Do you think then that there is a universality of this particular ratio?
I, for my part, highlighted this ratio in these different areas:
Preprint Genetic code, quantum physics and the 3/2 ratio
Preprint The ultimate numbers and the 3/2 ratio
Article Pi and Golden Number: not random occurrences of the ten digits
Dear Jean-Yves Boulay
The most famous ratio is the golden value. Anyway, this value generated by the famous Fibonacci recurrence Fn+1 = Fn + Fn-1 ,
{0,1,1,2,3,5,8,13,21,....} Fibonacci numbers
that is
lim Fn+1 / Fn = the golden value = (1 +sqrt5)/2
Also, one can see that the following sequence of numbers
Gn+1 = 4Gn - 3Gn-1
{ o,1, 4, 13, 40,....}
converges to the value 3/2,
that is lim Gn+1 / Gn = 3/2
I hope you can connect this sequence with your observations in nature and science.
Regards
Dear Jean-Yves Boulay
The most famous ratio is the golden value. Anyway, this value generated by the famous Fibonacci recurrence Fn+1 = Fn + Fn-1 ,
{0,1,1,2,3,5,8,13,21,....} Fibonacci numbers
that is
lim Fn+1 / Fn = the golden value = (1 +sqrt5)/2
Also, one can see that the following sequence of numbers
Gn+1 = 4Gn - 3Gn-1
{ o,1, 4, 13, 40,....}
converges to the value 3/2,
that is lim Gn+1 / Gn = 3/2
I hope you can connect this sequence with your observations in nature and science.
Regards
Dear Jean-Yves Boulay,
Yes, in the expression that defines the contribution of the gradient of an inhomogeneous magnetic field to the eigenenergies of the electron in the Stern–Gerlach experiment. Reference: J.D. Bulnes and I.S. Oliveira, Brazilian Journal of Physics, vol. 31, no. 3, September, 2001 [see , for example, the expression (38)].
Regards.
Juan
Following the Kepler's laws,
https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion
Here is the law of harmonies: (quoting):
The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. (The Law of Harmonies)
It is not clear where the ratio (3/2) in this concern.
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