%D T. Poston and I. Stewart, Catastrophe Theory and its Applications, Pitman Publishing Ltd, 1978, Chapter 5, page 76.
%H Stanislav Sykora, <a href="/A256719/b256719.txt">Table of n, a(n) for n = 1..2000</a>
%H D. Cross, <a href="http://www.haverford.edu/physics/dcross/projects/zcm/">Zeeman's Catastrophe Machine in HTML 5</a>
%H The Nonlinear Dynamics Group at Drexel University, <a href="http://lagrange.physics.drexel.edu/flash/zcm/">Zeeman's Catastrophe Machine</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Catastrophe_theory">Catastrophe theory</a>
%H E. C. Zeeman, <a href="https://www.jstor.org/stable/24950329">Catastrophe Theory</a>, Scientific American, April 1976, pages 65-70, 75-83.
%F Satisfies 3*a*(2*a-1)=2*(2*a+1).
%e 1.40407148348300872681218428457646870680801135728689701431...
%t RealDigits[(7 + Sqrt[97])/12, 10, 111][[1]] (* _Robert G. Wilson v_, Apr 20 2015 *)
%o (PARI) a=(7+sqrt(97))/12 \\ Use \p 2020, and keep 2000 digits
%Y Cf. A256720 (far bifurcation cusp).
%K nonn,cons
%O 1,2
%A _Stanislav Sykora_, Apr 09 2015
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